Internal Tides and Mixing in a Submarine Canyon with Time-Varying Stratiﬁcation

DECEMBER 2012 Z H A O E T A L . 2121

ZHONGXIANG ZHAO Applied Physics Laboratory, University of Washington, Seattle, Washington

MATTHEW H. ALFORD,REN-CHIEH LIEN, AND MICHAEL C. GREGG Applied Physics Laboratory and School of Oceanography, University of Washington, Seattle, Washington

GLENN S. CARTER Department of Oceanography, University of Hawaii at Manoa, Honolulu, Hawaii

(Manuscript received 7 March 2012, in ﬁnal form 25 May 2012)

ABSTRACT

The time variability of the energetics and turbulent dissipation of internal tides in the upper Monterey Submarine Canyon (MSC) is examined with three moored profilers and five ADCP moorings spanning February–April 2009. Highly resolved time series of velocity, energy, and energy flux are all dominated by the semidiurnal internal tide and show pronounced spring-neap cycles. However, the onset of springtime upwelling winds significantly alters the stratification during the record, causing the thermocline depth to shoal from about 100 to 40 m. The time-variable stratification must be accounted for because it significantly affects the energy, energy flux, the vertical modal structures, and the energy distribution among the modes. The internal tide changes from a partly horizontally standing wave to a more freely propagating wave when the thermocline shoals, suggesting more reflection from up canyon early in the observational record. Turbulence, computed from Thorpe scales, is greatest in the bottom 50–150 m and shows a spring-neap cycle. Depth- 2 integrated dissipation is 3 times greater toward the end of the record, reaching 60 mW m 2 during the last 2 2 spring tide. Dissipation near a submarine ridge is strongly tidally modulated, reaching 10 5 Wkg 1 (10–15-m overturns) during spring tide and appears to be due to breaking lee waves. However, the phasing of the breaking is also affected by the changing stratification, occurring when isopycnals are deflected downward early in the record and upward toward the end.

1. Introduction as well as primary productivity and particle transport along the coast (e.g., Shea and Broenkow 1982; Hunkins Submarine canyons of various shapes and sizes are 1988; Gardner 1989; Paull et al. 2005; Lee et al. 2009). common features on continental shelves and slopes, Observations in submarine canyons indeed ﬁnd diapycnal occupying as much as 40% of continental slopes on the 22 2 21 diffusivities Kr up to 10 m s , three orders of magni- west coast of the United States by some measures 2 2 tude greater than the open ocean value of O(10 5 m2 s 1) (Hickey 1995). Because of their ability to focus internal (e.g., Lueck and Osborn 1985; Carter and Gregg 2002; waves (Gordon and Marshall 1976; Wunsch and Webb Carter et al. 2005; Gregg et al. 2005). However, parame- 1979; Hotchkiss and Wunsch 1982), they have long been terizations of the mixing in terms of the usual internal wave identiﬁed as potential sites of intense internal wave ac- cascades underpredict the measured levels by two orders tivity and elevated turbulent mixing, and thus are likely of magnitude (Kunze et al. 2002), indicating different important in processes such as the large-scale circulation and/or additional mixing processes are likely at play in canyons than in the ocean interior. The energy source for the turbulence is assumed to Corresponding author address: Zhongxiang Zhao, Applied Physics Laboratory, University of Washington, 1013 NE 40th Street, Seattle, be the internal tides propagating in through their mouth WA 98105. or ocean end (though the possible additional role of E-mail: [email protected] baroclinic conversion within them has not been ruled

DOI: 10.1175/JPO-D-12-045.1

Ó 2012 American Meteorological Society Unauthenticated | Downloaded 10/11/21 10:22 AM UTC 2122 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 42

FIG. 1. (a) Map of the upper MSC. The red line denotes the canyon’s thalweg, or deepest path. The along-thalweg distance is marked with black dots at 1-km intervals and labeled at 5-km intervals. Isobaths are shown at 50-m intervals, with contours at 200-m intervals bold and labeled at left. The Wain et al. (2012, manuscript submitted to J. Geophys. Res.) SWIMS3 tracks are shown in light yellow. At each mooring, the depth-integrated semidiurnal energy and flux are shown with circles and arrows, respectively. Green and blue colors indicate time averages over the first spring- neap cycle (yearday 48–62) and the successive three (yearday 62–106), respectively. (b) Map of Monterey Bay and adjacent region. The green box shows the upper MSC as shown in (a). out; Wain et al. 2012, manuscript submitted to J. Geophys. at the canyon mouth; specifically, that the Sur Plateau Res.). Therefore, understanding the manner in which re- (Fig. 1b) is the primary source of internal tides into MSC motely incident internal tides propagate inside canyons, (e.g., Jachec et al. 2006; Hall and Carter 2011; Johnston navigate around their bends, and reflect off their steep et al. 2011; Kang and Fringer 2012). At the mouth of the walls is key to determining the total dissipation within canyon, the modeled cross-section up-canyon energy flux canyons and its horizontal and depth distribution, both of is about 9 MW (Hall and Carter 2011; Kang and Fringer which are necessary for determining the buoyancy flux. 2012), agreeing well with measurements by Kunze et al. Monterey Submarine Canyon (MSC), the largest sub- (2002). In the lower MSC, the canyon is usually subcritical marine canyon on the US west coast, has been the site of (i.e., less steep than semidiurnal internal-wave character- a number of observational and modeling studies in recent istics) in the along-thalweg direction so that semidiurnal years (e.g., Petruncio et al. 1998; Kunze et al. 2002; Carter internal tides are topographically steered around the gen- and Gregg 2002; Jachec et al. 2006; Hall and Carter 2011). tler Monterey and San Gregorio meanders (Petruncio et al. MSC runs across the continental shelf of Monterey Bay, 2002; Jachec et al. 2006; Hall and Carter 2011). However, with its head just off Moss Landing, California (Fig. 1). It the internal tide does not appear to follow the sharper bend features a winding thalweg (red), in contrast to some other at Gooseneck Meander (Hall and Carter 2011; Wain et al. canyons that are relatively straight (e.g., Ascension and 2012, manuscript submitted to J. Geophys. Res.). As a re- Kaoping, Gregg et al. 2011; Lee et al. 2009). Starting at the sult, the baroclinic velocities lead to flow perpendicular to canyon mouth, there are three sharp bends along the canyon the ridge near the bend, leading to a breaking lee wave that thalweg (Carter 2010): the San Gregorio, Monterey, and dominates the dissipation in the upper canyon (Wain et al. Gooseneck meanders (Fig. 1b), the latter of which (Fig. 1a) 2012, manuscript submitted to J. Geophys. Res.). is studied here in detail with a set of 8 moorings. Simulta- Recently, the role of low-frequency flows and strati- neous shipboard surveys are reported separately by Wain fication changes has become recognized in modulating et al. (2012, manuscript submitted to J. Geophys. Res.). the generation and propagation of internal tides in the Model simulations and field observations confirm open ocean (Alford and Zhao 2007a; Kelly et al. 2012), a substantial incident semidiurnal baroclinic energy flux their reflection from continental margins (Klymak et al.

Unauthenticated | Downloaded 10/11/21 10:22 AM UTC DECEMBER 2012 Z H A O E T A L . 2123

2011), their propagation on continental shelves Canyon experiment (Gregg et al. 2011), and the other (MacKinnon and Gregg 2003a,b; Kurapov et al. 2003), seven moorings were recovered on 16–17 April. Detailed and the interference patterns that arise from multiple instrument configurations of the moorings are listed in waves (Alford et al. 2006). In MSC, Petruncio et al. (1998) Table 1. observed progressive and standing waves in field experi- The moorings ranged from ;19 km (LR1) to ;2km ments conducted in April and October 1994, respectively, (WH1) from the canyon head, with the water depth ranging and they attributed the difference to changes in stratification from 604 m at LR1 to 153 m at WH1 (Fig. 1a). The ADCP between the two experiments. In the work presented here, moorings (LR1–LR4 and WH1) were deployed along the we demonstrate that the shoaling of the thermocline asso- canyon’s thalweg (Fig. 1a, red), whereas the MP moor- ciated with springtime upwelling-favorable winds markedly ings (MP1–MP3) were on the canyon’s southern flank. affects the patterns of velocity, displacement, energy, and The along- and cross-canyon structure of the energy energy flux, supporting model predictions by Hall and flux and dissipation rate were investigated on the second Davies (2007), Kurapov et al. (2010), and Osborne et al. cruise using SWIMS3, a towed profiler (Gregg et al. 2011; (2011), and observations by Petruncio et al. (1998). In our Wain et al. 2012, manuscript submitted to J. Geophys. case, the stratification changes are substantial enough to Res.), along 16 cross-canyon sections (Fig. 1a, light yellow necessitate their incorporation into the energy flux and lines). We focus here on mooring observations, referring modal structure calculations; use of a time-mean stratifica- interested readers to Wain et al. (2012, manuscript sub- tion results in substantial errors. The deeper thermocline mitted to J. Geophys. Res.) for the spatial features re- during the first period results in greater energy but similar vealed with the SWIMS3 surveys. net up-canyon energy flux, implying greater flux from b. MP moorings further up canyon. Though we cannot determine whether greater reflection of the incident waves, or stronger On each MP mooring (MP1–MP3), a McLane Moored up-canyon conversion, is responsible, ray analysis indicates Profiler (MP) crawled up and down along the cable be- the along-canyon slope changes from supercritical to near- tween about 40-m depth and 10 m above the bottom. 2 critical, suggesting the former. Additionally, turbulent dis- Each MP moved along the cable at a speed of 0.25 m s 1, sipation, which we estimate via Thorpe scales (Thorpe 1977; carrying a Falmouth Scientific acoustic current meter and Dillon 1982) appears to be phased differently relative to the a conductivity–temperature–depth instrument (CTD) to baroclinic flows in the two periods, with depth-integrated measure profiles of horizontal velocity, temperature, and values nearly a factor of 2 greater later in the record. salinity. The vertical resolution of gridded velocity and density are about 10 and 2 m, respectively (Doherty et al. 1999; Alford 2010). For MP1–MP3, the water depths 2. Data, techniques, and oceanographic were 600, 377, and 288 m, respectively; thus single pro- background files occurred each 60, 40, and 30 min. Velocity measurements above each MP were made using an upward a. Experiment looking 300-kHz ADCP (Table 1). Subsurface pressure The field experiment was conducted via two cruises measurements at each mooring revealed that mooring onboard R/V Wecoma in February and April 2009, re- pulldown was only 1–2 m owing to very taut design. spectively. During the first cruise, eight moorings were MP2 and MP3 performed well for their two-month deployed on 17–18 February (yearday 47–48; Fig. 1a). mission, each covering a total vertical distance of about We refer to time using yearday, which is defined as the 650 km (2068 and 2760 profiles, respectively). Unfor- decimal days starting from midnight on 31 December tunately, MP1 stopped profiling after only 11 days due to 2008 UTC. Of the eight moorings, three consisted primar- a mechanical problem. ily of a McLane moored profiler (MP) and were labeled as At MP2, temperature above the MP profiling range MP1, MP2, and MP3, respectively. Four moorings were was measured with a chain of 10 HOBO thermistors instrumented with bottom mounted 75-kHz long-range covering 18–36 m (Table 1). The instruments were at- acoustic Doppler current profilers (ADCPs) and were la- tached to the top of the mooring’s main subsurface float, beled as LR1, LR2, LR3, and LR4. LR4 was hooked with a weak link to avoid endangering the main mooring around yearday 92.93, likely by a midwater trawler, and in case the top HOBO chain, which was nominally at dragged several hundred meters before being freed. For- only 10 m depth, was hooked by fishing activity. The tunately, none of the instruments was damaged. The HOBO thermistors sampled every 40 min, matching eighth mooring contained a 300-kHz Workhorse ADCP, MP2’s temporal resolution. The nominal resolution labeled WH1. In the second cruise, WH1 was first re- and accuracy of the HOBO thermistors is 0.108C, sub- covered on 13 April 2009, and redeployed in the Ascension stantially poorer than that of Sea-Bird instruments

Unauthenticated | Downloaded 10/11/21 10:22 AM UTC 2124 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 42

TABLE 1. Mooring information and instrument conﬁgurations. An ADCP contains internal temperature and pressure sensors. Variable U indicates the three-dimensional measurement and u indicates the horizontal two-dimensional measurement.

Depth SN Sampling Vertical Time range Mooring Location (m) (No.) Variable interval resolution (yearday) MP1 36846.5469N, 121855.4009W 488 Upward-looking 300-kHz ADCP 35 7966 U, T, p 5 min 2 m 47.9–105.6 Downward-looking 300-kHz ADCP 35 8064 U, T, p 5 min 4 m 47.9–105.6 SBE37 CTD 36 6623 T, S, p 1 min — 48.3–105.6 McLane moored proﬁler 40–476 101 u, T, S, p 60–90 min 2 m 48.3–59.1 SBE37 CTD 478 3462 T, S, p 0.8 min — 48.3–98.0 SBE39 T-logger 485 3071 T 0.8 min — 47.9–105.6

MP2 36847.2329N, 121853.5839W 370 SBE39 T-logger (with pressure sensor) 18 3134 T, p 1 min — 48.0–105.7 (103) HOBO thermistors 18:2:36 — T 40 min 2 m 47.6–106.5 Upward-looking 300-kHz ADCP 40 10010 U, T, p 5 min 2 m 48.0–105.7 SBE37 CTD 40 6622 T, S, p 1 min — 48.3–105.7 McLane moored proﬁler 42–358 102 u, T, S, p 40–60 min 2 m 48.3–105.7 SBE37 CTD 359 6319 T, S, p 0.8 min — 48.3–103.3 SBE39 T-logger 364 3074 T 0.8 min — 48.0–105.7

MP3 36847.4339N, 121852.0389W 288 Upward-looking 300-kHz ADCP 35 11675 U, T, p 5 min 2 m 48.1–105.6 SBE37 CTD 36 6624 T, S, p 1 min — 48.3–105.6 McLane moored proﬁler 37–277 103 u, T, S, p 30–45 min 2 m 48.3–105.5 SBE37 CTD 278 6318 T, S, p 0.8 min — 48.3–105.6 SBE39 T-logger 283 3253 T 1 min — 48.1–105.5

LR1 36846.9459N, 121855.1159W 604 75-kHz long ranger ADCP 594 7753 U, T, p 5 min 16 m 47.9–106.7

LR2 36846.4169N, 121854.0079W 582 75-kHz long ranger ADCP 572 11681 U, T, p 5 min 16 m 47.1–106.7

LR3 36847.3709N, 121853.9949W 420 75-kHz long ranger ADCP 410 4019 U, T, p 5 min 8 m 47.1–106.1

LR4 36847.6769N, 121850.9889W 307 75-kHz long ranger ADCP 295 11181 U, T, p 5 min 8 m 47.8–105.7 (93) SBE39 T-loggers (one 34:33:294 1740 T 0.8 min 33 m 47.8–105.7 pressure sensor)

WH1 36848.0609N, 121848.6489W 153 300-kHz workhorse ADCP 148 3160 U, T, p 5 min 4 m 48.2–101.7

(0.0018C). Nonetheless, the resolution was more than coverage is nearly complete. Coverage in velocity is sufficient to resolve the large temperature signals in the similar at MP1 and MP3, but those moorings have no upper 40 m at our site, and the poor accuracy was ad- temperature above 40 m (see the appendix). dressed by cross-calibration with the SBE39 (#3134, Semidiurnal signals dominate the velocity, temperature, Table 1) tethered with the uppermost HOBO thermis- and salinity measurements. Velocities and isopycnal dis- 2 tor. RMS differences between the SBE39 and the placements are vigorous (;0.6 m s 1 and 100 m peak to HOBO were well below 0.108C after calibration. peak, respectively), and visibly dominated by the first two A 5-day sample of the merged measurements at MP2 vertical modes. A striking feature is the visual shoaling of is shown in Fig. 2. The velocity measurements from the the thermocline over the course of the five days, associated MP and ADCP, and the temperature measurements with the reestablishment of upwelling winds after a storm. from the MP and HOBOs, visually agree on either side The zero crossing of the observed baroclinic velocities of a narrow gap near 40 m (white). Aside from addi- responds in kind, moving upward from about 300 m to less tional small gaps near the top and bottom, the depth than 200 m over the 5-day period. The strong variability

Unauthenticated | Downloaded 10/11/21 10:22 AM UTC DECEMBER 2012 Z H A O E T A L . 2125

FIG. 2. A 5-day segment of the MP2 measurements. (a) Eastward velocity. (b) Northward velocity. In (a),(b), the velocity data between 6- and 40-m depths are from a 300-kHz ADCP. (c) Temperature. Data between 18- and 40-m depths are from a string of HOBO thermistors. Isothermal contours are shown every 0.58C and labeled every 18C. (d) Salinity. The gray lines in (d) represent the MP’s depth along the mooring cable, making a round trip from 40-m depth to 10-m height above the bottom each 80 min. of the stratification and the associated structure of the in- The temperature measurements, though only at 9 depths, ternal motions on such short time scales clearly indicates successfully captured both the low-frequency variation a need to properly account for time-variable stratifica- and the semidiurnal motions (Fig. 3d). The spikes in tion, which is the focus of the present study. vertical velocity measurements (Fig. 3c), which appear to be internal tidal bores and/or nonlinear waves, similar to c. ADCP moorings those reported by Key (1999) and Carter et al. (2005), will Each ADCP mooring (LR1–LR4) had an upward- be reported elsewhere. looking 75-kHz ADCP (300-kHz for WH1) 10 m above d. Vertical displacement thebottom.Theirbinsizeswere4,8,or16m(seeTable1). All ADCPs sampled at 30-s intervals, and were averaged The MP moorings measured temperature and salinity, into 5-min ensembles to reduce measurement noise. In but LR4 measured only temperature. Because temperature addition to the 10-m gap beneath the instrument, the up- dominates over salinity in determining density in MSC, per 20–40 m (10%–15% of the water depth) are discarded vertical displacement h(z, t) 5 [T(z, t) 2 T(z, t)]/Tz(z, t) because of contamination by the reflection of side-lobes is calculated from temperature measurements at each from the surface. mooring, where T(z, t)isthetemperaturemeasurement,

Because of the lack of density or temperature mea- T(z, t) is the time averaged temperature and Tz(z, t)is surements, the ADCP moorings cannot detect vertical the temperature gradient determined from MP2. T(z, t) displacements. The exception was LR4, which included a and Tz(z, t) are smoothed using a 2.1-day sliding window chain of nine Sea-Bird 39 temperature loggers, spanning (four semidiurnal periods) to account for slow (nontidal)

33- to 280-m depth (10 m above the bottom) with a 33-m variations in the background stratification. Tz(z, t)atMP2 spacing (Table 1). Thus, low-mode energy flux and available is used for the calculation at all moorings because of its potential energy can be estimated at LR4, but only kinetic full-depth coverage because lateral differences are small. energy can be measured at the other ADCP moorings. To ensure that salinity signals do not influence displace- Figure 3 shows sample measurements at LR4 during ment computed from temperature, the displacement was the same period as Fig. 2 for MP2. Again, the domi- also computed using potential density at the MP moorings. nance of the semidiurnal tidal signals and the upward The RMS differences between isotherm and isopycnal migration of the zero crossings in velocity are apparent. displacements are less than 1 m (compared to the measured

Unauthenticated | Downloaded 10/11/21 10:22 AM UTC 2126 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 42

FIG. 3. A 5-day segment of the LR4 measurements: (a) eastward velocity, (b) northward velocity, (c) upward velocity, and (d) temperature at nine depths. Isothermal contours are shown every 0.58C and labeled every 18C. Linear interpolation is used to obtain the contours. displacements of tens of meters; Fig. 2), indicating the displacement as functions of depth (Fig. 4). Because dominance of temperature in setting density in the canyon. spectra from all locations are similar, only those from MP2 and LR4 are plotted. For velocity, the rotary e. Frequency spectra spectrum (Mooers 1970; Gonella 1972) is computed, The sample data (Figs. 2 and 3) make the dominance with negative and positive frequencies indicating of the semidiurnal tide obvious; this statement is quanti- counterclockwise (CCW) and clockwise (CW) rota- ﬁed by examining frequency spectra of velocity and tion in time, respectively.

FIG. 4. Frequency spectra of (a),(b) rotary velocity and (c),(d) displacement at MP2 and LR4, respectively. Outstanding tidal peaks are labeled.

Unauthenticated | Downloaded 10/11/21 10:22 AM UTC DECEMBER 2012 Z H A O E T A L . 2127

For both the velocity and displacement spectra, the semidiurnal tidal constituents are dominant. They appear as wide bands (as opposed to lines), likely due to the presence of incoherent constituents. The presence of overtides and compound tides (e.g., MK3, M4, M6) indicate a degree of nonlinearity to the internal tide field. Similar spectral features have been observed previously in MSC (Key 1999; Kunze et al. 2002; Carter et al. 2005). All tidal constituents are bottom intensified, consistent with previous field observations (Carter and Gregg 2002; Xu and Noble 2009). In contrast, near-inertial motions are surface intensified due to their generation at the surface by the wind (e.g., Paduan and Rosenfeld 1996). In our data, they appear as a wide patch around f in the CW component of the velocity spectra (Figs. 4a,b), but not in the displacement spectra (Figs. 4c,d). Near- inertial motions extend to about 200 m and 80 m depth at MP2 and LR4, respectively. MSC lies poleward of the turning latitude of the diurnal internal tide, that is, vo1, K1 are lower than the local inertial frequency f [ 2V sin(latitude), where V is the rotation rate of the earth. Therefore, progressive diurnal internal tides are not allowed; nonetheless trapped diurnal internal tides may exist (e.g., Dale et al. 2001; Swart et al. 2011). The displacement spectra show diurnal peaks of similar magnitude to the semidiurnal FIG. 5. Frequency spectra of MP2 measurements at 200-m depth, constituent (Figs. 4c,d), indicating the motions are in- superimposed with GM76. The vertical gray band indicates the deed baroclinic and not simply the diurnal barotropic semidiurnal bandpass filter used in this study. tides. They appear to be vertical displacements caused by trapped diurnal internal tides, and will be reported both minimal mooring pulldowns, as asserted earlier, and elsewhere. a very small degree of spatial variability in tidal sea level Figure 5 presents the velocity and displacement spectra across the bay, as reported in a numerical model by from MP2 measurements at 200-m depth, with the Garrett- Carter (2010). Munk (GM76) spectrum superimposed for comparison Harmonic constants are extracted by harmonic anal- (Garrett and Munk 1975; Cairns and Williams 1976). The ysis using the T_TIDE toolbox (Pawlowicz et al. 2002). measured spectral level is higher than GM76 throughout For all moorings, the harmonic tidal constituents ac- most of the frequency range. The spectra levels from count for more than 95% of the pressure variance. measurements closer to bottom (such as at 300-m depth) Compared with Monterey tide station, the overall RMS are even higher. This is consistent with previous ob- differences are 1.3 cm and 3.88 for the M2 amplitude and servations that internal waves are elevated in canyons phase, respectively. The semidiurnal and diurnal tidal (Hotchkiss and Wunsch 1982; Carter and Gregg 2002). variations are shown in Figs. 6b,c, respectively. Barotropic current u(t) is estimated as the depth aver- f. Barotropic tide age of the moored velocity measurements at MP2, where As measures of the barotropic tide, we compute sea the near-complete depth coverage minimizes risk of ali- level and depth-averaged currents at our moorings, asing baroclinic motions onto the estimate of barotropic though measurements near the modeled generation site current (a real concern as the depth average is about 2 2 at Sur Plateau would obviously be preferable. For sea 0.15 m s 1 at most compared to 0.6 m s 1 for the baro- level, 18 sets of moored pressure measurements (Table 1) clinic motions). Total barotropic velocity (u// denotes the are examined. When the mean deployment depth is velocity component along local isobath; Fig. 6d) is sub- subtracted, they agree very well with each other and with stantially more variable than the corresponding quantity measurements at the Monterey tide station at 36836.39N, for sea level, which is completely dominated by the as- 121853.29W (Fig. 1b, red square). A sample comparison at tronomical forcing and shows little variation across the MP2 is shown in Fig. 6a. The close agreement indicates bay. When the semidiurnal components are isolated using

Unauthenticated | Downloaded 10/11/21 10:22 AM UTC 2128 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 42

FIG. 6. (a)–(c) Barotropic tidal height. (a) Measurements from MP2’s SBE #6622 (gray) and

Monterey tide gauge station (black). (b) The semidiurnal constituent (M2 1 S2 1 N2 1 K2) and (c) the diurnal constituent (O1 1 K1 1 P1 1 Q1). (d)–(f) Depth-averaged currents at MP2 (u// denotes along local isobath, i.e., toward 608 true). (d) Meaured, (e) semidiurnally band- passed, and (f) harmonic constituent (M2 1 S2 1 N2 1 K2).

T_TIDE and bandpass filtering (Figs. 6e,f), a spring-neap typical situation in early spring on the California coast cycle is seen, but with timing of the springs (SP1–SP4) that observed in detailed larger-scale studies (e.g., differs somewhat from that of sea level (Fig. 6b, SP1–SP4). Rosenfeld et al. 1994; Ramp et al. 2005). Early in the Specifically, the second and fourth spring tides occur record, relatively warm, freshwater is present in the several days later in currents than sea level. This is sur- upper 100 m. As stormier winter weather transitions to prising given the general impression of the barotropic tide more persistent upwelling-favorable winds near year- 2 as generally more deterministic. However, phase differ- day 65 (Fig. 7a), it disappears. For a 5 m s 1 wind, the ences between tidal height and barotropic velocity do exist rising velocity of bottom water may reach several cm owing to a feedback between internal tides in the canyon per hour, so that the ocean has a short response time and the barotropic velocities (Carter 2010). Though the (Ramp et al. 2005). Later in the record, when the up- details remain to be explored, the feedback appears to welling winds lapse for a few days, a weaker warm, fresh arise because internal tides alter the distribution of total layer reappears before disappearing again by the end of pressure, which affects the structure of the barotropic tide the record. Correspondingly, the thermocline deepens velocities, that in turn generate the internal tides. and then shallows again (Figs. 2 and 3). Buoyancy frequency is defined as g. Low-frequency variations in stratification and current ›s (z, t) 2 52g u N (z, t) r › , (1) Low-pass filtered temperature T(z, t) and salinity S(z, t) 0 z at MP2 over the course of the 2-month mooring de- ployments, plotted in Figs. 7b,c, are compared with wind where g is gravitational acceleration, r0 is a reference measured at National Oceanic and Atmospheric Admin- ocean water density, and su(z, t) is potential density istration (NOAA) buoy 46042 (36847.129N, 122828.159W), su(z, t) smoothed by a 2.1-day sliding window. su(z, t)is about 50 km to the west (Fig. 1b, red triangle). Our ob- slowly varying, and shows a maximum near 100 m be- servations do not resolve the full complexity of the ocean neath the warm, salty water originally present, shoaling response, which is likely three-dimensional (Rosenfeld as the layer disappears (Fig. 7d). It will be shown below et al. 1994) and larger-scale than our study. However, the that these changes are associated with substantial al- observed winds and ocean response are consistent with the terations in the modal shapes and energy fluxes.

Unauthenticated | Downloaded 10/11/21 10:22 AM UTC DECEMBER 2012 Z H A O E T A L . 2129

FIG. 7. Background wind, stratification and currents. (a) Wind vectors at NOAA buoy #46042 (see Fig. 1b for location), showing upwelling-favorable northwestly wind beginning yearday 65, except for a 5-day relaxation during yearday 95–100. (b) Temperature, (c) salinity, and (d) stratification measured at MP2 and smoothed by a 2.1-day sliding window. In (b),(c),(d), the black lines indicate the pycnocline depth before the storm; while during the storm the pycnocline depth rose to near surface and cannot be accurately determined. (e) Eastward and (f) northward velocity low-pass filtered by a fourth-order Butterworth filter with a 5-day cutoff period.

As a result of the upwelling-favorable winds, stratifi- in the structure of the propagating versus standing wave cation varies not only temporally but also spatially. pattern discussed later. Water properties at MP1 and MP3 (not shown) track Energy and flux are computed in the usual ways fol- those at MP2, as seen in buoyancy frequency profiles at lowing the same procedure as described in Kunze et al. the beginning of the first cruise (yearday 49, Fig. 8). All (2002), Nash et al. (2005), and Alford and Zhao (2007a), three MP’s (colors) agree closely, but a time-mean CTD but with stratification allowed to vary slowly in time. profile 100 km to the west (36836.59N, 1238009W; Fig. 1b, Because our focus is the semidiurnal internal tide, all red cross) differs sharply. The CTD profile was com- quantities are first run through a fourth-order Butter- puted from the mean of 7 profiles taken over the same worth bandpass filter, with the central frequency at 1.93 12-h period as that of the MP profiles, to average out cycles per day (cpd) and the cutoff frequencies [1.74, tidal heaving. The CTD profile at the same deep-water 2.13] cpd (Fig. 5, vertical gray band). location taken during the second cruise in April differed Available potential energy (APE) is then given by little from that in February, supporting that offshore ð ð stratification is much less variable. 0 0 1 APE 5 ape(z, t) dz 5 r N2(z, t)h92(z, t) dz, 2 2 2 0 h. Calculating energy and flux in time-variable H H stratification (2)

Energy and flux are often computed using time-mean and horizontal kinetic energy (HKE) by stratification profiles. In the open ocean, this is generally ð ð a good assumption. Here, as in many coastal locations, 0 0 5 5 1 r j 9 j2 HKE hke(z, t) dz 0 u (z, t) dz, (3) stratification varies enough that it must be taken into 2H 2H 2 account in computing energy and energy flux. Addi- tionally, stratification alters the mode shapes, affecting where r0 is the water density and u9 is the baroclinic the modal distribution of all three quantities. These effects current computed by subtracting the depth mean at each are described here, which are distinct from the changes time from the measured velocity. The angle brackets

Unauthenticated | Downloaded 10/11/21 10:22 AM UTC 2130 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 42

FIG. 8. Comparison of buoyancy frequency proﬁles from moorings (colors) and a CTD station 100 km to the west (see Fig. 1b for location). The CTD station was in 3700 m water; only the upper 0–500 m is plotted.

FIG. 9. Comparison of semidiurnal (a) HKE, (b) APE, and indicate an average over one tidal cycle, and ape(z, t) (c) flux magnitude at MP2, estimated using the time-averaged and and hke(z, t) are the nondepth-integrated horizontal -varying stratifications, respectively. Each quantity is computed as kinetic and available potential energies, in units of Joules the sum over the lowest ten modes. per cubic meter. The total energy E is calculated by Time-varying stratification also affects the shape of E 5 APE 1 HKE. (4) the vertical modes and therefore the partition of energy and flux between them. The normal modes for vertical 9 9 Energy flux F is computed as u p , where the pertur- displacement F(z) are determined by solving the Taylor– bation pressure is computed in the usual way from dis- Goldstein equation with zero background flow: placement, 2F 2 ð d (z) 1 N (z)F 5 0 2 2 (z) 0 (7) 9 5 r 2 ^ h9 ^ ^2 dz cn p (z, t) 0 N (z, t) (z, t) dz psurf(t), (5) 2z subject to the boundary conditions F(0) 5F(2H) 5 0, where the surface baroclinic pressure is computed by where n is the mode number, and cn is the eigenspeed ; 21 requiring the depth integral of p9 to be zero: (e.g., Gill 1982; Pedlosky 2003). In spite of the 0.1 m s low-frequency flows evident in Figs. 7e,f, we restrict our ð 0 attention to the effects of stratification, deferring effects p (t) 5 r N2(z, t)h9(z, t) dz. (6) surf 0 of sheared background flow for another paper. cn is re- 2H lated to the group velocity, cg, and the phase velocity, cp, Figure 9 shows the effect of the time-varying stratifi- via the dispersion relationship (Alford and Zhao 2007b). cation on the depth integral of each quantity. HKE is not F(z) is related to the corresponding modes for pressure affected, but APE and flux magnitude vary by up to 50% and horizontal velocity P(z) via (Gill 1982): when the time-varying stratification is considered. dF(z) Flat-bottom modes are used to describe the wave- P(z) 5 r c2 . (8) 0 n dz number distribution of the data at each mooring. While the slopes may invalidate their strict use and lead to Vertical gaps in the measurements place severe limi- terms involving mode-mode interactions (Kelly et al. tations on the precision of energy and energy flux esti- 2012), the freely-propagating part of the signal will mates; however, internal tides can be approximately nonetheless be estimated below by comparing E and F represented by a superposition of a number of discrete for each mode following Alford and Zhao (2007a). baroclinic modes (Nash et al. 2005). Our water column

Unauthenticated | Downloaded 10/11/21 10:22 AM UTC DECEMBER 2012 Z H A O E T A L . 2131

FIG. 10. Time-varying buoyancy frequency and baroclinic modes. (a) MP2 observed buoyancy frequency profiles on yearday 55 and 92. (b),(c) Baroclinic modes (yearday 55 solid; 92 dashed) derived from the buoyancy frequency profiles shown in (a): (b) velocity modes and (c) displacement modes. The first three baroclinic modes are in red, blue, and green, respectively. (d) Zero-crossing depth [e.g., indicated by brown dots in (b)] of the first baroclinic mode for velocity. (e) Eigenvalue, phase speed, and group speed of the first baroclinic mode. coverage is excellent at MP2 and decent at the other (Fig. 12). As noted, energy and flux are computed via the moorings, allowing us to fit 10 modes at MP2 and 3 modes sum of modes at LR4 owing to the discrete-depth sam- at the other moorings (see the appendix). pling, so its depth-dependent quantities are not plotted. The effect of variable stratification on the modal shapes Baroclinic velocity and displacement both clearly show is demonstrated in Fig. 10. The buoyancy profiles on four spring-neap cycles. Signals at spring tide are visu- yearday 55 and 92 (pre- and postupwelling) are shown in ally greatest near the surface and bottom for velocity Fig. 10a. The corresponding baroclinic modes for velocity (Figs. 11a,b and 12a,b), and in the middle of the water and displacement are shown in Figs. 10b,c. The zero- column for displacement (Figs. 11c and 12c), consistent crossing depth of the mode 1 velocity profile (b, brown with a primarily first-mode signal. Energy and flux (Figs. dots) ranges between 100–200 m (d). During the de- 11d–k and 12d–g) reflect these patterns, with HKE and ployment period the mode 1 group and phase speeds energy flux magnitude showing shallow and deep maxima decrease as the stratification weakens (e). and APE greatest at middepth. Again, these imply a primarily first-mode signal, as confirmed in stacked histograms of total depth-integrated energy (Figs. 11h–j and 12d–f) 3. Observed energy and flux and flux magnitude (Figs. 11k and 12g). The spring-neap The full records of baroclinic velocity, displacement, cycle is evident in these histograms of energy and flux, energy, and flux are plotted for MP2 (Fig. 11) and LR4 with modulation of about a factor of 4. Mode 1 signals

Unauthenticated | Downloaded 10/11/21 10:22 AM UTC 2132 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 42

FIG. 11. Semidiurnal internal tides at MP2. (a) Eastward velocity, (b) northward velocity, (c) vertical displacement, (d) horizontal kinetic energy (hke), (e) available potential energy (ape), (f) eastward energy flux, (g) northward energy flux, (h) HKE, (i) APE, (j) E, and (k) flux magnitude. In (h)–(k), the lowest 10 baroclinic modes are extracted, and modes 1–5 are shown as stacked histograms. contain on average 80% of the energy, as seen by the up-canyon flux at shallow depths. However, energy and modal spectrum at MP2 (Fig. 13), with the content in the the ratio of potential to kinetic energy are both signifi- other modes varying somewhat during the time series. cantly greater during the first spring, implying interference The vertical profile of flux during the first spring is from signals traveling down canyon. This assertion will be markedly different than at the other three, showing examined in more detail in section 4. down-canyon fluxes at about 120 m and at depth (Figs. Mean energy flux averaged over the first spring-neap 11f,g). The magnitude of the flux is not greatly different cycle (Fig. 1, green arrows) and the successive three (blue from the other spring tide periods owing to the greater arrows) is up canyon and generally (but not monotonically)

Unauthenticated | Downloaded 10/11/21 10:22 AM UTC DECEMBER 2012 Z H A O E T A L . 2133

FIG. 12. Semidiurnal internal tides at LR4. (a) Eastward velocity, (b) northward velocity, and (c) vertical displacement. (d)–(g) Depth-integrated quantities computed as the sum over the ﬁrst three modes: (d) HKE, (e) APE, (f) E, and (g) ﬂux magnitude.

2 decreases from about 1 to ;0.4–0.5 kW m 1 moving to- by either barotropic tidal height (Fig. 14e) or current ward the canyon head, as also found by Kunze et al. (2002), (Fig. 14f). To examine the timing of each maximum in Hall and Carter (2011), and Wain et al. (2012, manuscript the baroclinic quantities relative to the barotropic forc- submitted to J. Geophys. Res.). Flux magnitude does not ing, the time of the spring tide maxima of energy and flux differ greatly between the first and ensuing spring tides, are determined and shown by different vertical lines in but the direction changes about 258 atMP2andafull908 Figs 14a–d. Note that the times of maxima at LR1–LR3 at LR4. Additionally, total energy (circles) is higher at all and WH1 are less reliable, because of the large uncer- moorings in the first spring-neap cycle than the last three. tainties in the HKE calculation associated with the sur- The spring-neap cycles evident at MP2 and LR4 are face and bottom gaps (see the appendix). For the first and present at all moorings in HKE (Figs. 14a,b), and in third spring tides, the observed maxima in the baroclinic APE (Fig. 14c) and F (Fig. 14d) at MP1–3 and LR4, the quantities occur approximately at the same time as the moorings for which these quantities can be computed. maxima in both sea level and barotropic current. At the Energy and flux rise and fall generally in phase at all second and fourth spring tides, the observed baroclinic moorings, although magnitude is different at each site maxima lag those in sea level, but are more or less in line primarily owing to the patterns of generation and dis- with those in barotropic current. Figure 14 shows that the sipation within the canyon (Hall and Carter 2011; Wain mismatches (SP2, SP4) occur during the greatest rate of et al. 2012, manuscript submitted to J. Geophys. Res.). temporal change in the background conditions, and that The modulation between spring and neap is about a the good match occurs at SP1 while there is no upwelling factor of 4 for HKE and flux. Except for at LR4, the mod- or at SP3 while the upwelling is steady. ulation of APE is less than that for the other quantities. Both the timing and the magnitude of energy and flux 4. Standing and progressive waves at each spring (SP1–SP4) are variable. At each site the HKE magnitude at spring tide varies by about 20%–30%, We hypothesize that the differences between the baro- with the greater and lower values poorly predicted clinic response at the various spring tides arise because

Unauthenticated | Downloaded 10/11/21 10:22 AM UTC 2134 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 42

horizontally standing waves. Their evidence included the horizontal and vertical variations of the phase of the baroclinic velocity and displacements (their Figs. 5 and 11). Here we examine 1) the ratio between horizontal kinetic and available potential energy, 2) the ratio between ﬂux magnitude and total energy compared to the group speed, and 3) the along-channel phase following Petruncio et al. (1998). The three methods all indicate a partly- standing wave early in the record when the thermocline was deeper, transitioning to a more progressive wave later in the record as the thermocline shallowed. a. HKE/APE ratio For a progressive semidiurnal internal wave at the latitude of Monterey Submarine Canyon, the HKE to APE 2 2 2 2 ratio rE [ (v 1 f )/(v 2 f ) ’ 2.2, where v is the tidal frequency, and f is the local inertial frequency. Two mode-1 waves traveling in opposite directions show an inter- FIG. 13. Time-mean modal distribution of semidiurnal HKE, APE, , F and F at MP2. ference pattern wherein APE, HKE and all vary with spatial location. Because the minima and maxima of HKE

and APE are offset from each other, rE can range from of stratification changes associated with spring transi- zero to infinity depending on the location of the measure- tion winds (Fig. 7). Specifically, we explore the hypoth- ments relative to the nodes and antinodes within the in- esis of Petruncio et al. (1998) that internal tides within terference pattern (Nash et al. 2004; Alford and Zhao MSC transition between progressive waves and partly, 2007b; Martini et al. 2007). For multiple waves traveling in

FIG. 14. Time series of (a)–(d) the moored semidiurnal energy and ﬂux and (e),(f) barotropic forcing: (a) HKE at LR1–LR3 and WH1; (b) HKE at MP1–MP3 and LR4: (c) APE; (d) ﬂux magnitude; (e) semidiurnal barotropic tidal height; and (f) depth-averaged current at MP2 (toward 608 true). In (e),(f), the times of the four spring tides SP1–SP4 are highlighted in gray. In (a)–(d), the vertical lines give the maximum value of each quantity at each spring tide. Note the scale difference between (a),(b) HKE and (c) APE.

Unauthenticated | Downloaded 10/11/21 10:22 AM UTC DECEMBER 2012 Z H A O E T A L . 2135

FIG. 15. Mode-1 standing and progessive waves. (a) The HKE to APE ratio rE. The horizontal black line indicates the theoretical value of ;2.2. (b) The ratio of ﬂux magnitude to total ^ energy, cg, estimated from the moorings (colored lines). The theoretical group speed cg (black line for MP1; gray band for MP2, MP3, and LR4) is a function of time owing to the varying stratiﬁcation. The vertical spread of the gray band accounts for the varying water depth at the

moorings, on which cg also depends. (c) Greenwich phase of mode-1 M2 displacement. different directions on a compass rose, the interference used successfully in a variety of ocean situations (Alford patterns can be more complicated still (Rainville et al. 2010; et al. 2006; Alford and Zhao 2007b; Martini et al. 2007; Zhao et al. 2010). However, in general, the cycle mean for Klymak et al. 2011). Here, c^g is estimated for mode 1 at a standing and partly-standing wave is less than the theo- MP1–MP3 and LR4 (Fig. 15b, colored lines), and com- retical value shown by a progressive wave. pared to the theoretical mode-1 value cg (black line for Observed rE at MP1–MP3 and LR4 is shown in Fig. 15a. MP1; gray band for MP2, MP3 and LR4), which also For all moorings, there is an obvious change before and changes in time owing to the changing stratification after yearday 70 (vertical dashed line). Before yearday 70, (Fig. 10). The finite thickness of the mode-1 curve (gray rE at MP2 (Fig. 15a, blue) is much lower than the theo- band) represents the dependence on depth, with the upper retical value (black), while after yearday 70 it varies around values corresponding to deeper depths. For all moorings, ^ the theoretical value, suggesting that the internal tide field cg is less than cg during yearday 48–70, and is close to changed from a partly-standing wave to a progressive wave theoretical values during yearday 70–104, again suggesting around yearday 70. MP3 (red) and LR4 (green) display partly-standing waves in the first period, and progressive a similar trend, but never reach the theoretical value during waves in the second period. the later period, potentially implying spatial variations c. Greenwich phase (examined below). As a final test, we compute the Greenwich phase of b. Group speed mode-1 semidiurnal displacement at each mooring as a The ratio of flux magnitude to total energy c^g [ F/E function of slowly-varying stratification by harmonic anal- can also be used to test for progressive versus standing ysis over sliding 2.1-day windows (Fig. 15c). Mode-1 dis- waves. For a progressive wave, c^g equals the group speed placement is in phase at all moorings for the first part of the cg, with standing or partly-standing waves again showing record, a signature of a standing or nearly-standing wave. an interference pattern. In a modally-decomposed wave- However, in the second period, phase at MP2, MP3, and field, the degree of free propagation can be assessed for LR4 increases shoreward, indicating up-canyon phase prop- each mode by comparing the observed ratio of flux to en- agation. For example, the phase lags between MP2 and ergy with the theoretical value of the group speed for each MP3 are about 208–508, equivalent to 0.7–1.7 h. The prop- mode (Alford and Zhao 2007b). The technique has been agationtimescanbecomparedtothatexpectedfromthe

Unauthenticated | Downloaded 10/11/21 10:22 AM UTC 2136 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 42

the greater value of c^g at MP1 than at the other locations (Fig. 15b), but not with the values of rE at MP1 or its display of the same phase as the other moorings (Fig. 15c). Hence, the evidence is somewhat conﬂicting at MP1, but does at least suggest that the partly-standing wave behavior is restricted to up canyon of Gooseneck Meander.

5. Turbulence Turbulent kinetic energy dissipation rate, , is computed from Thorpe scales using the moored potential density data (Thorpe 1977; Dillon 1982; Alford et al. 2006). Given the CTD sample interval of about 0.125 m 2 2 and its density uncertainty of about 10 4 kg m 3, and the background stratiﬁcation, overturns of less than a meter can be reliably resolved (Galbraith and Kelley 1996)—much smaller than the observed overturning scales of tens of meters that dominate the dissipation in our data. Dissipation rate is then estimated as

5 : 2 3 (z, t) 0 64LT N (z, t), (9)

2 where LT is the Thorpe scale, and N is the buoyancy frequency. Dissipation rate for the whole record is plotted in Figs. 17c–e, together with the barotropic tidal forcing (Fig. 17a) and the depth-integrated energy flux (Fig. 17b). Dissipation is bottom-intensified at both locations, with a decay scale of about 50–150 m, as found at these loca- FIG. 16. Vertical profiles of along-canyon energy flux at MP1–MP3 and LR4 on yearday (a) 56 and (b) 86. The along-canyon bathymetry tions and elsewhere in MSC by Carter and Gregg (2002), is plotted, and internal tide characteristics for each stratification Kunze et al. (2012), and Wain et al. (2012, manuscript profile are overlaid. The width of the gray bands shows the spread of submitted to J. Geophys. Res.). The spring-neap cycle so characteristics during yearday (a) 53–59 and (b) 83–89. evident in energy and energy flux (Fig. 17b) appears clearly as a modulation both in this decay scale and in theoretical phase speed and the distance between the the depth-integrated value (Fig. 17c). However, the 2 moorings. Taking a phase speed of 0.5–0.7 m s 1 (Fig. 10e) modulation is only about a factor of 1.5 or 2, compared and a 2.5 km MP2–MP3 distance, the propagation time is to about 4 for the energy flux. The greater dissipation as estimated to be 1–1.4 h. Observed and theoretical free-wave a fraction of energy flux at neap tides may imply that travel times are similar, consistent with a progressive wave. some of the energy cascades through the internal wave spectrum via nonlinear interactions. Because the time d. Vertical profiles scale for these interactions is a few days, some dissipation The observed pattern of along-canyon energy flux at neap tide may result from energy input at the previous profiles is shown in Fig. 16 for the early period (Fig. 16a) spring. and the late period (Fig. 16b). The flux profiles at MP2, The intensity of the turbulence and its decay scale are MP3 and LR4 during the later period (Fig. 16b) generally both greater at MP2 than at MP3, likely because MP2 is indicate the expected pattern of top- and bottom- near the top of a ridge associated with the Gooseneck intensified up-canyon flux for an up-canyon-propagating Meander, and flow is nearly perpendicular to it (Fig. 18 mode 1 wave, while during the early period the deep and and Wain et al. 2012, manuscript submitted to J. Geo- middepth regions of down-canyon flux are seen that were phys. Res.). In the vicinity of MP2, depth-integrated evident for MP2 in Fig. 11. However, the flux profile at dissipation is approximately equal to observed conver- MP1 during this period resembles that expected for a gent fluxes measured there (Wain et al. 2012, manuscript progressive wave, with no reversals. This is consistent with submitted to J. Geophys. Res.).

Unauthenticated | Downloaded 10/11/21 10:22 AM UTC DECEMBER 2012 Z H A O E T A L . 2137

FIG. 17. Turbulent dissipation rate at MP2 and MP3. (a) Semidiurnal and diurnal barotropic tidal forcing. (b) Semidiurnal energy ﬂux. (c) Depth-integrated dissipation rate at MP2 and MP3, smoothed with a 4-day running window. (d) Turbulent dissipation rate measured at MP2, and smoothed using a 1-day running window. (e) As in (d), but for MP3. In (d),(e) the y axis is height above the bottom (HAB) in meters.

The character of the dissipation is different in the first stratification changes from a standing (Fig. 19, left) spring tide period and the subsequent ones, as seen by to a progressive-favorable pattern (Fig. 19, right). The plotting 2-day time series of along-canyon velocity (Fig. overall depth-integrated dissipation increases gradually 19, upper panels) and dissipation rate (Fig. 19, middle toward the end of the record (Fig. 17c). It is possible that panels) at MP2. the greater dissipation contributes to the progressive- During the first period (Fig. 19, left panels), dissipation wave behavior late in the record by dissipating internal 2 2 occurs primarily in bursts exceeding 5 3 10 5 Wkg 1 tides that otherwise might have reflected. once each 12.4 h, when isopycnals at depth are at their deepest (Fig. 19b). The flow in the bottom 100 m at MP2 is oriented perpendicular to a ridge (Fig. 18). Tidal excursion ellipses, computed as the time integral of the semidiurnal velocities averaged over the bottom 100 m, are about 62 km, causing water to transit the ridge each tidal cycle. Downward deflection of isopycnals occurs following flow to the southwest (Fig. 19a, blue). The geometry and phasing of the dissipation are similar to those collected near a ridge crest in Luzon Strait (Alford et al. 2011), where lee waves formed by baroclinic flow over the ridge become unstable once per period when flow is downslope (Legg and Klymak 2008; Buijsman et al. 2012). During subsequent spring tide periods (as exemplified by the fourth spring tide, plotted at right in Fig. 19), dissipation is somewhat less deterministic, occurring more continuously throughout the semidiurnal cycle. Some bursts are seen every 12.4 h, but they now occur when isopycnals are at their highest, following flow to FIG. 18. Bathymetry in the vicinity of MP2 and semidiurnal tidal the northeast (Fig. 19b). It is possible that the struc- excursions averaged over the bottom 100 m for each spring tide ture of the lee wave response shifts subtly when the period. See the gray box in Fig. 1a for location.

Unauthenticated | Downloaded 10/11/21 10:22 AM UTC 2138 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 42

FIG. 19. Velocity, displacement, and dissipation rate during the (left) ﬁrst and (right) last spring tides at MP2.

(a),(b) Velocity u//,thatis,toward608 true; (c),(d) turbulent dissipation rate; and (e),(f) semidiurnal velocity (blue), displacement (red), and dissipation rate (green) averaged over the bottom 100 m.

6. Discussion These characteristics are initialized at an arbitrary along- canyon location (here chosen as 5 km from the canyon The observed partly standing wave pattern must head; Fig. 16). The thalweg slope (gray shading) is fairly arise from down-canyon fluxes at MP2, MP3, and LR4 constant spatially, with a slope of about 0.025. For the that superpose with the incident up-canyon fluxes. The early stratification (Fig. 16a), semidiurnal characteristics down-canyon fluxes may arise from greater generation are shallower than the thalweg, suggesting back reflection up canyon of the moorings, or greater reflection of consistent with the observed flux profiles indicating flux in the incident fluxes. The tendency of internal waves both directions. For the later period (Fig. 16b), the al- to back-reflect from topography depends on the rel- tered stratification steepens the wave characteristics. ative slope of the wave characteristics relative to the Over a broad range in depth and along the canyon axis, topography. That is, waves with characteristic slopes they are nearly equal to the thalweg slope. It is therefore steeper than the topography will forward reflect, possible that the observed lack of down-canyon fluxes while wave slopes shallower than the topography will during this period is because the incident internal tide is back-reflect. Waves with slopes near the topographic more effectively dissipated owing to the near-critical slope will undergo ‘‘critical reflection’’ (Eriksen 1982), slope. Dissipation is indeed greater during the last spring wherein the vertical wavenumber of the reflected waves tide, but not during the second and only marginally dur- becomes large, and energy density enhances, breaks, ing the third (Fig. 17c). Since we attribute much of the and dissipates. Numerical simulations of waves incident turbulence at MP2 to likely lee waves rather than critical- upon critically-sloping topography show formation of slope interactions, this may be a coincidence. It is possible internal tidal bores and elevated mixing (Slinn and that critical-slope dissipation occurs up canyon from our Levine 2003). observations. To compare the wave slopes in the two different pe- This analysis is therefore at least consistent with greater riods to the topographic slope, early- and late-period reflection leading to the down-canyon fluxes during the characteristics are computed from the stratification first period. On the other hand, the overall net up-canyon profile at yearday 56 6 3 and 86 6 3 by integrating the flux is similar during all four spring tides, with the first wave slope, one showing greater energy (Fig. 11). This would suggest qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi instead that the stratification in the first period leads s 5 (v2 2 f 2)/(N2 2 v2). (10) to greater up-canyon generation, which would in turn

Unauthenticated | Downloaded 10/11/21 10:22 AM UTC DECEMBER 2012 Z H A O E T A L . 2139 presumably lead to greater dissipation during that period, dissipation associated with marked changes in the contrary to observed. More observations and/or high- ocean stratification due to the onset of springtime resolution, three-dimensional modeling are needed to upwelling-favorable winds. Our major conclusions in- distinguish between these two different explanations. clude the following. Our observations have several important implications d The thermocline shoals from 100 to 40 m with the onset for modeling internal tides incident on topography in of upwelling favorable winds during our observations. coastal regions and for understanding the variability of The associated changes in stratification are substantial internal tides in general. The lateral differences in enough to necessitate inclusion of time-varying strati- stratification brought on by the upwelling pose difficul- fication in calculations of potential energy, energy flux. ties in that the stratification in the remote generation The modal shapes and the distribution of energy and region, which is further offshore, likely differs from the flux among them are also affected. stratification in the canyon, where the waves interact, d Because of these changes in stratification, the internal reflect and dissipate. For example, assumption of a lat- tide field changes from a partly-standing wave during erally constant stratification might be correct for the the first period (yearday 48–70) to a more progressive processes inside the canyon, but incorrect for the gen- wave during the second period (yearday 70–106). eration and propagation of the waves feeding the canyon d The dissipation rate and diapycnal diffusivity are bot- from remote generation sites. tom intensified with a decay scale of 50–150 m. The These data show one more example of the variability in decay scale shows a spring-neap cycle in phase with internal tides. Stratification has here been demonstrated energy and flux, with depth-integrated dissipation about to alter the structure of the wave field in a submarine 3 times greater in the last spring tide than in the first. canyon. Sheared mesoscale flows, not considered here, d Dissipation at MP2, which sits near the top of a sub- likely also contribute by modifying the modal shapes and marine ridge near the Gooseneck Meander, appears tied even leading to critical layers as described by the Taylor– to a breaking lee wave associated with the baroclinic Goldstein equation. The observed changes in the phasing flow over the ridge. However, the phasing of the and magnitude of the dissipation suggest that these pro- dissipation relative to the baroclinic motions changes cesses could influence the patterns and magnitude of markedly between the first spring tide and the dissipation in general. successive ones, apparently indicating that the lee- Therefore, the list of potential feedbacks between wave response may be altered in association with the internal tides and their forcing mechanisms is growing changed stratification. long. The generation process itself has been demonstrated to be strongly sensitive to the presence and phasing of remotely-incident internal tides (Kelly and Acknowledgments. This work was supported by NSF Nash 2010). Reflection depends not only on stratifica- through Grants OCE 0751226 and 0751420. We are tion, as suggested here, but also on the modal content grateful to caption Rick Verlini, marine technician and phasing of the incident internal tide (Klymak et al. Daryl Swensen and the entire crew of R/V Welcoma for 2011). Finally, the internal tide appears able to affect their expertise and hard work. We are grateful to Paul the barotropic tide itself via its alteration of the pres- Aguilar, Eric Boget, Andrew Cookson, John Mickett, and sure gradients, as argued in Carter (2010). This sug- David Winkel for their skill in designing, deploying, gestion is supported here by the dissimilarity in the and recovering the moorings. Discussions with Rob Hall spring-neap cycles of barotropic sea level and currents, and Danielle Wain were very helpful. with the latter greater during periods of greater baroclinic energy (Fig. 14). For accurate global maps of APPENDIX internal tides, it may be necessary to properly account for all of these processes. Errors in Flux and Energy Estimates of energy and energy flux are notoriously 7. Conclusions sensitive to gaps in the water column coverage. With We have presented two-month, nearly-full-depth full-depth data, baroclinic pressure can be un- moored observations of internal tides and their breaking ambiguously determined and the resulting profiles sim- in the upper MSC. Our observations of net up-canyon ply integrated. With less than perfect water column flux and strong spring-neap cycles in energy and flux coverage, the calculation is done by projecting onto are in agreement with past studies. The current work modes (Alford 2003), but the surface intensification of focuses on the effects on the baroclinic signals and their the pressure and velocity modes for typical ocean

Unauthenticated | Downloaded 10/11/21 10:22 AM UTC 2140 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 42

FIG. A1. Energy and flux errors due to data gaps at MP2 and MP3. (a)–(d) Vertical profiles of u, h variance at (a), (b) MP2 and (c),(d) MP3. Gaps are shown in red. (e) APE, (g) HKE, and (i) flux magnitude at MP2 obtained from both the raw and filled data. (f),(h),(j) As in (e),(g),(i) but for MP3. profiles of stratification makes this method particularly black) matches the modally-summed quantities very well, sensitive to gaps at the surface (Nash et al. 2005). The but that of HKE and flux magnitude underestimates problem is less severe for displacement modes, which them by 10%–40% owing to the gaps near 40 m and the decrease to zero at the surface. bottom. It is discouraging that even with as nearly com- Here we take advantage of the near full-column cov- plete coverage at MP2, the flux must still be computed erage at MP2 (Fig. A1, left panels) to directly assess the with modal fits or interpolation for quantitative reli- errors associated with modal fits and interpolation ability. Still, particularly given the redness of the modal through the gaps. We then demonstrate the degree to spectrum, the gaps are quite reliably filled with inter- which the errors increase at the moorings with less polation such that the errors in the depth-integrated coverage, starting with MP3 (Fig. A1, right panels) and quantities is only a few percent at MP2. then moving to the ADCP moorings (Fig. A2). For MP3, the absence of the HOBO data reduces The profiles of displacement and velocity variance and the number of displacement modes that can be fit from the coverage for each quantity are indicated in Fig. A1 at ten to three, as seen by the unstable solutions for ten top. At MP2, the vertical gaps are small enough that 10 modes (f, blue). Depth-integrated APE agrees very modes can be reliably fit. However, the first few modes well with the sum of modes 1–3, except for two pe- dominate (see Fig. 13). As a result, time series of APE, riods. Flux is again underestimated by a slightly larger HKE, and flux magnitude from three and ten modes amount owing to the relatively larger gaps for dis- agree nearly perfectly (Figs. A1e,g,i, red and blue), and placement. interpolation through the gaps makes no difference The gaps at the ADCP moorings (;40-m gap at the (dashed lines). The direct depth integral of APE (e, surface and ;20-m gap at the bottom, account for

Unauthenticated | Downloaded 10/11/21 10:22 AM UTC DECEMBER 2012 Z H A O E T A L . 2141

——, and Z. Zhao, 2007a: Global patterns of low-mode internal- wave propagation. Part I: Energy and energy flux. J. Phys. Oceanogr., 37, 1829–1848. ——, and ——, 2007b: Global patterns of low-mode internal-wave propagation. Part II: Group velocity. J. Phys. Oceanogr., 37, 1849–1858. ——, M. C. Gregg, and M. A. Merrifield, 2006: Structure, propagation and mixing of energetic baronlinic tides in Mamala Bay, Oahu, Hawaii. J. Phys. Oceanogr., 36, 997–1018. ——, and Coauthors, 2011: Energy flux and dissipation in Luzon Strait: Two tales of two ridges. J. Phys. Oceanogr., 41, 2211– 2222. Buijsman, M. C., S. Legg, and J. Klymak, 2012: Double-ridge internal tide interference and its effect on dissipation in Luzon Strait. J. Phys. Oceanogr., 42, 1337–1356. Cairns, J. L., and G. O. Williams, 1976: Internal wave observations from a midwater float, 2. J. Geophys. Res., 81, 1943–1950. Carter, G. S., 2010: Barotropic and baroclinic M2 tides in the Monterey Bay region. J. Phys. Oceanogr., 40, 1766–1783. ——, and M. C. Gregg, 2002: Intense, variable mixing near the head of Monterey submarine canyon. J. Phys. Oceanogr., 32, 3145– 3165. ——, ——, and R.-C. Lien, 2005: Internal waves, solitary-like waves, and mixing on the Monterey Bay shelf. Cont. Shelf Res., 25, 1499–1520. Dale, A. C., J. M. Huthnance, and T. J. Sherwin, 2001: Coastal- trapped waves and tides at near-inertial frequencies. J. Phys. Oceanogr., 31, 2958–2970. Dillon, T. M., 1982: Vertical overturns: A comparison of Thorpe and Ozmidov length scales. J. Geophys. Res., 87, 9601– 9613. FIG. A2. Comparison of depth-averaged HKE computed from Doherty, K. W., D. E. Frye, S. P. Liberatore, and J. M. Toole, 1999: modal fits (colors) and direct integration (black) at the ADCP A moored profiling instrument. J. Atmos. Oceanic Technol., moorings. 16, 1816–1829. Eriksen, C. C., 1982: Observations of internal wave reflection off sloping bottoms. J. Geophys. Res., 87, 525–538. 10%–20% of the water column; Table 1) are substan- Galbraith, P. S., and D. E. Kelley, 1996: Identifying overturns in tially greater, leading to larger errors (Fig. A2). In the first CTD profiles. J. Atmos. Oceanic Technol., 13, 688–702. place, only three or four modes can be stably fit compared Gardner, W. D., 1989: Periodic resuspension in Baltimore Canyon to ten modes for MP2. More troublesome, the degree of by focusing of internal waves. J. Geophys. Res., 94, 18 185– 18 194. disagreement among the modes varies in time as the Garrett, C., and W. H. Munk, 1975: Space-time scales of internal modal shapes and the partition of energy among them waves: A progress report. J. Geophys. Res., 80, 291–297. changes with the stratification. Errors are worst during Gill, A. E., 1982: Atmosphere-Ocean Dynamics. Academic Press, the periods of rapid change (yearday 65–75 and 90–95). In 662 pp. general, the directly depth-integrated HKE underesti- Gonella, J., 1972: A rotary-component method for analysing me- ; teorological and oceanographic vector time series. Deep-Sea mates the modally summed quantities by 20%, again Res., 19, 833–846, doi:10.1016/0011-7471(72)90002-2. owing to the gap at the surface. Based on the differences Gordon, R. L., and N. F. Marshall, 1976: Submarine canyon in- between the various curves, we estimate an uncertainty ternal wave traps? Geophys. Res. Lett., 3, 622–624. of about 20% for HKE determined from the ADCP Gregg, M. C., G. S. Carter, and E. Kunze, 2005: Corrigendum. moorings, recognizing that errors can be greater during J. Phys. Oceanogr., 35, 1712–1715. ——, R. A. Hall, G. S. Carter, M. H. Alford, R.-C. Lien, D. P. rapidly changing stratification. Winkel, and D. J. Wain, 2011: Flow and mixing in Ascension, a steep, narrow canyon. J. Geophys. Res., 116, C07016, REFERENCES doi:10.1029/2010JC006610. Hall, P., and A. M. Davies, 2007: Internal tide modeling and the Alford, M. H., 2003: Redistribution of energy available for ocean influence of wind effects. Cont. Shelf Res., 27, 1357–1377, mixing by long-range propagation of internal waves. Nature, doi:10.1016/j.csr.2006.09.008. 423, 159–162. Hall, R. A., and G. S. Carter, 2011: Internal tides in Monterey ——, 2010: Sustained, full-water-column observations of internal Submarine Canyon. J. Phys. Oceanogr., 41, 186–204. waves and mixing near Mendocino Escarpment. J. Phys. Hickey, B. M., 1995: Coastal submarine canyons. Topographic Oceanogr., 40, 2643–2660. Interactions in the Ocean: Proc. ‘Aha Huliko‘a Hawaiian

Unauthenticated | Downloaded 10/11/21 10:22 AM UTC 2142 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 42

Winter Workshop, Honolulu, HI, University of Hawaii at Mooers, C. N. K., 1970: The interaction of an internal tide with the Manoa, 95–110. frontal zone in a coastal upwelling region. Ph.D. thesis, Ore- Hotchkiss, F. S., and C. Wunsch, 1982: Internal waves in Hudson gon State University, 480 pp. Canyon with possible geological implications. Deep-Sea Res., Nash, J. D., E. Kunze, J. M. Toole, and R. W. Schmitt, 2004: In- 29, 415–442. ternal tide reﬂection and turbulent mixing on the continental Hunkins, K., 1988: Mean and tidal currents in Baltimore Canyon. slope. J. Phys. Oceanogr., 34, 1117–1134. J. Geophys. Res., 93, 6917–6929. ——, M. H. Alford, and E. Kunze, 2005: Estimating internal wave Jachec, S. M., O. B. Fringer, M. G. Gerritsen, and R. L. Street, energy ﬂuxes in the ocean. J. Atmos. Oceanic Technol., 22, 2006: Numerical simulation of internal tides and the resulting 1551–1570. energetics within Monterey Bay and the surrounding area. Osborne, J. J., A. L. Kurapov, G. D. Egbert, and P. M. Kosro, 2011:

Geophys. Res. Lett., 33, L12605, doi:10.1029/2006GL026314. Spatial and temporal variability of the M2 internal tide gen- Johnston,T.M.S.,D.L.Rudnick,G.S.Carter,R.E.Todd,andS.T. eration and propagation on the Oregon shelf. J. Phys. Oce- Cole, 2011: Internal tidal beams and mixing near Monterey Bay. anogr., 41, 2037–2062. J. Geophys. Res., 116, C03017, doi:10.1029/2010JC006592. Paduan, J. D., and L. K. Rosenfeld, 1996: Remotely sensed surface Kang, D., and O. B. Fringer, 2012: Energetics of barotropic and currents in Monterey Bay from shore-based HF radar (coastal baroclinic tides in the Monterey Bay area. J. Phys. Oceanogr., ocean dynamics application radar). J. Geophys. Res., 101 (C9), 42, 272–290. 20 669–20 686. Kelly, S. M., and J. D. Nash, 2010: Internal-tide generation and Paull,C.K.,P.Mitts,W.UsslerIII,R.Keaten,andH.G.Greene,2005: destruction by shoaling internal tides. Geophys. Res. Lett., 37, Trail of sand in upper Monterey Canyon: Offshore California. L23611, doi:10.1029/2010GL045598. Geol. Soc. Amer. Bull., 117, 1134–1145, doi:10.1130/B25390.1. ——, ——, M. H. Alford, and K. I. Martini, 2012: The cascade of Pawlowicz, R., B. Beardsley, and S. Lentz, 2002: Classical tidal tidal energy from low to high modes on a continental slope. harmonic analysis including error estimates in MATLAB us- J. Phys. Oceanogr., 42, 1217–1232. ing T_TIDE. Comput. Geosci., 28, 929–937. Key, S. A., 1999: Internal tidal bores in the Monterey Canyon. Pedlosky, J., 2003: Waves in the Ocean and Atmosphere: In- M.S. thesis, Department of Oceanography, Naval Postgraduate troduction to Wave Dynamics. Springer, 268 pp. School, 91 pp. Petruncio, E. T., L. K. Rosenfeld, and J. D. Paduan, 1998: Obser- Klymak, J. M., M. H. Alford, R. Pinkel, R.-C. Lien, Y. J. Yang, vations of the internal tide in Monterey Canyon. J. Phys. and T.-Y. Tang, 2011: The breaking and scattering of the Oceanogr., 28, 1873–1903. internal tide on a continental slope. J. Phys. Oceanogr., 41, ——, J. D. Paduan, and L. K. Rosenfeld, 2002: Numerical simula- 926–945. tions of the internal tide in a submarine canyon. Ocean Kunze, E., L. K. Rosenfeld, G. S. Carter, and M. C. Gregg, 2002: Modell., 4 (3–4), 221–248, doi:10.1016/S1463-5003(02)00002-1. Internal waves in Monterey submarine canyon. J. Phys. Oce- Rainville,L.,T.M.S.Johnston,G.S.Carter,M.A.Merriﬁeld, anogr., 32, 1890–1913. R. Pinkel, P. F. Worcester, and B. D. Dushaw, 2010: Interference ——, C. MacKay, E. E. McPhee-Shaw, K. Morrice, J. B. Girton, pattern and propagation of the M2 internal tide south of the and S. R. Terker, 2012: Turbulent mixing and exchange with Hawaiian Ridge. J. Phys. Oceanogr., 40, 311–325. interior waters on sloping boundaries. J. Phys. Oceanogr., 42, Ramp, S. R., J. D. Paduan, I. Shulman, J. Kindle, F. L. Bahr, and 910–927. F. Chavez, 2005: Observations of upwelling and relaxation Kurapov, A. L., G. D. Egbert, J. S. Allen, R. N. Miller, S. Y. events in the northern Monterey Bay during August 2000.

Erofeeva, and P. M. Kosro, 2003: The M2 internal tide off J. Geophys. Res., 110, C07013, doi:10.1029/2004JC002538. Oregon: Inferences from data assimilation. J. Phys. Oceanogr., Rosenfeld, L. K., F. B. Schwing, N. Garfield, and D. E. Tracy, 1994: 33, 1733–1757. Bifurcated flow from an upwelling center: a cold water source ——, J. S. Allen, and G. D. Egbert, 2010: Combined effects of for Monterey Bay. Cont. Shelf Res., 14, 931–964, doi:10.1016/ wind-driven upwelling and internal tide on the continental 0278-4343(94)90058-2. shelf. J. Phys. Oceanogr., 40, 737–756. Shea, R. E., and W. W. Broenkow, 1982: The role of internal tides Lee, I.-H., R.-C. Lien, J. T. Liu, and W.-S. Chuang, 2009: Turbulent in nutrient enrichment of Monterey Bay, California. Estuarine mixing and internal tides in Gaoping (Kaoping) Submarine Coastal Shelf Sci., 15, 57–66. Canyon, Taiwan. J. Mar. Syst., 76, 383–396, doi:10.1016/ Slinn, D., and M. Levine, 2003: Modeling internal tides and mixing j.jmarsys.2007.08.005. over ocean ridges. Dynamics of Oceanic Internal Gravity Legg, S., and J. Klymak, 2008: Internal hydraulic jumps and over- Waves, II: Proc. ‘Aha Huliko‘a Hawaiian Winter Workshop, turning generated by tidal flow over a tall steep ridge. J. Phys. Honolulu, HI, University of Hawaii at Manoa, 59–68. Oceanogr., 38, 1949–1964. Swart, N. C., S. E. Allen, and B. J. W. Greenan, 2011: Resonant Lueck, R. G., and T. R. Osborn, 1985: Turbulence measurements in amplification of subinertial tides in a submarine canyon. a submarine canyon. Cont. Shelf Res., 4, 681–698. J. Geophys. Res., 116, C09001, doi:10.1029/2011JC006990. MacKinnon, J. A., and M. C. Gregg, 2003a: Mixing on the late- Thorpe, S., 1977: Turbulence and mixing in a Scottish loch. Philos. summer New England shelf–solibores, shear and stratification. Trans. Roy. Soc. London, 286A, 125–181. J. Phys. Oceanogr., 33, 1476–1492. Wunsch, C., and S. Webb, 1979: The climatology of deep ocean ——, and ——, 2003b: Shear and baroclinic energy flux on the internal waves. J. Phys. Oceanogr., 9, 235–243. summer New England shelf. J. Phys. Oceanogr., 33, 1462– Xu, J. P., and M. A. Noble, 2009: Currents in Monterey Sub- 1475. marine Canyon. J. Geophys. Res., 114, C03004, doi:10.1029/ Martini, K. I., M. H. Alford, J. D. Nash, E. Kunze, and M. A. 2008JC004992. Merrifield, 2007: Diagnosing a partly-standing internal wave in Zhao, Z., M. H. Alford, J. A. MacKinnon, and R. Pinkel, 2010: Long- Mamala Bay, Oahu. Geophys. Res. Lett., 34, L17604, doi:10.1029/ range propagation of the semidiurnal internal tides from the 2007GL029749. Hawaiian Ridge. J. Phys. Oceanogr., 40, 713–736.

Unauthenticated | Downloaded 10/11/21 10:22 AM UTC