Internal Tides in Monterey Submarine Canyon 1 Introduction

Internal tides in Monterey Submarine Canyon

R. A. Hall1 and G. S. Carter1

1Department of Oceanography, University of Hawai’i at Manoa, Honolulu, Hawaii, USA.

Abstract

The M2 internal tide in Monterey Submarine Canyon is simulated using a modified version of the Princeton Ocean Model. Most of the internal tide energy entering the canyon is generated to the south, on Sur Slope and at the head of Carmel Canyon. The internal tide is topographically steered around the large canyon meanders. Depth-integrated baroclinic energy fluxes are up-canyon and largest near the canyon axis, up to 1.5 kW m−1 at the mouth of the upper canyon and increasing to over 4 kW m−1 around Monterey and San Gregorio Meanders. The up-canyon energy flux is bottom-intensified, suggesting topographic focusing occurs. Net along-canyon energy flux decreases almost monotonically from 9 MW at the canyon mouth to 1 MW at Gooseneck Meander, implying high levels of internal tide dissipation occur. The depth-integrated energy flux across the 200 m isobath is of order 10 W m−1 along the majority of the canyon rim, but increases by over an order of magnitude near the canyon head where internal tide energy escapes onto the shelf. Reducing the size of the model domain to exclude remote areas of high barotropic-to-baroclinic energy conversion decreases the depth-integrated energy flux in the upper canyon by 20%. However, quantifying the role of remote internal tide generation sites is complicated by a pressure perturbation feedback between baroclinic energy flux and barotropic-to-baroclinic energy conversion.

1 Introduction approach a slope from deep water, the onshore/offshore direction of propagation after reflection is determined by Submarine canyons are a common feature along conti- the ratio of the topographic slope to the internal wave nental shelves. They are estimated to cover approxi- characteristic slope, mately 20% of the shelf along the west coast of North s ∂H/∂x America (Hickey, 1995). Canyons can be efficient gen- α = topog = , (1) 1/2 erators of internal tides (internal gravity waves with swave [(ω2 − f 2) / (N 2 − ω2)] tidal frequencies) through scattering of the barotropic tides from sloping topography (Bell, 1975; Baines, 1982). where H is the total depth, x is distance, ω is the angular They are also thought to trap internal waves from out- frequency of the wave, f is the inertial frequency, and N side the canyon, through reflection from the sloping to- is the buoyancy frequency. If α < 1 (subcritical) waves pography, and channel the energy towards the canyon will continue to shoal after reflection. If α > 1 (super- head (Gordon and Marshall, 1976; Hotchkiss and Wun- critical) reflected waves will propagate back into deeper sch, 1982). water. If α = 1 (critical) linear theory breaks down, Unlike internal tide generation, which may be dom- leading to nonlinear effects and potentially wave break- inated by topographic blocking (Garrett and Kunze, ing. In a three-dimensional ocean it is more apt to vi- 2007), reflection of internal tide beams is entirely de- sualize internal wave ‘sheets’ rather than beams (Carter termined by the topographic slope. Reflection is often et al., 2006; Jachec, 2007). The slope of an internal wave considered in only two-dimensions; when internal waves beam in a horizontal/vertical section will depend on the orientation of the section with respect to the internal Corresponding author address: Dr. Rob Hall, Department wave sheet. If section is in the same plane as the sheet of Oceanography, University of Hawai’i at Manoa, Marine Sci- ence Building, 1000 Pope Road, Honolulu, HI 96822, USA. the slope of the beam will equal swave. If the section is ([email protected]) perpendicular to the sheet the beam will be horizontal.

1 HALL AND CARTER: INTERNAL TIDES IN MSC

37oN 0 1 2 3 4 Depth (km)

55’

Monterey Meander 50’

Soquel Canyon 25 Smooth 45’ Ridge Gooseneck Meander

50 40’ San Gregorio Carmel Canyon Meander

35’ 100 75

30’

Sur Slope

30’ 25’ 20’ 15’ 10’ 5’ 122o W 55’ 50’

Figure 1: Bathymetry of Monterey Submarine Canyon. The contour interval is 100 m. The line along the axis of the canyon is the thalweg. Distance along the thalweg from Moss Landing is marked with a cross at 5 km intervals.

Internal waves above the rim of the canyon are focused density increases upon reflection because the separation towards the canyon floor by supercritical reflection from between adjacent internal wave characteristics narrows, the steep canyon walls (Gordon and Marshall, 1976), concentrating the energy into a smaller area. Increases while internal waves entering the canyon from offshore in internal wave energy density have been observed in are focused towards the canyon head by subcritical re- Hydrographers Canyon (Wunsch and Webb, 1979), Hud- flection along the typically gentle sloping canyon floor son Canyon (Hotchkiss and Wunsch, 1982), and recently (Hotchkiss and Wunsch, 1982). In both cases, energy in Gaoping Canyon off Taiwan (Lee et al., 2009).

2 HALL AND CARTER: INTERNAL TIDES IN MSC

Monterey Submarine Canyon (MSC) is located within sured depth-varying velocities and so considered all ve- and offshore of Monterey Bay in central California. It is locities to be baroclinic. However, numerical model sim- the largest submarine canyon along the west coast of the ulations of the tides in Monterey Bay (Jachec, 2007; United States, extending over 100 km from the abyssal Rosenfeld et al., 2009; Wang et al., 2009; Carter, 2010) plain at the base of the continental slope to within and have suggested barotropic M2 velocities may be sig- 100 m of Moss Landing in the centre of the bay. The nificantly larger. Jachec (2007) showed barotropic veloc- bathymetry of the canyon is very complex, with several ities in the upper canyon reach 0.06 m s−1. Both Rosen- sharp meanders in the upper reaches and two smaller feld et al. (2009) and Wang et al. (2009) quote barotropic side-canyons (Fig. 1). Following the canyon thalweg (the current magnitudes in the range 0.03–0.04 m s−1 for deepest part of the canyon axis) from Moss Landing, the Monterey Bay area. Most recently, Carter (2010) the first major meander is between 12 and 20 km, re- showed depth-averaged velocities in the bay can exceed ferred to as Gooseneck Meander. Between 30 and 55 km, 0.1 m s−1 and are spatially variable. there are two large meanders, Monterey and San Gre- Kunze et al. (2002) measured depth-integrated inter- gorio Meanders, that form an S-shaped bend. Soquel nal tide energy fluxes of 5 kW m−1 around San Gregorio Canyon merges with MSC from the north at around and Monterey Meanders, decreasing to order 1 kW m−1 32 km, just up-canyon of the apex of Monterey Mean- around Gooseneck Meander. Other energy flux measure- der. Carmel Canyon merges with MSC at around 60 km, ments have been made up-canyon of Monterey Mean- down-canyon of San Gregorio Meander. Further down- der. Petruncio et al. (1998) estimated the semi-diurnal canyon the canyon intersects two regions of smooth shelf internal tide energy flux to be 1.3 kW m−1 at a sta- slope, Smooth Ridge to the north and Sur Slope to the tion 22 km along the thalweg, slightly down-canyon of −1 south. The canyon floor is gently sloping (stopog = 0.03 Gooseneck Meander, and 0.8 kW m at 6 km, near to 0.06) and is subcritical to semi-diurnal internal tides the canyon head. Carter and Gregg (2002) made sev- down-canyon of San Gregorio Meander; up-canyon of eral measurements of internal tide energy flux, between the meander, the floor is near-critical. The canyon walls 2 and 11 km along the thalweg1, ranging from 0.3 to are steep (slopes up to 0.7) and supercritical along the 1.9 kW m−1. These internal tide energy fluxes are larger whole length of the canyon. than those typically found at continental shelf edges (or- The currents in MSC are dominated by a semi-diurnal der 0.1 W m−1, Sherwin, 1988; Green et al., 2008), but internal tide. Velocity amplitudes > 0.2 m s−1 have been less than half that observed at the mouth of Gaoping observed in the canyon (Shepard et al., 1974; Rosenfeld Canyon (Lee et al., 2009). et al., 1994; Petruncio et al., 1998) and are intensified Previous measurements of internal tide energy fluxes near the bottom (Xu et al., 2002). Key (1999) observed have been predominantly in a net up-canyon direction, strongly bottom-intensified currents near the head of the suggesting the majority of internal tide generation oc- canyon that were associated with internal tidal bores. curs offshore or in the lower reaches of the canyon. On Semi-diurnal vertical isopycnal displacements with 30 the basis of internal tide characteristics, Petruncio et al. to 60-m amplitudes have also been observed near the (1998) suggested Smooth Ridge and the steep ridge in- canyon head (Broenkow and McKain, 1972; Petruncio side San Gregorio Meander as likely generation sites, but et al., 1998; Carter and Gregg, 2002). later studies found no evidence for internal tide gen- The M2 is the dominant tidal constituent in the eration at these locations (Kunze et al., 2002; Jachec canyon and four largest constituents (M2, S2, K1, and et al., 2006; Carter, 2010). Kunze et al. (2002) and O1) account for 90% of the total current variability (Xu Carter and Gregg (2002) identifed along-canyon flux di- and Noble, 2009). Near-inertial oscillations are absent vergences and down-canyon energy fluxes near Goose- (Kunze et al., 2002), possibly due to the presence of neck Meander, suggestive of local internal tide genera- the steep canyon walls. At all depths M2 tidal ellipses tion in the upper canyon. are more rectilinear than predicted by linear theory and Petruncio et al. (2002) used a three-dimensional nu- the semi-major axes are aligned in the along-canyon di- merical model to investigate the generation of semi- rection (Petruncio et al., 1998; Xu and Noble, 2009), diurnal internal tides in idealized canyons with dimen- suggesting the internal tide is topographically steered. From a mass balance approach, Petruncio et al. (1998) 1The distances stated here are longer than those reported by estimated barotropic tidal velocities in Monterey Bay to Carter and Gregg (2002) because higher resolution bathymetry be small, around 0.006 m s−1. They considered this data is used to define the thalweg. This results in a longer along- thalweg distance between any two points on the canyon axis be- barotropic flow to be negligible compared to the mea- cause small-scale bends between the points are resolved.

3 HALL AND CARTER: INTERNAL TIDES IN MSC sions similar to MSC, but with varying floor slopes and 2 Numerical model setup canyon geometry. Strong shoreward propagating internal tides were generated in canyons with near-critical A modified version of the Princeton Ocean Model floor slopes along much of their length. Along-slope ve- (POM, Blumberg and Mellor, 1987) is used to simu- locity and energy density were bottom-intensified, con- late the M2 tide in the Monterey Bay region. POM is a sistent with internal tide characteristics emanating from three-dimensional, nonlinear, hydrostatic, free-surface, the shelf break at the foot of the canyon. The largest finite-difference, terrain-following (σ coordinate), prim- internal tides were generated in a canyon that was near- itive equation model. The Mellor and Yamada (1982) critial at its foot. However, little internal tide energy second-moment turbulence-closure scheme is used to cal- made it onto the shelf because the canyon floor was su- culate diffusivities and viscosities in the vertical and the percritical further shoreward. Smagorinsky (1963) scheme used in the horizontal3. The From baroclinic energy flux divergence in a three- model setup and domain is the same as used by Carter dimensional, nonhydrostatic, unstructured grid model (2010). The Flather condition (Flather, 1976) is applied of the M2 tide in the Monterey Bay region, Jachec et al. at the boundaries so that barotropic energy is transmit- (2006) identified Sur Slope and Sur Platform as key gen- ted out of the domain. Baroclinic energy is absorbed at eration sites for the internal tide in MSC. Other gener- the boundaries using the relaxation scheme described by ation sites occur in the canyon itself. However, energy Carter and Merrifield (2007). flux divergence can only provide a lower bound on inter- The model domain extends from 123◦ 430 5900W, nal tide generation because it does not account for local 35◦ 310 1300N to 121◦ 440 800W, 37◦ 90 5000N with 250- baroclinic energy dissipation (Carter et al., 2008). m horizontal resolution; the bathymetry is derived from High levels of mixing are observed at the head of Monterey Bay Aquarium Research Institute multibeam MSC. Carter and Gregg (2002)2 estimated the av- data and is higher resolution than previous models of the erage turbulent kinetic energy dissipation rate to be region. Fifty-one evenly spaced sigma levels are used, 1.9×10−7 W kg−1, two orders of magnitude higher than giving a vertical resolution between 0.3 and 80 m. typical values for the interior of the open ocean (Gregg, The hydrostatic pressure assumption is valid when the 1989; Ledwell et al., 1993; Toole et al., 1994), and is horizontal scales of motion are much greater than the in agreement previous estimates by Lueck and Osborn vertical scales (Mahadevan, 2006). This is true for inter- (1985). The enhanced mixing is assumed to be caused by nal tides except during wave breaking, when steepening dissipation of the internal tide; approximations of dissi- to form highly nonlinear solitary waves, and during the pation rate from the convergence of internal tide energy formation of hydraulic jumps. The horizontal resolution fluxes (Petruncio et al., 1998; Carter and Gregg, 2002; of the model is too course to resolve these nonhydrostatic Kunze et al., 2002) have shown reasonable agreement processes. For example, nonlinear solitary-like waves with microstructure measurements (Lueck and Osborn, have been observed on the continental shelf in Monterey 1985; Carter and Gregg, 2002). Jachec et al. (2006) Bay (Carter et al., 2005), but the horizontal scale of calculated 8.3 MW net dissipation in the canyon from the waves is less than half the horizontal resolution of baroclinic M2 energy flux divergence. the model. Jachec (2007) showed that nonhydrostatic This study focuses on generation of the internal tide pressure effects are generally small in the Monterey Bay on Sur Slope and its propagation through MSC using a region, but may be important within MSC. high-resolution numerical model of the M2 tide in the Initial conditions are no flow and horizontally uniform Monterey Bay region. In Section 2, the model setup is stratification; the initial temperature and salinity pro- described. Generation of the internal tide on Sur Slope files are the average of 7 CTD casts at 123◦ 000 0000W, is assessed in Section 3. Propagation of the internal 36◦ 360 3000N taken over 12 hours on 18–19 February tide through MSC and onto the shelf is investigated in 2009. The model is forced at the boundaries with M2 Sections 4 and 5. In Section 6, possible remote internal barotropic velocities. Elevations and normal velocities tide generation sites are considered. A summary is given used to calculate the Flather boundary condition are in Section 7. taken from the TPXO6.2 inverse model (Egbert, 1997; Egbert and Erofeeva, 2002). As the simulation is of a generic M2 tide, surface buoyancy and momentum fluxes are set to zero. Diffusivities 2Turbulent kinetic energy dissipation rates reported by Carter and Gregg (2002) and Kunze et al. (2002) were later decreased 3Mean horizontal viscosity over the entire model domain is because of a processing error (Gregg et al., 2005). 0.016 m2 s−1

4 HALL AND CARTER: INTERNAL TIDES IN MSC are not applied to the temperature and salinity fields stants was seen around the Hawaiian Islands (Carter so the stratification is not eroded by mixing in the ab- et al., 2008). sence of a restoring buoyancy flux. This setup, with a The internal (baroclinic) hydrostatic tidal energy flux single tidal constituent and non-evolving stratification, is calculated as F = hu0p0i, where u0 is the velocity allows a relatively short simulation time because model perturbation, p0 is the pressure perturbation, and h·i spin-up is rapid. The simulation is run for 20 M2 tidal denotes an average over a tidal cycle (e.g. Kunze et al., 0 0 cycles (10.35 days) and a M2 harmonic analysis per- 2002; Nash et al., 2005). u and p are reconstructed formed over the last six tidal cycles. Previous appli- from the harmonic constants. Kelly et al. (2010) noted cations of the model, to the Hawaiian Islands (Carter that surface tide pressure contains a depth-dependent et al., 2008) and Mid-Atlantic Ridge (Zilberman et al., component (due to isopycnal heaving by movement of 2009), showed near steady state conditions were reached the free surface) as well as the depth-average component. within 12 tidal cycles. In comparison, Rosenfeld et al. Neglecting the depth-varying component introduces an (2009) forced their model with 8 tidal constituents and error to the energy flux calculation, but this error is allowed stratification to evolve with time. They found small in regions with large internal tides such as MSC. 22 days of model spin-up was required, longer than the Barotropic-to-baroclinic energy conversion is calculated entire simulation time used here. as 0 Sigma-coordinate models, such as POM, suffer erro- Econv = hp (−H)(u · ∇H)i , (2) neous low-frequency velocities from the calculation of where u is depth-averaged velocity from the harmonic horizontal pressure gradients over steep topography (e.g. analysis output (Niwa and Hibiya, 2001). Positive Haney, 1991; Mellor et al., 1994). These erroneous ve- conversion indicates energy being transferred from the locities are effectively removed by harmonic analysis. In barotropic tide to the baroclinic tide. Negative conver- addition, the erroneous velocities are interleaved verti- sion indicates work being done on the barotropic tide by cally so cancel out during depth-integration. the baroclinic tide (Zilberman et al., 2009). Carter (2010) found the harmonic analysis output for this simulation to be in excellent agreement with surface elevation measurements from tide gauges (RMS er- 3 Internal tide generation on Sur ror ∼ 1%) and reasonable agreement with velocity measurements from moored and shipboard ADCPs within Slope the canyon (RMS error 30% to 209%). In comparison, Interpretation of internal tide energy fluxes in the MSC the RMS error of inter-annual variation observed at the region is complicated by the existence of multiple gen- Monterey Bay Aquarium Research Institute mooring in eration sites. Rainville et al. (2010) showed that inter- MSC was 46% to 157%. No further model validation is nal tides from multiple sources constructively and de- provided here. structively interfere, resulting in depth-integrated en- Depth-averaged velocities in Monterey Bay, both in ergy flux beams appearing and disappearing in the open the canyon and on the shelf, are significantly larger than ocean. However, it is possible to make realistic infer- barotropic velocities inferred from a diagnostic model ences about the internal tide generation by comparing run in which temperature and salinity are not advected. depth-integrated baroclinic M2 energy fluxes (Fig. 2a) Carter (2010) explained this phenomenon as the result with the spatial distribution of barotropic-to-baroclinic of a feedback in which sea surface elevation anomalies M2 energy conversion (Fig. 2b). associated with the internal tide change the pressure gra- Most of the internal tide energy entering the upper dient forces driving depth-averaged currents in the bay. reaches of MSC (< 60 km along the thalweg) originates Despite this, we define baroclinic velocity as total minus to the south, on Sur Slope and at the head of Carmel depth-averaged to allow comparison with previous work. Canyon. Depth-integrated baroclinic energy fluxes at In this study, the depth-dependent structure of the in- the mouth of the upper canyon (defined here as between ternal tide is of interest, therefore baroclinic energy flux Smooth Ridge and Carmel Canyon) are directed north- and barotropic-to-baroclinic energy conversion are cal- east, while the appearance of depth-integrated energy culated from the harmonic analysis output rather than fluxes on Sur Slope and at the head of Carmel Canyon is using the depth-integrated energy equations derived by consistent with areas of high (> 0.1 W m−2) barotropic- Carter et al. (2008). Only a ∼ 1% difference between to-baroclinic energy conversion. This is in agreement quantities calculated from the depth-integrated energy with the inferences of internal tide generation from baro- equations and those calculated from the harmonic con- clinic energy flux divergence in the Monterey Bay region

5 HALL AND CARTER: INTERNAL TIDES IN MSC

(a) Baroclinic energy flux (b) Baroclinic energy conversion

37oN

50’ A

40’

30’

Sur 20’ Ridge Sur Platform

10’

Sur Canyon 30’ 20’ 10’ 122oW 50’ 30’ 20’ 10’ 122oW 50’

0 1 2 3 4 −0.5 −0.25 0 0.25 0.5 (kW m−1) (W m−2)

Figure 2: (a) Depth-integrated baroclinic M2 energy flux in the MSC region. Vectors are plotted every 10 grid points (2.5 km) in each direction. The underlying color is the energy flux magnitude. The blue line is the location of across-canyon section A shown in Fig. 3. (b) Barotropic-to-baroclinic M2 energy conversion. Positive values are sources of baroclinic energy. The bathymetry contour interval is 200 m. by Jachec et al. (2006). Other, more remote, internal Platform, the lower slope west of Sur Ridge, and the tide generation sites are considered in Section 6. southern part of the slope (including the northern rim of Internal tide generation on Sur Slope can be roughly Sur Canyon). The internal tide generated on the north- divided into four areas where barotropic-to-baroclinic ern part of the slope and along the northern flank of Sur energy conversion is high, the northern part of the slope Platform propagates north, into MSC. The internal tide near Monterey and Carmel Canyons, the flanks of Sur generated on the southern part of the slope and along

6 HALL AND CARTER: INTERNAL TIDES IN MSC

0 15 A (56 km along thalweg) 10 0.5 5 ) −2 1 0 Northern Southern (W m

Depth (km ) shelf shelf −5 1.5 −10 −15 10 8 6 4 2 0 −2 −4 −6 −8 Distance from thalweg (km) 0 B (45 km) C (38 km)

0.5

1 Depth (km )

0 D (31 km) E (24 km)

0.5 Depth (km )

0 F (20 km) G (12 km)

0.5 Depth (km ) 3 2 1 0 −1 −2 −3 3 2 1 0 −1 −2 −3 Distance from thalweg (km) Distance from thalweg (km)

Figure 3: Along-canyon baroclinic M2 energy flux at across-canyon sections A to G. Positive values are towards the head of the canyon. The horizontal axes are across-canyon distance from the thalweg, positive towards the shelf north of the canyon. All the sections are shown looking up-canyon and have the same vertical scale, sections B to G also have the same horizontal scale. The dashed line is the location of the ‘dogleg’ in section A. the southern flank of Sur Platform appears to mostly The internal tide does not propagate shoreward along propagate southeast, along the shelf slope. Finally, the the whole length of MSC. Over the lower reaches of internal tide generated on the lower slope appears to at the canyon, to the northwest of the Sur Slope (about least partly propagate offshore. 122◦ 200W, 36◦ 350N), the depth-integrated energy flux

7 HALL AND CARTER: INTERNAL TIDES IN MSC is down-canyon (Fig. 2a). The switch to up-canyon en- compensated for by work done on the barotropic tide ergy flux occurs at approximately 80 km along the thal- by the baroclinic tide in adjacent areas of negative con- weg, between Smooth Ridge and Sur Slope, as baroclinic version. Negative barotropic-to-baroclinic energy con- energy enters from the south. At the mouth of the up- version results from phase differences between remote per canyon, depth-integrated energy fluxes increase up and locally generated internal tides, so is evidence for to 1.5 kW m−1. Across-canyon section A, located across multiple generation sites (Zilberman et al., 2009). the mouth, shows the up-canyon energy flux is focused There are some trends in the spatial distribution of en- near the bottom, over the right hand slope when look- ergy conversion; at the ridges inside the meanders, pos- ing up-canyon (Fig. 3). This core of baroclinic energy itive conversion tends to occur on the up-canyon flank, enters the upper canyon from the southwest, apparently while negative conversion tends to occur on the down- originating where Carmel Canyon merges with MSC. canyon flank. Kunze et al. (2002) observed a decrease in depth-integrated energy flux at Monterey Meander and suggested local internal tide generation by scattering of 4 Internal tide propagation the barotropic tide from canyon topography could ac- through MSC count for the increase in energy flux further up-canyon. Although positive energy conversion on the up-canyon In the upper reaches of MSC, the depth-integrated baro- flank of the ridge inside Monterey Meander is consistent with this argument, there is no noticeable decrease clinic M2 energy fluxes are almost entirely up-canyon and largest near the canyon axis (Fig. 4a). Maximum in depth-integrated energy flux around the meander. At energy fluxes (> 4 kW m−1) occur around San Gregorio the apex of Monterey Meander, Kunze et al. (2002) only and Monterey Meanders and are in good agreement with measured the energy flux at a single location, so the de- previous observations of the internal tide in the canyon crease is more likely a result of under-sampling the band by Kunze et al. (2002) (see Carter, 2010). Petruncio of maximum energy. et al. (1998) assumed the internal tide could not navi- gate San Gregorio Meander without significant dissipa- 4.1 Tidal ellipses tion or scattering. However, the modeled internal tide has no difficulty propagating around this meander or the Horizontal baroclinic M2 tidal ellipses along the canyon other sharp meanders in the upper canyon. The spatial thalweg, and the thalwegs orientation, are shown in distribution of depth-integrated energy flux in MSC is Fig. 5. The down-canyon direction of the thalweg is in agreement with Jachec et al. (2006) and qualitatively primarily towards the west, but varies in its north-south similar to Wang et al. (2009), although the magnitude orientation. However, at a few locations the thalweg of the energy fluxes in the latter study are smaller than turns back on itself so that the down-canyon direction is calculated here by roughly a factor of two. towards the southeast, for example, between San Grego- The narrow band of maximum energy follows a less rio and Monterey Meanders and at the apex of Goose- meandering path through the canyon than the thal- neck Meander (Fig. 4a and 5a). weg. This is particularly evident at Gooseneck Meander, Baroclinic tidal ellipses every 5 km along the thal- where depth-integrated energy flux vectors are directed weg are shown in Fig. 5b. Horizontal baroclinic velocity over the ridge inside the meander rather than around amplitudes and phases are vertically averaged in 100-m it. Similarly, at approximately 8 km along the thal- bins before the ellipse parameters are calculated. Down- weg, the majority of baroclinic energy enters Butterfly canyon of 65 km, the tidal ellipses display a range of ec- Bowl rather than continuing towards the canyon head. centricities (semi-major axis/semi-minor axis) and ori- In contrast, around the larger San Gregorio and Mon- entations. There is however, a trend of increasing tidal terey Meanders, depth-integrated energy flux vectors are amplitude towards the surface and bottom, consistent orientated along isobaths. This suggests that although with dominance by low-mode internal waves. The el- the internal tide is topographically steered around the lipses with large amplitudes also tend to have low eccen- large canyon meanders, it is not effected by smaller-scale tricities with many close to ω/f = 1.6, the theoretical bathymetric features. eccentricity for a propagating internal wave. Barotropic-to-baroclinic energy conversion in the up- At 65 km the ellipses in the bottom 500 m of the per canyon is positive and negative in roughly equal pro- water column have eccentricities < 0.2 and are orien- portions (Fig. 4b). This implies local internal tide gener- tated NE-SW, the same direction as the thalweg. This ation in areas of positive conversion is at least partially agreement between semi-major axis and thalweg orien-

8 HALL AND CARTER: INTERNAL TIDES IN MSC

52’ (a) 51’ 0 1 2 3 4 (kW m−1) 50’ Butterfly Bowl 49’

48’ 15 D 10 47’ 35 5 G 25 20 46’ C 30 E F 45’ 40

44’ (b) 1

43’ 45 0.5 )

42’ −2 B 0

50 (W m 41’ −0.5 40’ −1 39’ 4’ 2’ 122oW 58’ 56’ 54’ 52’ 50’ 48’

Figure 4: (a) Depth-integrated baroclinic M2 energy ﬂux in the upper reaches of MSC. Vectors are plotted every 2 grid points (500 m) in each direction. The underlying color is the energy ﬂux magnitude. The black lines are the locations of the sections used for the canyon energy budget, the blue lines are also the locations of across-canyon sections B to G shown in Fig. 3. The line along the axis of the canyon is the thalweg, marked with a cross at 5 km intervals. (b) Barotropic-to-baroclinic M2 energy conversion. Positive values are sources of baroclinic energy. The bathymetry contour interval is 100 m. tation suggests topographic steering of the internal tide direction as the thalweg. This increase in tidal ellipse also occurs down-canyon of San Gregorio Meander. By eccentricity and alignment along the canyon axis has 50 km the near-bottom ellipses are almost rectilinear previously been observed by Petruncio et al. (1998) and (i.e. the semi-minor axis is negligible compared to the Xu and Noble (2009). semi-major axis) and consistently orientated in the same As well as becoming increasingly rectilinear, the semi-

9 HALL AND CARTER: INTERNAL TIDES IN MSC

E (a) SM MM GM N W S E 0 (b)

0.5

1.5 Depth (km )

2 N

E 2.5 0.12 m s-1 0.2 m s-1 3 100 90 80 70 60 50 40 30 20 10 0 Distance along thalweg (km)

Figure 5: (a) Down-canyon direction of the thalweg with distance from Moss Landing. The shaded areas are the locations of the meanders, SM is San Gregorio Meander, MM is Monterey Meander, and GM is Gooseneck Meander. (b) Horizontal baroclinic M2 tidal ellipses in 100-m vertical bins every 5 km along the thalweg. The ellipse in the key has an eccentricity of ω/f = 1.6, the theoretical eccentricity for a propagating internal wave. The crosses in (a) show the thalwegs orientation at the location of the tidal ellipses shown in (b). major axes of the near-bottom tidal ellipses increase to intensification of the along-canyon tidal flow. Bottom- > 0.15 m s−1 up-canyon of 65 km, indicating bottom- intensified along-canyon tidal currents have previously

10 HALL AND CARTER: INTERNAL TIDES IN MSC been observed at San Gregorio Meander by Xu et al. canyon head where weak down-canyon energy fluxes oc- (2002) and near the canyon head by Key (1999). Up- cur (Fig. 6b). The up-canyon energy flux is bottom- canyon of 30 km, the along-canyon tidal flow is intensi- intensificatied between 55 km and 25 km, suggesting to- fied at all depths. pographic focusing occurs. Maximum energy fluxes at the seabed are > 15 W m−2. Around the 24 km and 12 km marks there are weak down-canyon energy fluxes 4.2 3-D structure near the bottom. These are actual fluxes of energy to- The three-dimensional structure of the internal tide is wards the canyon mouth (rather than artifacts of the shown using six sections across the upper canyon (B to meandering thalweg) and are also apparent in across- G, Fig. 3) and one section along the thalweg (Fig. 6). canyon sections E and G (Fig. 3). The down-canyon For the across-canyon sections, the along-canyon com- energy fluxes may result from supercritical reflection of ponent of the baroclinic energy flux is shown. This is the up-canyon propagating internal tide from the steep simply defined as the energy flux normal to the section. canyon walls. Near-bottom, down-canyon energy fluxes Distance across the canyon is referenced to the thal- were observed by Kunze et al. (2002) up-canyon of Mon- weg; positive distances are towards the shelf north of terey Meander. the canyon (i.e. on the left when looking up canyon). The energy flux across the canyon is spatially inco- For the along-thalweg section, both the along-canyon herent and mostly smaller than the along-canyon en- and across-canyon components of the baroclinic energy ergy flux (Fig. 6c). The small-scale spatial structure is flux are shown. These are defined as the energy flux primarily due to the meandering nature of the thalweg tangential and normal to the local orientation of the relative to the band of maximum energy. thalweg. Distance along the canyon is referenced to the The bottom-intensification of up-canyon energy flux is Moss Landing. a result of correlation between large velocity and pres- The along-thalweg section is noisier than the across- sure perturbations. The real component [A cos(φ)] of canyon sections because of the meandering nature of along-canyon velocity perturbation is mostly positive in the thalweg when compared to the smoother path fol- the upper half of the water column and negative in the lowed by the band of maximum energy. For example, lower half (Fig. 6d). Up-canyon of 65 km, the real com- the depth-integrated along-canyon energy flux along the ponent of pressure perturbation is also positive in the thalweg (Fig. 6a) features several down-canyon energy upper half of the water column and negative in the lower fluxes in the upper 20 km of the canyon. These occur at half (Fig. 6e). Between approximately 30 km and 10 km locations where the thalweg turns back on itself (such the real component of the along-canyon velocity pertur- as at the apex Gooseneck Meader) so the down-canyon bation is up-canyon near the bottom, explaining for the direction varies by > 90◦ depending on whether it is de- near-bottom, down-canyon energy fluxes. fined as the orientation of the thalweg or the orientation of the band of maximum energy. The down-canyon en- 4.3 Kinetic and potential energy ergy fluxes are therefore an artifact of the ambiguous definition of ‘down-canyon’, rather than actual fluxes of Baroclinic horizontal kinetic energy density is calculated 1 2 2 energy towards the canyon mouth. HKE = 4 ρ(uA +vA) where uA and vA are perpendicular The depth-integrated along-canyon energy flux in- horizontal velocity amplitudes. Depth-integrated HKE creases from near-zero at 80 km along the thalweg to is maximum (∼ 4 kJ m−2) around San Gregorio and > 4 kW m−1 between San Gregorio and Monterey Mean- Monterey Meanders (Fig. 7a) and closely matches the ders (Fig. 6a). It then decreases to < 2 kW m−1 between spatial distribution of depth-integrated baroclinic en- Monterey and Gooseneck Meanders and to near-zero at ergy flux in the canyon (Fig. 2a). HKE is also elevated 4 km. The minimum near the apex of Monterey Mean- in Carmel Canyon. The spatial distribution of HKE is der is not an actual decrease in up-canyon energy flux, similar to that shown by Jachec (2007), but the absolute but is due to the band of maximum energy deviating values calculated here are larger by roughly a factor of from the path of the thalweg (see Fig. 4). Therefore, at two. this location along the canyon, the energy flux over the The amplitude of vertical displacement by the inter- thalweg does not fully represent of the band of maximum nal tide (ξA) is inferred from vertical velocity amplitude energy. and has a maximum (∼ 250 m) around San Gregorio The along-canyon internal tide energy flux is up- and Monterey Meanders (not shown). Further towards canyon or near-zero at all depths, except near the the head of MSC displacement amplitudes are smaller,

11 HALL AND CARTER: INTERNAL TIDES IN MSC

(a) Depth integrated along-canyon energy flux ) GM −1 4 2

(kW m 0 SM MM (b) Along-canyon energy flux 0 15 G 1 E F 10 C D B

5 )

Depth (km ) 2 A −2 (c) Across-canyon energy flux 0 0 (W m −5 1 −10

Depth (km ) 2 −15 (d) Real component of along-canyon velocity perturbation 0 0.2 1 0.1

Depth (km ) 2 ),(Pa)

(e) Real component of pressure perturbation 0 −1 0 (m s 1 −0.1

−0.2

Depth (km ) 2

80 70 60 50 40 30 20 10 0 Distance along thalweg (km)

Figure 6: (a) Depth-integrated along-canyon baroclinic M2 energy ﬂux with distance along the thalweg. The shaded areas are the locations of the meanders, SM is San Gregorio Meander, MM is Monterey Meander, and GM is Gooseneck Meander. (b) Along-canyon and (c) across-canyon baroclinic M2 energy ﬂux with distance along the thalweg. Positive along-canyon values are towards the head of the canyon. Positive across-canyon values are to the left when looking up-canyon. The black lines are the locations of across-canyon sections A to G shown in Fig. 3. (d) Real component [A cos(φ)] of the along-canyon velocity perturbation. (e) Real component of the pressure perturbation. of order 50 m, and in general agreement with previous (Broenkow and McKain, 1972; Petruncio et al., 1998; observations of the internal tide near the canyon head Carter and Gregg, 2002). The vertical displacement

12 HALL AND CARTER: INTERNAL TIDES IN MSC

et al., 2008; Kang and Fringer, 2010). Depth-integrated (a) HKE APE is intensified over a larger area of the canyon than 50’ HKE (Fig. 7b). Elevated APE occurs all the way to the head of MSC and in Carmel Canyon; maximum values are > 5 kJ m−2. 46’ In the upper reaches of MSC, HKE/APE is smaller than the theoretical value for an M2 internal tide, (ω2 + f 2)/(ω2 − f 2) = 2.2 (Gill, 1982). This is ex- 42’ plained by Petruncio et al. (1998) as an effect of the canyon topography constraining across-canyon motion; if the motion is considered irrotational, the theoreti- 38’ cal HKE/APE value is one. However, in 81% of the upper canyon by area, the energy ratio less than one 34’ (i.e. APE > HKE), inconsistent with free hydrostatic internal waves. Kunze et al. (2002) argue that the excess APE is due to vertical isopycnal displacements in- 30’ duced by barotropic tidal flow over the sloping bottom. They show that removing the barotropic contribution (b) APE increases the energy ratio to near the theoretical value. 50’ Following Kunze et al. (2002), we calculate the barotropic contribution to vertical displacement (ξbt) as a linear least-squares fit to ξ(z) with zero at the sur- 46’ face. ξbt is then subtracted from ξ before recalculating APE. This decreases depth-integrated APE throughout 42’ the upper-canyon (not shown) and reduces the fractional area in which APE > HKE to 33%. The mean energy ratio in the upper canyon is increased from 0.7 to 2.0, 38’ close to the theoretical value. An alternate explanation for the areas of excess APE in the canyon is the existence of partly standing internal 34’ waves. A standing wave (the superposition of two free waves, with the same frequency and amplitude, propagating in opposite directions) was observed in MSC 30’ by Petruncio et al. (1998) during October 1994, while 12’ 6’ 122oW 54’ 48’ in April of that year the internal tide was observed to propagate up-canyon. They attributed the difference to changes in stratification. Martini et al. (2007) showed 0 1 2 3 4 5 that for partially standing waves (where the two free (kJ m−2) waves have different amplitudes) HKE/APE oscillates between zero and infinity with half the wavelength of

Figure 7: (a) Depth-integrated baroclinic M2 horizontal the incident waves. It is possible that partially stand- kinetic energy in MSC. (b) Depth-integrated baroclinic ing waves occur in the canyon, from superposition of the M2 available potential energy. The bathymetry contour up-canyon propagating internal tide and reflected waves interval is 200 m. from the supercritical canyon walls. Indeed, down- canyon energy fluxes are apparent near the bottom in across-canyon sections E and G. However, the meander- maximum occurs in the lower third of the water column, ing canyon topography complicates the diagnosis and no consistent with bottom-intensification of the energy flux. coherent pattern in HKE/APE is observed in this study. The associated available potential energy density is cal- 1 2 2 culated from linear theory, APE = 4 ρN ξA, a good approximation if stratification is slowly varying (Carter

13 HALL AND CARTER: INTERNAL TIDES IN MSC

10 2 between them, depth and horizontally integrated along SM MM GM (a) the section. In each region, baroclinic energy flux diver- 8 1.5 gence (net energy flux out of the region), net barotropic- to-baroclinic energy conversion, and baroclinic energy 6 B 1 dissipation (defined as net energy conversion minus en- 4 C ergy flux divergence) are calculated. (MW) D F 2 G 0.5 Hotchkiss and Wunsch (1982) note that for the case E of internal waves propagating along the axis of a canyon 0 0 towards its head, energy density should increase, not −2 only because of the depth change, but because the walls −0.5 tend to converge. In the absence of dissipation, the energy density increase should therefore be inversely (b) proportional to the decrease in canyon cross-sectional 1 area. This effect is accounted for in the area (depth and along section) integrals of along-canyon energy flux at the across-canyon sections. If there is no internal tide 0 generation or dissipation in the canyon, and no energy (MW) flux across the canyon rim, net energy flux will be con- stant along the canyon. −1 Net along-canyon energy flux at the mouth of the upper canyon (section A) is 9.0 MW. This accounts for 50 40 30 20 10 all energy entering the upper canyon from offshore, in- Distance along thalweg (km) cluding Sur Slope, Carmel Canyon, and Smooth Ridge. At the apex of San Gregorio Meander the along-canyon energy flux decreases to 7.0 MW and continues to de- Figure 8: (a) Net along-canyon baroclinic M2 energy flux with distance along the thalweg (black line, left crease almost monotonically to 1.1 MW at Gooseneck axis). Positive values are towards the head of the Meander (Fig. 8a). Up-canyon of Gooseneck Meander, canyon. Also shown is net energy flux across the 200 m the along-canyon energy flux remains around 1 MW. isobath and the ridges inside San Gregorio and Monterey The decrease in along-canyon energy flux between the Meanders (gray line, right axis). Positive values are out mouth and Gooseneck Meanders implies either high lev- of the canyon (i.e. onto the shelf). The shaded areas are els of internal tide dissipation occur in the canyon, or the locations of the meanders, SM is San Gregorio Mean- a large fraction of the baroclinic energy escapes over der, MM is Monterey Meander, and GM is Gooseneck the canyon rim onto the shelf. The second explanation Meander. (b) Baroclinic energy flux divergence (solid is discounted because the depth-integrated energy flux −1 black line), net barotropic-to-baroclinic energy conver- across the 200 m isobath is small (order 10 W m along sion (dashed black line), and baroclinic energy dissipa- the majority of the canyon rim) compared to the along- −1 tion (net conversion minus energy flux divergence, gray canyon energy flux (order 1 kW m ). line) with distance along the thalweg. Net energy flux across the 200 m isobath sections and ridge sections inside San Gregorio and Monterey Mean- ders is shown by the gray line and right axis in Fig. 8a. The energy flux across the 200 m isobath between each 4.4 Canyon energy budget across-canyon section is typically < 25 kW, compared To better assess the flux of internal tide energy around with a 500 kW average decrease in along-canyon energy the meanders in the upper reaches, the canyon is divided flux between the sections. However, at two locations into 17 separate regions. These regions are bounded by the energy flux onto the shelf is substantial, Gooseneck 16 across-canyon sections, 17 sections along the 200 m Meander (18 km) where there is a 0.2 MW energy flux isobath (the approximate depth of the shelf break), 4 over the southern rim, and near the canyon head (7 km) sections along the ridges inside San Gregorio and Mon- where there is an 0.9 MW flux over the northern rim, terey Meanders, and one section across the mouth of So- mostly into Butterfly Bowl. The energy flux onto the quel Canyon (Fig. 4). Net baroclinic energy flux between shelf here, and at other locations along the shelf break, adjacent regions is the energy flux normal to the section is examined in Section 5. The energy fluxes across the

14 HALL AND CARTER: INTERNAL TIDES IN MSC ridges inside the meanders are large compared to the 4.5 Rotational effects typical energy flux across the 200 m isobath, but small compared to the along-canyon energy flux. Inside Mon- Across the mouth of the upper canyon, the along-canyon terey meander the across-ridge energy flux is 0.4 MW, baroclinic energy flux is asymmetrically distributed. apparent as a maximum at 41 km and a minimum at The up-canyon energy flux is focused over the right hand 30 km. The across-ridge energy flux inside San Gre- slope when looking up-canyon (Fig. 3A). This asymme- gorio Meander is 0.5 MW, apparent as a minimum at try is also apparent, but to a lesser extent, further to- 39 km. wards the canyon head at across-canyon sections E to As expected from the decrease in net along-canyon en- G. Petruncio et al. (2002) find a similar energy density ergy flux towards the head canyon head, baroclinic en- asymmetry with idealized canyon topography and sug- ergy flux divergence is negative (i.e. convergent) along gest it is due to rotational effects. the majority of the upper canyon (Fig. 8b). The two ex- To test this hypothesis, the model is re-run with- ceptions are Monterey and Gooseneck Meanders, where out rotation. Interestingly, the across-canyon distri- there are small positive energy flux divergences. Net en- bution of the along-canyon energy flux is not signif- ergy conversion alternates between positive and negative icantly altered in the non-rotating case (not shown). values along the canyon, implying that there are areas of At section A, the up-canyon energy flux remains fo- local internal tide generation (positive values) as well as cused over the right hand slope when looking up-canyon. areas where work is done on the barotropic tide by the However, the amount of internal tide energy entering baroclinic tide (negative values). The largest positive the upper canyon is reduced in the non-rotating case values occur at Monterey Meander, while the largest (Fig. 9). The net along-canyon energy flux at section A negative values occur at Gooseneck Meander and be- is only 6.9 MW, a decrease of 23% relative to the orig- tween San Gregorio and Monterey Meanders. inal rotating case. In the upper reaches of the canyon, There is not, however, any consistent evidence for sig- depth-integrated energy fluxes are decreased by up to −1 nificant dissipation and regeneration of the internal tide 2 kW m , with the largest reductions occurring around around Monterey Meander, as suggested by Kunze et al. San Gregorio Meander. This suggests that although ro- (2002). The small increase in along-canyon energy flux tation may aid the funneling of internal tide energy into on the up-canyon side of Monterey Meander is consistent canyons, within meandering canyons such as MSC, topo- with the band of positive energy conversion on the up- graphic steering is the more important control on across- canyon flank of the ridge inside the meander, but is small canyon energy distribution. compared to the large decrease in energy flux between San Gregorio and Monterey Meanders. The decrease in depth-integrated energy flux at Monterey Meander ob- 5 Internal tide propagation onto served by Kunze et al. (2002) is more likely a result of the shelf under-sampling the band of maximum energy. Total baroclinic energy dissipation in the upper Depth-integrated baroclinic M2 energy fluxes on the canyon (a summation of all 17 regions between section A continental shelf are small compared to those in MSC, and the canyon head), inferred from only baroclinic en- typically < 10 W m−1. However, near the head of the ergy flux divergence, is 7.6 MW. This is comparable to canyon and along the northern edge of Sur Platform en- the 8.3 MW net dissipation in the canyon calculated by ergy fluxes > 250 W m−1 occur (Fig. 10a). These energy Jachec et al. (2006). However, the estimate of total baro- fluxes are mostly onshore or along the shelf break. clinic dissipation should also include any barotropic-to- The large energy fluxes near the canyon head are the baroclinc energy conversion that occurs in the upper end of the band of maximum energy that follows the canyon. Net energy conversion in the upper canyon is canyon axis. The majority of the baroclinic energy en- positive, but only 50 kW. It therefore has little effect ters the Butterfly Bowl, but some continues towards the on total baroclinic energy dissipation. Dividing total canyon head. Baroclinic energy also escapes over the barotropic energy dissipation by the area of the upper southern rim at Gooserneck Meander. At these three canyon (225 km2) yields a depth-integrated dissipation −2 locations the internal tide is almost entirely dissipated rate of 0.03 W m . by the 100 m isobath. Either side of Smooth Ridge there are smaller, ∼ 50 W m−1 energy fluxes, where baroclinic energy is funneled up Cabrillo Canyon and Horseshoe Scarp and

15 HALL AND CARTER: INTERNAL TIDES IN MSC

(a) Non-rotating (b) Rotating (c) Magnitude difference

54’

48’

42’

36’

30’ 8’ 4’ 122oW 56’ 52’ 48’ 8’ 4’ 122oW 56’ 52’ 48’ 8’ 4’ 122oW 56’ 52’ 48’

0 1 2 3 4 −2 −1 0 1 (kW m−1) (kW m−1)

Figure 9: Depth-integrated baroclinic M2 energy flux from (a) the non-rotating model run and (b) the rotating model run. Vectors are plotted every 5 grid points (1.25 km) in each direction. The underlying color is the energy flux magnitude. (c) Energy flux magnitude difference between the non-rotating and rotating model runs (non-rotating minus rotating). The bathymetry contour interval is 200 m. onto the shelf. In contrast, the internal tide on the Sur flux off of the shelf between Gooseneck Meander and Platform is most likely generated locally, on the flanks of the canyon head. At the head of Carmel Canyon and the platform where barotropic-to-baroclinic energy con- along the northern edge of Sur Platform (between −80 version is high. and −35 km) energy fluxes are both onto and off of the The baroclinic energy flux across the shelf break is shelf, including a 300 W m−1 energy flux into Carmel taken to be the energy flux normal to the 200 m isobath Canyon (−57 km) from Sur Platform to the south. (Fig. 10b). Similar to the along-thalweg section, the en- Levels of mixing from microstructure measurements ergy flux across the 200 m isobath is noisy because of the on Smooth Ridge and at the head of MSC are described winding nature of the isobath, especially at the head of by Lien and Gregg (2001) and Carter and Gregg (2002). MSC and Carmel Canyon. The depth-integrated energy The microstructure profiles on the shelf from these stud- flux across the 200 m isobath is of order 10 W m−1 along ies are reanalyzed by Carter et al. (2005); the locations the majority of the shelf break, but increases by over an of these profiles are shown in Fig. 10a and are clustered order of magnitude near the head of MSC where inter- in four groups. One group of profiles (those from Lien nal tide energy escapes onto the shelf. Maximum energy and Gregg, 2001, denoted ‘Fan’ in Carter et al., 2005) flux onto the shelf, 500 W m−1, occurs in Butterfly Bowl are at the top of the Smooth Ridge, between Cabrillo (2 km along the shelf break). On the southern rim of Canyon and Horseshoe Scarp. Two groups (‘North’ and MSC there is a 200 W m−1 energy flux onto the shelf ‘South’) are on the rim of MSC, up-canyon of Gooseneck at Gooseneck Meander (−6 km) and a smaller energy Meander. The final group (‘Test’) are on the shelf north

16 HALL AND CARTER: INTERNAL TIDES IN MSC

(a) (b) 60 60 Fan North 40 50’ 20

40 Test 0 20 Cabrillo –20 South Canyon 0 40’ Horseshoe Scarp −20 –40

30’ –60 −40 Distance along shelf break (km ) −60 –80 20’ −80

20’ 10’ 122oW 50’ −500 −250 0 250 500 (W m−1) 0 50 100 150 200 250 (W m−1)

Figure 10: (a) Depth-integrated baroclinic M2 energy flux on the continental shelf. Vectors are plotted every 5 grid points (1.25 km) in each direction where the water depth is less than 200 m. The underlying color is the energy flux magnitude. The bathymetry contour interval is 50 m on the shelf and 200 m in the canyon. The black line is the 200 m isobath, the approximate depth of the shelf break. Distance along the 200 m isobath from the head of MSC is marked with a cross at 20 km intervals. The blue dots on the shelf are the locations of microstructure profiles used by Carter et al. (2005). (b) Depth-integrated across-slope baroclinic M2 energy flux with distance along the 200 m isobath. Positive values are onto the shelf. of MSC, down-canyon of Gooseneck Meander. files are located close to areas where internal tide energy Carter et al. (2005) find no significant difference in escapes onto the shelf and is rapidly dissipated, resulting mean turbulent kinetic energy dissipation rate from the in elevated turbulent kinetic energy dissipation rates. In fan, north, and south profiles (∼ 5 × 10−8 W kg−1 for contrast, the test profiles are in an area where the baro- each group). However, mean dissipation rate from the clinic energy flux is negligible. Even higher dissipation test profiles is five times lower. They suggest the differ- rates may be expected in Butterfly Bowl and on Sur ence may result from the test profiles being made during Platform where the energy fluxes gradients are largest. neap tide or the presence of coastal upwelled water on the shelf. The model results presented here suggest an alternative explanation. The fan, north, and south pro-

17 HALL AND CARTER: INTERNAL TIDES IN MSC

features a band of maximum energy that follows a topo- 37oN graphically steered path around San Gregorio and Mon- terey Meanders and dissipates towards the canyon head 50’ (Fig. 12). However, the magnitude of the energy flux Davidson is smaller throughout the canyon; energy fluxes around 40’ Seamount Small San Gregorio and Monterey Meanders are reduced by up to 1 kW m−1. The decrease relative to the energy 30’ domain flux from the large domain run is around 20% throughout the upper canyon. Net along-canyon energy flux at 20’ the mouth of the upper canyon (section A) is 7.3 MW in the small domain run, 1.7 MW less than the 9.0 MW in 10’ the large domain run (19% relative decrease). In Carmel 36oN Canyon, depth-integrated energy fluxes are reduced by Guide ∼ 800 W m−1 (60%). 50’ Seamount The energy flux decrease in the canyons is not a sim- ple subtraction of internal tide energy generated outside 40’ the area common to both domains. The hydrostatic pressure perturbation due to internal waves (p0) af- 30’ 15’ 123oW 45’ 30’ 15’ 122oW fects barotropic-to-baroclinic energy conversion through equation (2). Therefore, any change to the internal Figure 11: Bathymetry of the large model domain. The wave field potentially feeds back on internal wave gen- contour interval is 200 m. The rectangle in the upper eration. Differences in energy conversion between the right corner is the small model domain. two domains may also result from adjustment of depth- averaged velocity (u). In this case however, reducing the size of the domain has a negligible effect on depth- 6 Remote internal tide genera- averaged currents inside the common area; differences in tion energy conversion (Fig. 13) are almost entirely the result of changes to the internal wave field. Barotropic-to- baroclinic energy conversion is decreased on the north- By comparing depth-integrated baroclinic M2 energy fluxes with the spatial distribution of barotropic-to- ern part of Sur Slope, in Carmel canyon, and along the flanks of Sur Platform. These are areas where the inter- baroclinic M2 energy conversion, we infer that most of the internal tide energy entering the upper reaches nal tides in MSC and Carmel Canyon are assumed to be of MSC is generated on Sur Slope and at the head of generated, which may explain the energy flux decrease Carmel Canyon. It is of interest however, to quanti- in the canyons. tatively assess how much of the internal tide energy in Net energy conversion in the common area is 56.7 MW MSC originates at more remote sites. To this end, the for the large domain run and 49.6 MW for the small model is run for a smaller domain, from 122◦ 390 5200W, domain run (Table 1), a decrease of 7.1 MW (13%). 35◦ 590 900N to 121◦ 440 800W, 37◦ 90 5000N, a subset of This is the result of a 16.7 MW decrease in positive con- the original large model domain (Fig. 11). The small do- version, mostly compensated by a 9.5 MW decrease in main excludes three remote areas of high barotropic-to- negative conversion. Integrating over the area of the up- baroclinic energy conversion that feature in the large do- per canyon only, net energy conversion actually increases main (see Fig. 12a of Carter, 2010); these are Davidson from 50 kW to 2.2 MW, but this is the result of a 3.2 MW and Guide Seamounts, and the corrugated shelf slope decrease in negative conversion (partially compensated northwest of MSC (about 122◦ 500W, 37◦ 00N). How- by a 0.9 MW decrease in positive conversion), rather ever, it retains the areas of high conversion on Sur Slope than an actual increase in internal tide generation. and the flanks of Sur Platform. The same initial tem- Although the 7.1 MW energy conversion decrease in perature and salinity profiles are used and the model the common area is more than enough to explain the re- duction in energy entering the upper canyon (1.7 MW), is again forced at the boundaries with M2 barotropic velocities from TPXO6.2. the direct influence of internal tides generated at remote Depth-integrated baroclinic energy flux in the upper sites cannot be ruled out. Unfortunately, the exact value reaches of MSC from the small domain model run still of the energy flux into the common area is unknown for

18 HALL AND CARTER: INTERNAL TIDES IN MSC

(a) Small domain (b) Large domain (c) Magnitude difference

37oN

50’

40’

30’

20’

10’

30’ 20’ 10’ 122oW 50’ 30’ 20’ 10’ 122oW 50’ 30’ 20’ 10’ 122oW 50’

0 1 2 3 4 −1 −0.5 0 0.5 −1 (kW m−1) (kW m )

Figure 12: Depth-integrated baroclinic M2 energy flux from (a) the small domain model run and (b) the large domain model run. Vectors are plotted every 10 grid points (2.5 km) in each direction. The underlying color is the energy flux magnitude. (c) Energy flux magnitude difference between the small domain and large domain model runs (small domain minus large domain). The bathymetry contour interval is 200 m.

Table 1: Net barotropic-to-baroclinic M2 energy conversion (MW) in the area common to both model domains and the area of the upper canyon, for the large domain and small domain model runs. Also included is total positive (Pos.) and total negative (Neg.) energy conversion.

Model run Common area Upper canyon Net Pos. Neg. Net Pos. Neg. Large domain 56.7 99.9 −43.2 < 0.1 8.9 −8.9 Small domain 49.6 83.2 −33.7 2.2 8.0 −5.7

the large domain run, because the incoming and outgo- as for the small domain run4. This yields an incoming internal tides cannot be separated (hu0p0i only gives ing energy flux of 4.5 MW. However, this assumption the net energy flux). An approximate value can be ar- rived at by assuming the outgoing energy flux is the same 4The incoming energy flux at the boundaries of the small domain (i.e. the boundaries of the common area) is zero because the forcing is only barotropic. The net energy flux is therefore equal to the outgoing energy flux.

19 HALL AND CARTER: INTERNAL TIDES IN MSC

Conversion difference is inferred by comparing depth integrated baroclinic M2 energy fluxes with the spatial distribution of barotropic- to-baroclinic M2 energy conversion. Most of the internal tide energy entering the upper reaches of the canyon is o generated to the south, on Sur Slope and at the head of 37 N Carmel Canyon. Positive energy conversion on the up- canyon flanks of the ridges inside the meanders, implies some local internal tide generation occurs in the canyon, but this is at least partially compensated by adjacent 50’ areas of negative conversion. In the upper reaches of the canyon, the internal tide is topographically steered around the large meanders. Depth-integrated energy fluxes are almost en- 40’ tirely up-canyon and largest near the canyon axis, up to 1.5 kW m−1 at the mouth of the upper canyon and increasing to over 4 kW m−1 around Monterey and San Gregorio Meanders. The narrow band of maximum en- 30’ ergy follows a less meandering path through the canyon than the thalweg. Near the apex of Monterey Meander, the band of maximum energy deviates from the path of the thalweg. The decrease in depth-integrated energy 20’ flux observed by Kunze et al. (2002) at this meander is most likely a result of under-sampling the band of maximum energy with a single energy flux measurement over the thalweg. 10’ The up-canyon energy flux is bottom-intensified between 55 km and 25 km (along the thalweg), suggesting topographic focusing occurs. The bottom-intensification is a result of correlation between large velocity and pressure perturbations. o 30’ 20’ 10’ 122 W 50’ Baroclinic M2 tidal ellipses in the upper canyon typically have eccentricities larger than ω/f = 1.6, the −0.2 −0.1 0 0.1 0.2 theoretical eccentricity for a propagating internal wave, −2 and are orientated in the same direction as the thalweg. (W m ) The ratio of horizontal kinetic energy to available potential energy is smaller than the theoretical value for Figure 13: Barotropic-to-baroclinic M energy conver- 2 an M internal tide (2.2) and, in the majority of the sion difference between the small domain model run and 2 upper canyon, less than one. The energy ratio can be the large domain model run (small domain minus large brought closer to the theoretical value if the barotropic domain). The bathymetry contour interval is 200 m. contribution to vertical displacement is first removed. Net along-canyon energy flux decreases almost mono- is unlikely to be strictly valid, due to the pressure per- tonically from 9 MW the mouth of the upper canyon turbation feedback between baroclinic energy flux and to 1 MW at Gooseneck meander, implying high lev- barotropic-to-baroclinic energy conversion. els of internal tide dissipation occur. Net barotropic- to-baroclinic energy conversion in the upper canyon is positive, but only 50 kW. Total baroclinic energy dissi- 7 Summary pation is 7.6 MW, comparable to the value calculated by Jachec et al. (2006). A modified version of the Princeton Ocean Model is used Asymmetric distribution of the along-canyon energy flux across the mouth of the upper canyon is not an ef- to simulate the M2 internal tide in Monterey Submarine Canyon. The origin of internal tide energy in the canyon fect of rotation as it is also apparent in a non-rotating

20 HALL AND CARTER: INTERNAL TIDES IN MSC

model run. However, the net along-canyon energy flux Carter, G. S., 2010: Barotropic and baroclinic M2 at the mouth is decreased by 23% in the non-rotating tides in the Monterey Bay region. Journal of Phys- case. This suggests rotation aids the funneling of inter- ical Oceanography, 40, 1766–1783. nal tide energy into the canyon, but topographic steering is the more important control on across-canyon energy Carter, G. S. and M. C. Gregg, 2002: Intense, variable distribution. mixing near the head of Monterey Submarine Canyon. The depth-integrated energy flux across the 200 m Journal of Physical Oceanography, 32, 3145–3165. isobath is of order 10 W m−1 along the majority of the canyon rim, but increases by over an order of magnitude Carter, G. S., M. C. Gregg, and R.-C. Lien, 2005: In- near the canyon head where internal tide energy escapes ternal waves, solitary-like waves, and mixing on the onto the shelf. The internal tide is almost entirely dis- Monterey Bay shelf. Continental Shelf Research, 25, sipated by the 100 m isobath. 1499–1520. Reducing the size of the model domain to exclude remote areas of high barotropic-to-baroclinic energy con- Carter, G. S., M. C. Gregg, and M. A. Merrifield, 2006: version decreases the depth-integrated energy flux in the Flow and mixing around a small seamount on Kaena upper canyon by 20%. However, quantifying the role of Ridge, Hawaii. Journal of Physical Oceanography, 36, remote internal tide generation sites is complicated by 1036–1052. a pressure perturbation feedback between baroclinic en- Carter, G. S. and M. A. Merrifield, 2007: Open bound- ergy flux and barotropic-to-baroclinic energy conversion. ary conditions for regional tidal simulations. Ocean Care must therefore be taken when comparing internal Modelling, 18, 194–209. wave fields in numerical models with different domain sizes, because any change to the energy flux can affect Carter, G. S., et al., 2008: Energetics of M2 barotropic- internal wave generation in other areas of the domain. to-baroclinic tidal conversion at the Hawaiian Islands. Journal of Physical Oceanography, 38, 2205–2223. Acknowledgments. Helpful comments on the Egbert, G. D., 1997: Tidal data inversion: interpolation manuscript were provided by Mike Gregg, Matthew Al- and interference. Progress in Oceanography, 40, 53– ford, Ren-Chieh Lien, Danielle Wain, and three review- 80. ers. This work was funded by the National Science Foun- dation grant OCE0751226. Egbert, G. D. and S. Y. Erofeeva, 2002: Efficient inverse modeling of barotropic ocean tides. Journal of References Atmospheric and Oceanic Technology, 19, 183–204. Flather, R. A., 1976: A tidal model of the north-west Baines, P. G., 1982: On internal tide generation models. European continental shelf. Memoires de la Societe Deep-Sea Research, 29, 307–338. Royale des Sciences de Liege, 6, 141–164.

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