Turbulent Mixing and Exchange with Interior Waters on Sloping Boundaries

910 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 42

ERIC KUNZE Applied Physics Laboratory, University of Washington, Seattle, Washington

CHRIS MACKAY North Saanich, British Columbia, Canada

ERIKA E. MCPHEE-SHAW AND KATIE MORRICE Moss Landing Marine Laboratories, San Jose State University, Moss Landing, California

JAMES B. GIRTON AND SAMANTHA R. TERKER Applied Physics Laboratory, University of Washington, Seattle, Washington

(Manuscript received 21 April 2011, in ﬁnal form 14 November 2011)

ABSTRACT

Microstructure measurements along the axes of Monterey and Soquel Submarine Canyons reveal 200– 300-m-thick well-stratiﬁed turbulent near-bottom layers with average turbulent kinetic energy dissipation rates h«i 5 4 3 1028 Wkg21 and eddy diffusivities K 5 16 3 1024 m2 s21 (assuming mixing efﬁciency g 5 0.2) to at least thalweg depths of 1200 m. Turbulent dissipation rates are an order of magnitude lower in overlying waters, whereas buoyancy frequencies are only 25% higher. Well-mixed bottom boundary layer thicknesses

hN are an order of magnitude thinner than the stratified turbulent layer (hN h«). Because well-stratified turbulent layers are commonly observed above slopes, arguments that mixing efficiency should be reduced on sloping boundaries do not hold in cases of energetic internal-wave generation or interaction with topography. An advective–diffusive balance is used to infer velocities and transports, predicting horizontal upslope flows of 10–50 m day21. Extrapolating this estimate globally suggests that canyon turbulence may contribute 2–3 times as much diapycnal transport to the World Ocean as interior mixing. The upcanyon turbulence-driven transports are not uniform, and the resulting upslope convergences will drive exchange between the turbulent layer and more quiescent interior. Predicted density surfaces of detrainment and entrainment are consistent with observed isopycnals of intermediate nepheloid and clear layers. These data demonstrate that turbulent mixing dynamics on sloping topography are fundamentally 2D or 3D in the ocean, so they cannot be accu- rately described by 1D models.

1. Introduction 2004b; Koch-Larrouy et al. 2007; Jochum 2009), air–sea interactions (Jochum 2009), abyssal ventilation, and Diapycnal mixing is a key component to the large- the Southern Hemisphere westerlies (Friedrich et al. scale ocean thermohaline overturning circulation (Saenko 2011) all depend, not only on the average mixing, but 2006; Kuhlbrodt et al. 2007; Jayne 2009). Numerical sim- also on its vertical and horizontal distributions. Direct ulations reveal that the deep overturning cell and abyssal microstructure and inferred diffusivity estimates are circulation (Samelson 1998; Hasumi and Suginohara sparse but ﬁnd turbulent diffusivities to be highly het- 1999; Huang and Jin 2002; Saenko and Merryﬁeld 2005; erogeneous and intermittent. Diffusivities are weak Katsman 2006), water-mass properties (Simmons et al. O(1025 m2 s21) in most of the interior and over abyssal plains (Toole et al. 1994; Kunze and Sanford 1996), while they can be orders of magnitude higher over Corresponding author address: Eric Kunze, Applied Physics Lab- oratory, University of Washington, 1013 NE 40th St., Box 355640, rough topography (Polzin et al. 1997; Ledwell et al. Seattle, WA 98105-6698. 2000; St. Laurent et al. 2001; Toole et al. 1997; Naveira E-mail: [email protected] Garabato et al. 2004; Kunze et al. 2006; Sto¨ ber et al.

DOI: 10.1175/JPO-D-11-075.1

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2008). Even over sloping topography, turbulence can exchange of fluid between the bottom boundary layer be extremely variable (Moum et al. 2002; Carter et al. (BBL) and stratified interior. 2005; Nash et al. 2007; Klymak et al. 2006). Strong mixing However, these arguments assume the bottom slope at a few locales, mediated by rough topography, will extends to infinity; that is, uniform mixing along the impact the abyssal basin-scale circulation (McDougall slope induces uniform flow parallel to the bottom. In 1989) and provide narrow pathways of exchange between a finite body of water, mixing necessarily raises the deep and shallow water (Kunze et al. 2002, 2006), im- available potential energy of the fluid (Condie 1999) plying shorter local exchange times than bulk budget and, for a steady state, there has to be exchange with inferences. the interior at some depth. Moreover, ocean slopes, The energy for mixing of the stratified ocean interior topographic roughness (Goff and Jordan 1988), along- comes from tides (Munk and Wunsch 1998; Egbert and isobath flows, stratification, internal-wave forcing, and Ray 2003), wind-generated internal waves (Wunsch and near-bottom turbulence are all nonuniform (Nash et al. Ferrari 2004), and abyssal subinertial currents (Weatherly 2004, 2007). Resulting 2D and 3D convergences and and Martin 1978; Bryden and Nurser 2003; Nikurashin divergences of upslope turbulence-driven transports will and Ferrari 2010a,b). The bulk of the internal-wave en- drive exchanges between the turbulent near-bottom ergy flux appears to radiate away from its sources as low- boundary layer and the interior (Ivey 1987; Imberger and mode internal waves (Ray and Mitchum 1997; Morozov Ivey 1993; McPhee-Shaw and Kunze 2002; McPhee-Shaw 1995; Althaus et al. 2003; Lee et al. 2006; Simmons et al. 2006; Inall 2009). Armi (1978, 1979, 1980) provides in- 2004a; Alford 2003; Klymak et al. 2006; Zhao et al. 2010; controvertible if anecdotal evidence for exchange be- Dushaw et al. 2011), its fate as yet unknown. This implies tween boundary and interior waters, though his mean-flow that turbulent mixing parameterizations based only on generation argument was challenged on energetic local forcing will fall short. In a global assessment of grounds (Garrett 1979). Further evidence for such ex- internal-wave-driven turbulence in the ocean inferred change comes from observations of intermediate neph- from a finescale parameterization, Kunze et al. (2006) eloid layers (INLs) extending seaward from continental could not account for surface tide losses (Egbert and Ray margins. Studies have linked intermediate nepheloid 2003) by more than a factor of 3. In their data, the bulk of layers to topographic slopes critical at semidiurnal fre- the turbulent dissipation was associated with rough ba- quencies (Cacchione and Drake 1986; Dickson and thymetry, but such topography was only poorly covered, McCave 1986; Thorpe and White 1988; McPhee-Shaw with continental slopes particularly undersampled. Evi- et al. 2004; McPhee-Shaw 2006), presumed to be regions dence has been found for low-mode internal tides breaking associated with energetic turbulent shear. on continental slopes (Moum et al. 2002; Nash et al. 2004, Bottom boundary mixing has been found to dominate 2007; Martini et al. 2011; Klymak et al. 2011) and in shelf in smaller lakes (Goudsmit et al. 1997), where interior canyons (Carter and Gregg 2002; Gregg et al. 2011; Lee mixing is also weak (Wu¨ est et al. 1996; MacIntyre et al. et al. 2009). 1999; Lorke et al. 2008), and in small coastal basins One argument against near-boundary turbulence con- (Ledwell and Bratkovich 1995; Ledwell and Hickey tributing to global ocean mixing is that it only stirs 1995; Gregg and Kunze 1991). In fjords, where turbulent already-mixed waters (Phillips 1970; Phillips et al. 1986; mixing is largely associated with internal tides gener- Garrett 1990, 1991, 2001; Garrett et al. 1993) so will have ated at the sill, which then dissipate at sloping topog- low mixing efficiency. However, observations frequently raphy within the fjord, Stigebrandt and Aure (1989) find ;O(100 m)-thick well-stratified intensely turbulent inferred bulk mixing efficiencies of 0.04–0.11 (20%– layers overlying sloping topography (Toole et al. 1997; 50% of canonical 0.2 value). In a lake boundary layer Lueck and Mudge 1997; Eriksen 1998; Carter and Gregg dye-injection study, Wain and Rehmann (2010) found 2002; McPhee-Shaw et al. 2004; Nash et al. 2004, 2007; that 60% of the dye injected on the slope moved into Carter et al. 2006; Klymak et al. 2006). Based on a 1D the interior in under a day. Inall (2009) reported en- bottom-normal model, Garrett (1990) showed that slop- trainment of dye into the boundary layer in 2 days, ing near-bottom isopycnals will drive a two-layer coun- followed by detrainment along interior isopycnals terflow to reestablish the stratification, which would 2 days later, also finding net mixing efficiencies of restore higher mixing efficiency. Numerical simulations 0.044. However, boundary layers make up a much with variations only normal to the bottom (e.g., Ramsden larger fraction of isopycnal surface area in these basins 1995; Umlauf and Burchard 2011) have confirmed many than in the deep ocean. In general, the magnitudes of of these theoretical results. Such 1D bottom-normal boundary mixing’s contribution to the ocean total and boundary layer models disallow internal-wave radiation, exchange between bottom boundary and ocean interior reflection, and interaction. In addition, they permit no waters remain unquantified.

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In this paper, the effect of near-bottom turbulent amplitude, both changes conducive to breaking and tur- mixing on slopes will be further explored using fine- and bulence production. For oblique (nonnormal) incidence, microstructure profile time series of temperature, salin- supercritical slopes tend to turn internal waves toward ity, transmissivity, and turbulent dissipation rate collected shallower water like beaching surface waves rather than along the axes of Monterey and Soquel Submarine reflect them back into deeper water (Eriksen 1982; Thorpe Canyons in water depths 370–1200 m. These data will be 1999; Martini et al. 2011) so that more low-frequency used to establish a link between boundary mixing non- energy is transmitted into shallow water than for normal uniformity and along-isopycnal exchange with less tur- incidence. Typically, canyon walls are supercritical and bulent interior waters. Canyons are typified by extremely their thalwegs near critical for semidiurnal frequencies, so energetic internal tides (Shepard et al. 1974, 1979; internal tides are focused into intense near-bottom beams Gordon and Marshall 1976; Hotchkiss and Wunsch 1982; running parallel to the axes’ bottoms. The axis of Mon- Hunkins 1988; Matsuyama et al. 1993; Petruncio et al. terey Submarine Canyon is subcritical at the semidiurnal 1998; Lafuente et al. 1999; Kunze et al. 2002; Lee et al. frequency so will transmit internal tides toward its 2009) and turbulence (Lueck and Osborn 1985; Carter head. The axis of Soquel Canyon is supercritical so will and Gregg 2002; Lee et al. 2009). By blocking alongslope reflect internal tides back into the main canyon. Regional geostrophic flow (MacCready and Rhines 1991, 1993; numerical models (Jachec et al. 2006; Rosenfeld et al. Trowbridge and Lentz 1991), narrow canyons can also 2009; Wang et al. 2009; Carter 2010; Hall and Carter 2011) enhance upwelling and exchange with the interior suggest that the primary source for internal tides in (Freeland and Denman 1982; Hickey 1995; Allen 1996; Monterey Canyon is Sur Platform on the continental Allen and de Madron 2009). In section 2, pertinent pre- margin south of Monterey Bay. These internal waves vious work in Monterey Submarine Canyon is reviewed. radiate north before being funneled into the canyon by The relevant fine- and microstructure measurements are topographic interactions. described in section 3. Section 4 shows that turbulent As would be expected with elevated internal-wave boundary layers on the sloping axis are well stratified and levels, intense turbulence with « ; O(1026 Wkg21) has much thicker than well-mixed bottom boundary layers. been reported in Monterey Canyon in the near-bottom The implications of these stratified turbulent bottom layers along the canyon axis (Lueck and Osborn 1985; layers for ocean mixing and their nonuniformity on ex- Carter and Gregg 2002). These turbulence levels are change with the ocean interior are discussed in section 5. roughly a factor of 6 higher than predictions from a fi- Finally, in section 6, these results are summarized, and nescale parameterization based on weakly nonlinear their implications for mixing dynamics on slopes and internal-wave/wave interactions cascading energy toward possible global impacts are assessed. high wavenumber and breaking (Kunze et al. 2002; Carter and Gregg 2002). A more coherent wave field or interactions with topography appear to short circuit the cascade 2. Background: Internal tides and turbulence in by transforming incoming low modes directly into unstable Monterey Submarine Canyon waves. Kunze et al. reported the vertically integrated en- Previous measurements in Monterey Submarine Can- ergy flux diminishing from 5 kW m21 at the shelf break to yon (Petruncio et al. 1998; Kunze et al. 2002; Carter and 1kWm21 toward the head, consistent with observed tur- Gregg 2002) found its internal-wave field dominated by bulent kinetic energy dissipation rates « as a sink. semidiurnal internal tides, consistent with past measure- Although fine sediments drape the walls of the can- ments in numerous other canyons (Shepard et al. 1974, yon, the thalweg is characterized by sandy substrate to 1979), particularly in a 200–300-m-thick bottom-hugging depths of at least 1500 m, indicative of an energetic flow beam along the canyon axis. This is explicable from the environment (Paull et al. 2005; Xu and Noble 2009). The reflection behavior of internal waves by canyon topogra- processes responsible for transport of fine sediments phy (Cacchione and Wunsch 1974; Eriksen 1982; Hotchkiss differ from those transporting coarse sand (Paull et al. and Wunsch 1982). 2005). It is thought that fine mud and silts do not settle For 2D (normal) incidence, internal waves encoun- because of continuous erosion by internal tidal currents tering a bottom slope steeper than their characteristics (Xu and Noble 2009), whereas coarser material is de- (supercritical) will reflect horizontally as if from a verti- livered by episodic gravity currents (Xu et al. 2004). cal wall back into deeper water, while internal waves encountering a gentler (subcritical) slope will be reflected 3. Measurements upward as if from a flat bottom, preserving their horizontal direction of propagation. Internal waves encountering During 18–30 August 2008, spanning the spring tide near-critical slopes will reflect to higher wavenumber and of 21 August, 77 fine- and microstructure profiles were

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FIG. 1. Locations of the eight 12-h microstructure VMP plus 12-h CTD–LADCP profile time series stations (red numbers), five 12-h CTD–LADCP-only profile time series stations (black numbers) and an ADCP mooring (green dot under station 32) on the axes of Monterey and Soquel Submarine Canyons. Station numbers are part of a larger cruise-numbering scheme. Black dots denote microstructure profiles with good temperature data, and open circles denote microstructure profiles with defective temperature data where a conductivity–temperature relation was used to reconstruct the finescale water-mass profiles. The bottom-right insert shows the timeline of stations with respect to the spring–neap cycle (red denotes VMP plus CTD–LADCP and black denotes CTD–LADCP only). collected using a Rockland Scientific vertical microstruc- be collected in 12 h (sampling interval dt ; 1hor2 ture profiler (VMP; http://www.rocklandscientific.com) buoyancy periods), while, at deeper stations, at least rated to 2000-m depth at seven stations along the axes 8 profiles were collected (dt ; 3 buoyancy periods). In the of Monterey Submarine Canyon and its branch, Soquel early part of the cruise, problems were experienced with Canyon (Fig. 1). Water depths of 370–1200 m were sam- a new data tether, which subsequently reduced data rates pled. Finescale pressure, temperature, and conductivity, by a factor of 2. Estimated dissipation rates were not im- 2 as well as microscale shear and temperature gradient, pacted. Dissipation rates « 5 15nuz/2, where the kinematic were measured. The deepest microstructure station (42) molecular viscosity n 5 1.1 3 1026 m2 s21 is the kinematic was up canyon of San Gregorio Bend near the shelf break molecular viscosity and uz 5 ›u/›z is a single component of (Fig. 1), while the shallowest within Monterey Canyon the transverse microscale shear, were computed by fitting (7) was just up canyon of Gooseneck Bend. Profiles half-overlapping 4-m binned shear spectra to the Nasmyth sampled to within 0–262 m above the bottom (mab), on (1970) model spectrum (Oakey 1982) over the resolved average 30 (660) mab. Each station included a 12-h time wavenumber range, which typically includes neither the series of repeated VMP casts, except the deepest station Ozmidov nor Kolmogorov scales, then integrating over (42), where a combination of problems with the data tether the model spectrum. Uncertainties are a factor of 2 for cable, long cast time, and inclement weather prevented 10210 , « , 1026 Wkg21 based on fitting over different collecting a time series during a single day; at this station, resolved wavenumber ranges. A SeaBird thermistor ca- profiles were collected on three separate days to gather ble also failed and was replaced after the first 2 days. For adequate statistics. At shallow stations, 12–13 profiles could impacted stations 22, 27, and 42, the tight water-property

Unauthenticated | Downloaded 09/24/21 04:52 PM UTC 914 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 42 relations observed at other stations were used to infer Optical attenuation was also elevated in a near-bottom temperature, salinity, and density from conductivity. layer a few hundred meters thick, particularly at station Additional 12-h time series of lowered ADCP–CTD– 12 (Fig. 2c). Elevated optical attenuation near 100-m transmissometer (CTD–LADCP) profiling were collected depth in Soquel Canyon was likely a signature of inter- before or after each VMP time series (except at station mediate nepheloid layers originating from the branch 42), as well as at five other axis locations (Fig. 1), to pro- canyon’s nearby rim (Carter et al. 2005). duce 24-h-long time series of isopycnal heaving at the The two stations in Soquel Canyon (stations 17 and stations with both VMP and CTD–LADCP profiles. Also 19) were sampled 5 days apart with the shallowest station on this cruise, expendable current profiler (XCP) surveys (Fig. 2b) sampled 1 day after neap and station 19 sampled were collected near Monterey Bend and an ADCP– 2 days after spring tide. The two stations in Monterey thermistor chain mooring placed near the canyon axis Canyon proper (stations 7 and 12) were collected one day 1100-m isobath between San Gregorio and Monterey apart near neap. The mooring (Fig. 1) exhibited a fort- Bends for 2 months; these data will be used to examine nightly cycle of near-bottom-intensified flows not more the internal-wave climatology and energy budget else- than a day out of phase with the local surface tide, sug- where. This paper will focus on the microstructure, CTD, gesting a local source. Although internal tides in Monte- and transmissivity [beam attenuation coefficient (BAC)] rey Canyon are generated remotely on the California profiles. XCP temperature profiles were used to estimate continental margin to the south (Jachec et al. 2006; Carter the thickness of the well-mixed bottom boundary layer. 2010), with group velocities O(100 km day21) for mode- The beam attenuation coefficient is linearly related one internal tides, little spring–neap phase lag is expected. to the concentration of suspended particulate matter Averaging over the station time series reveals h« 5 (SPM) for the fine-size particles and low concentrations 200–300-m-thick turbulent layers (Fig. 3) above the (1–5 mg L21) found over continental margins (Baker bottom with average dissipation rates h«i 5 4 3 and Lavelle 1984; Gardner 1989; McPhee-Shaw et al. 1028 Wkg21 (Fig. 4) at all seven stations. This is an order 2004). Where density bands of suspended particulate of magnitude above the O(4 3 1029 Wkg21) dissipation matter are elevated compared to waters above and below rates (Figs. 3, 4) in the overlying 300–400 mab of the that could be traced through multiple stations back to the water column. Scatterplots of instantaneous 1-m dissi- canyon seafloor, these features are identified as INLs. pation rates « and buoyancy frequencies N (Fig. 5) show Persistent INLs (those seen over many days) were used to no preference for high dissipation rates in low stratifica- infer regions of persistent offshore transport. tion or vice versa, so these averages are not biased; unstable instantaneous 1-m stratifications (N2 , 0) cluster toward higher dissipation rates and lower jN2j.Thisnear- 4. Results bottom layer of elevated turbulence (Fig. 3) is well Profile time series at the four shallowest stations in stratified with the 0–200-mab average buoyancy fre- Soquel and Monterey Canyons (Fig. 2) are illustrative of quency hNi 5 3.5 3 1023 rad s21 compared to the 300– the signals at all seven VMP stations. Semidiurnal and 400-mab hNi 5 4.5 3 1023 rad s21 (Fig. 4) in overlying longer periods dominated 50–100-m isopycnal displace- waters. We define these bottom few hundred meters as ment j variability in the bottom one- to two-thirds of the the ‘‘stratified turbulent layer’’ to distinguish them from water column, although unresolved time scales shorter any well-mixed bottom boundary layers arising from than the profiling rate were also apparent. Mode 1 domi- bottom stress or the diffusive bottom boundary condition nated in the two Monterey time series, whereas higher (Phillips 1970). The buoyancy Reynolds number Reb 5 modes were evident in Soquel. Elevated turbulent dissi- «/(nN2) is 3000 in the stratified turbulent layer and 200 in pation rates « in the bottom 200–300 m extended well the overlying water column. Maximum Ozmidov lengths 3 1/2 into the stratified water column. The near-bottom layer of LO 5 («max/N ) in the stratified turbulent layer are less elevated turbulent dissipation rate « changed its strength, than 10 m based on measured dissipation rates « and thickness, and vertical distribution during the course of a buoyancy frequencies N so the bulk of the stratified tidal cycle, but sampling was too coarse (2–3 buoyancy turbulent layer has no direct interaction with the bot- periods) to identify the internal tidal bores that have been tom. The stratified turbulent layer is likely due to break implicated in strong turbulence production on slopes (Key down of large-amplitude internal waves after reflection 1999; Rosenfeld et al. 1999; Carter and Gregg 2002; from canyon topography (e.g., Hotchkiss and Wunsch Klymak and Moum 2003). Midwater « extrema may be 1982; Thorpe 1998; Eriksen 1998) or formation of hy- due to topographic focusing of internal waves (Hotchkiss draulic internal lee waves at topographic irregularities and Wunsch 1982), but we have insufficient data to es- (Klymak et al. 2008). In support of this interpretation, tablish their cause. isopycnal displacements j are 50–100 m in the bottom

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FIG. 2. Profile time series from the two shallowest stations in (top) Soquel Canyon [(left) 19 and (right) 17] and (bottom) Monterey Canyon [(left) 12 and (right) 7]. Dissipation rates « (red) from the two independent VMP shear probes are plotted as mirror images about the dotted vertical line denoting the profile time. Optical transmissometer beam attenuation coefficient (blue) is proportional to suspended particulate matter. Isopycnal displacements j (black solid curves) are derived from both VMP and CTD density profiles. Their semidiurnal fits are shown as black dotted curves. Drop numbers are indicated along the upper axes.

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FIG. 3. Sections of tidally averaged dissipation rate log(«) (red) and (negative) buoyancy frequency log(N) (green) profiles along the axes of (top) Soquel and (bottom)Ð Monterey h Canyons. Also shown are profiles of the horizontal upcanyon transport TU 5 0 U‘y dh (dark blue) up to 300 (200) mab in Monterey (Soquel) and tidally averaged isopycnals (black lines). Horizontal axes are in distance along the thalweg from the head of Monterey Canyon. Station numbers (Fig. 1) are indicated along the upper axes. The dotted diagonal lines denote semidiurnal characteristic slopes (0.03–0.04), indicating that Monterey Canyon’s axis is subcritical and Soquel Canyon’s axis supercritical. Well-stratified 200–300-m-thick turbulent near-bottom layers of bottom-intensified dissipation rates « 5 1028 to 1027 Wkg21 are found as deep as 1200 m. Dissipation rate peaks near 300-m depth at station 42 and 400-m depth at station 22 may be related to the nearby crests of ridges west of 42 and northeast of 22. one- to two-thirds of the water column (Fig. 2), a sub- boundary. Although recent numerical and laboratory ex- stantial fraction of the water depth. periments (Shih et al. 2005; Barry et al. 2001) have reported The inferred turbulent layer eddy diffusivity K 5 lower mixing efficiencies at high Reynolds numbers, these gh«i/hN2i is 16 3 1024 m2 s21, assuming a mixing effi- suffered from domain sizes that could not simultaneously ciency g 5 0.2 (Osborn 1980). The use of this mixing resolve the Ozmidov and Kolmogorov length scales at efficiency is justified because the stratified turbulent high Reynolds number. Microstructure observations col- layer is much thicker than the Ozmidov length scale lected multiple Ozmidov lengths from boundaries in the

LO so that its turbulence is not affected by the bottom ocean consistently ﬁnd high-Reynolds-number turbulent

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FIG. 4. Depth-average dissipation rates « (red) and buoyancy frequencies N (blue) in the stratified turbulent bottom layer (0–200 mab) (solid dots) and the 300–400-mab layer overlying it (open triangles); these depth ranges were chosen to ensure that the averages were either incontrovertibly inside or outside the stratified turbulent boundary layer (Fig. 3). The horizontal axis is drop number. Dissipation rates are an order of magnitude larger in the near- bottom layer (4 3 1028 Wkg21, eddy diffusivity K 5 16 3 1024 m2 s21, and Ozmidov length 29 21 scale LO 5 1.6 m) compared to overlying waters (4 3 10 Wkg ), whereas buoyancy frequencies differ by only 25% (3.5 3 1023 vs 4.5 3 1023 rad s21). mixing efficiencies g 5 0.20 60.05 (Oakey 1982; 2006 sampling and inferred eddy diffusivities were Gargett et al. 1984; Moum 1996; St. Laurent and ;O(1024 m2 s21). Schmitt 1999). Estimates of the well-mixed bottom boundary layer 24 21 Similar diffusivities were reported in stratified tur- thickness hN span 0–60 m based on Tz , 5 3 10 8Cm bulent layers near the bottom at shallower locations (equivalent to N , 1023 rad s21) and visual inspection of along the canyon axis by Carter and Gregg (2002). 97 XCP profiles, which measured into the bottom, with Microstructure profiles collected near station 31 dur- roughly 50% less than 5 m thick and 90% less than 30 m ing a spring tide of August 2006 reveal even higher thick (Fig. 6), an order of magnitude thinner than the 27 21 near-bottom dissipation rates h«i ; 2 3 10 Wkg stratified turbulent layer thicknesses h« (Fig. 3). Because and eddy diffusivities K in excess of 1023 m2 s21.Be- the 2008 XCP measurements were largely confined to cause this sampling was not synoptic with the 2008 data the vicinity of Monterey Bend, we also examined more and was collected closer to the spring tide, it is not wide-ranging 129 XCP and 129 XCTD profiles collected included in the following analysis but provides support in the canyon and on the continental slope to the north for consistently elevated « along the canyon axis. At during 1997 (Kunze et al. 2002). These exhibit similar similar water depths on the continental margin south statistics, though two XCTD profiles had well-mixed of Monterey Bay, distant from the canyon, average bottom boundary layers thicker than 100 m. CTD bottom dissipation rates did not exceed 1028 Wkg21 during boundary layer thicknesses range over 17–57 m (Morrice

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2 FIG. 5. Scatterplots of 1-m dissipation rate log(«)vsstratificationlog(jN j)/2 in (a) the stratified turbulent near- 2 bottom layer and (b) overlying waters. Red dots correspond to N . 0andOzmidovlengthsLO , 1 m, red circles 2 2 correspond to N . 0andLO . 1 m, and blue dots correspond to N , 0. Dotted vertical and horizontal lines correspond to total averages for N2 . 0(red)andN2 , 0 (blue). Red (N2 . 0) and blue (N2 , 0) horizontal bars represent log(jN2j) bin averages. The number of points for each stratification condition and the few that had to be rejected are 3 1/2 indicated in the top left of each panel. Black diagonal dotted lines correspond to Ozmidov lengths LO 5 («/N ) of 1, 2, 2 and 5 m as indicated along the upper axis. Unstable 1-m N (,0) are mostly found to the left of LO 5 1m. et al. 2010) but are upper bounds because the CTD pro- a. Upcanyon transports files did not reach the bottom. No attempt to infer well- Maintenance of stratification in the canyon’s stratified mixed bottom boundary layer thicknesses from VMP turbulent layer can be interpreted using steady buoy- profiles was made because these rarely reached the bot- ancy conservation for a thread of fluid extending across tom and were not accompanied by an altimeter. the canyon width ‘y(x, z) of cross-sectional area dxdz (Fig. 7), 5. Implications for turbulent mixing and exchange with the interior ›[(UB 1hu9b9i)‘ ] ›[(WB 1hw9b9i)‘ ] y 1 y 5 0, (1) ›x ›z Restratification of the near-bottom waters must be occurring to maintain the density gradient in the face of where x is the upchannel coordinate and a Reynolds persistent turbulent mixing. To mix the bottom 200– decomposition has been employed (u 5 U 1 u9, w 5 W 1 300 m to completion would require changing the avail- w9,andb 5 B 1 b9), U the time-mean horizontal velocity able potential energy density APE by oriented along the canyon axis, B 52g[r(z) 2 r0]/r0 the ð ð h h mean buoyancy anomaly, hu9b9i the upchannel perturba- g « « h DAPE 5 Dr(h)hdh 5 hN2i h 2 « h dh tion buoyancy flux oriented up the canyon axis, W the r 2 0 0 0 time-mean vertical velocity, and hw9b9i the turbulent dia- hN2ih3 pycnal buoyancy flux. From mean continuity 5 « 5 10 2 30 J m kg21, 12 ›(U‘ ) ›(W‘ ) y 1 y 5 0, (2) ›x ›z where height above canyon axis bottom h 5 z 2 zb is positive upward. Assuming a mixing efficiency g 5 0.2 so (1) simplifies to and the observed stratified turbulent layer dissipation rate h«i 5 4 3 1028 Wkg21 implies mixing times Dt 5 ›(hu9b9i‘y) ›(hw9b9i‘y) DAPE/(gh«ih ) 5 2–5 months so that restratification U‘ B 1 W‘ N2 52 2 . (3) « y x y ›x ›z processes, such as exchange with the interior (McPhee-

Shaw and Kunze 2002) or upslope ﬂow Uk (Garrett 1990; It is customary to assume that diapycnal mixing (second 1991), must operate on similar time scales. term on right) is balanced by vertical advection (second

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FIG. 7. Schematic illustrating flow geometry in a canyon channel. FIG. 6. Cumulative probability distribution functions of well- (a) Along-axis section showing upchannelÐ horizontalÐ flow U through cross-sectional area A 5 h‘ (h9) dh954 hh9 dh952h2 mixed bottom boundary layer thicknesses hN in Monterey Canyon x 0 y Ð 0 Ð x1 x1 from 2008 XCP (thick solid), 1997 XCP (thin solid), and 1997 and upwelling W through flat surface Az 5 0 ‘y(h) dx 5 4 0 hdx. (b) 3D projection of the same depicting a thread of fluid ‘ (h)dxdz XCTD (dotted) profiles into the bottom (based on Tz , 5 3 y 24 21 extending across the canyon, where height above canyon axis 10 8Cm ). Well-mixed boundary layer thicknesses hN range over 0–60 m, with 50% less than 5 m thick and 90% less than 30 m bottom h 5 z 2 zb and zb is the canyon axis bottom depth. thick, an order of magnitude thinner than the stratified turbulent layer thicknesses h« (Fig. 3). as will be seen, it is not measurable by conventional means. Dropping this term also neglects narrowing of the term on left) so that (3) reduces to a vertical advection– channel up-canyon ›‘y/›x. flux-divergence balance similar to that described by Using the Osborn (1980) relation, the diapycnal Munk (1966), though, in this case, it is necessary to take buoyancy flux hw9b9i 52gh«i, where g is the mixing canyon narrowing with depth (i.e., hypsometry) into efficiency. The diapycnal velocity in (4) can be recast as account (Stigebrandt and Aure 1989; McDougall 1989; Kawase 1993), g ›(h«i‘y) gh«i ›‘y gh«i W(h) 5 ffi ffi , (5) 2 ›z 2 ›z 2 ›(hw9b9i‘ ) N ‘y N ‘y N h WN2‘ 52 y , (4) y ›z with the last equality arising because canyon width ‘y where canyon width ‘y(z) ; 4h, assuming a triangular depends linearly on h. We have used the observation canyon cross section with wall slopes ›H/›y ; 0.5 and that h«i and N2 are more or less constant in the strati- h 5 0 at the canyon axis bottom. From Fig. 3, isopycnal fied turbulent layer (Fig. 3) in the second equality, slopes ›j/›x are much gentler than the along-axis though this is not strictly true, and assume the same for bathymetric slope s 5 ›H/›x in the stratified turbulent the mixing efficiency g. In this layer, W(h) . 0(upwell- layer so the upcanyon mean buoyancy gradient Bx [ ing) arises from narrowing of the canyon with depth 2 N ›j/›x is small [i.e., UBx/WBz ; (›j/›x)/s 1], justi- ›‘y/›z (hypsometry) rather than the vertical structure fying neglect of the first left-hand term in (3); this will of stratification N2 or dissipation rate «; over sloping notholdinanywell-mixed bottom boundary layer topography not so constrained (e.g., continental slopes, where ›j/›x ; s21, but, because the well-mixed BBL is ridges, or seamounts), increased turbulent mixing toward thin and the canyon narrows as h approaches zero, there the bottom will cause downwelling because then W 5 will be little transport associated with this well-mixed (g/N2)›«/›z with ›«/›z , 0. As will be seen, 1D balances bottom boundary layer (Fig. 3). The upcanyon hori- (4) and (5) are not the whole story because they cannot zontal buoyancy-flux divergence ›hu9b9i/›x represents sustain the stratification in the presence of the bottom fluctuating exchange between the stratified turbulent boundary and do not account for along-axis variability. layer and interior but cannot be quantified at this point; As h / 0, canyon narrowing causes the left-hand side of

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FIG. 8. Inferred upcanyon transports TU (7) (black) along the axis of Monterey Canyon based on integrals over 200 mab. Solid black bars denote integrals that are stable, whereas open black bars are not. Transport divergence between stations 27 and 22 (r 5 32–34.5 km) implies entrainment from the interior to satisfy continuity, and convergence between stations 22 and 12 (r 5 24–32 km) implies injection of boundary water into the interior.

(5) to blow up because the assumption of small Bx no Ridge (Klymak et al. 2006). If these flows are supported longer holds in the well-mixed bottom boundary layer. by either cross-canyon geostrophic or accelerating up- However, we will confine our use of (5) to the thicker canyon pressure gradients, corresponding isopycnal overlying stratified turbulent layer. displacements are O(1 cm) over kilometers across or Plugging h«i 5 4 3 1028 Wkg21 and hN2i 5 1.2 3 along the canyon, which are also not measurable. With 1025 s22 into (5) produces W(h) ; (4 3 1024 m2 s21)/h these magnitudes, we can infer the ratio of the ne- ranging from 1 m day21 at h 5 40 mab (which may be glected mean horizontal advection to the inferred ver- 2 intermittently in a well-mixed bottom boundary layer; tical advection terms in (3), UBx/WN 5 (U/W)(›j/›x) , e.g., White 1994) to 0.2 m day21 at the top of the strati- 1023, justifying neglect of the mean horizontal advection

fied turbulent layer (h« 5 300mab).Thesearetwoto term in (4) for the stratified turbulent layer. three orders of magnitude larger than the diapycnal ve- The upcanyon transport locity of O(1 cm day21) inferred for the ocean interior (Munk 1966). ðð ð h« From the bottom boundary condition (v Á $)H 5 0, TU 5 UdAx 5 U‘y(h) dh A h the mean bottom flow must be parallel to the bottom N ð ð h h Uk 5 (U 5 W/s,0,W), where s 5 ›H/›x 5 0.027 is the g « ›(h«i‘ ) gh«i ›‘ « 5 y dh 5 y dh along-axis bottom slope. We will assume that this re- 2 2 sN h ›z sN ›z h lation holds in the stratified turbulent layer in keeping N N 2gh«ih with (4) and previous bottom-normal 1D models to 5 «, (7) estimate U. This does not contradict dropping of up- sN2 canyon mean advection U›B/›x in (4) and (5), because this term was deemed small based on near-zero ›B/›x 5 where dA 5 ‘ (h)dh 5 4hdh because of the assumed 2 x y N ›j/›x, not U, as will be verified shortly. The mean up- triangular cross section of the canyon and canyon wall canyon flow is then slope of 0.5. Numerically integrating the fourth term (7) at each station over the stratified turbulent near-bottom W(h) gh«i ›‘y 2 U(h) 5 ffi . (6) layer (Fig. 3) without assuming constant « and N pro- s 2 ›z 3 21 sN ‘y duces upcanyon transports TU 5 3–15 m s (Fig. 8) in the bottom 300 m in Monterey Canyon; estimates in This takes the same form as (11) of McPhee-Shaw and Soquel Canyon were not stable to small changes in in- Kunze (2002) though the right-hand side of the latter was tegration bounds so are not included here. This trans- expressed in terms of internal-wave energy-flux conver- port can be interpreted as either (i) an area integral over gence at a boundary. Inferred magnitudes range from dAx 5 ‘y(h)dh 5 4hdh of time-mean up-canyon flow U 21 50 m day at h 5 40 mab (which again may be intermit- or (ii) an area integral dAz 5 ‘y(h)dx 5 4hdx of the di- tently in a well-mixed bottom boundary layer) to 10 apycnal velocity W. Thus, in much the same way that 21 mday at the top of the stratified turbulent layer (h« 5 global upwelling and stratification can be used to quantify 300 mab), so they are not measurable. Similar magnitudes basin-average diapycnal diffusivities (Munk 1966; Munk have been previously inferred in Monterey Canyon and Wunsch 1998), turbulent mixing, stratification, and (Kunze et al. 2002), on the flanks of the Mid-Atlantic topography reported here can be used to infer mean Ridge (St. Laurent et al. 2001), and along the Hawaiian mixing-driven diapycnal and upcanyon velocities. We

Unauthenticated | Downloaded 09/24/21 04:52 PM UTC JUNE 2012 K U N Z E E T A L . 921 caution that only one term, (›hw9b9i/›z), in (3) could be quantiﬁed directly from the measurements, and it might be balanced by any or all of the other three terms (though we argued above that mean horizontal advection term is small). For example, diapycnal mixing might be balanced by horizontal perturbation ﬂuxes,

›hu9b9i/›x 52›hw9b9i/›z 5 g›(h«i‘y)/›z. b. Upcanyon divergence and convergence Assuming that 1D balance (4)–(7) is not too far wrong, that is, that the horizontal buoyancy-flux terms are smaller than the vertical terms, we may further explore the consequences. Though most of the inferred transports from (7) are in the 3–8 m3 s21 range (Fig. 8), the transport TU at station 22 (Fig. 1) is twice as large at 15 m3 s21; this is because the vertical gradient of « is weaker, so it competes less with ›‘y /›z [fourth equality in (7)] than at other stations (Fig. 3). The excess transport at station 22 implies upslope transport divergence between stations 27 and 22 and convergence between stations 22 and 12. These slope-parallel divergences and FIG. 9. Beam attenuation coefficient profiles as a function of density convergences must be balanced by entrainment from su at stations 45, 42, and 32 (Fig. 1) offshore of the water depths predicted to have divergent and convergent up-canyon transport the interior and injection of boundary layer fluid into (Fig. 8). Average depths of isopycnals hz(su)i are shown along the the interior (McDougall 1989), respectively (see Fig. right axis. Optical attenuation is elevated near the bottom and in an 10, which is discussed in detail in section 6), likely along INL in su 5 27.17–27.31 (hzi 5 740–900 m) sandwiched between isopycnals. The resulting exchange transport will be com- clear water in su 5 27.08–27.17 (hzi 5 660–740 m) and su 5 27.31– parable in magnitude to the upslope transports [though 27.38 (hzi 5 900–1020 m). 2 the small magnitude inferred for UBx compared to WN suggests that the neglected perturbation (bolus) transport stations 32, 42, and 45 (Fig. 1). This INL remained on hu9b9i may dominate exchange along isopycnals; e.g., roughly the same isopycnals for all three stations and Gemmrich and van Haren 2002]. Despite these limitations, persisted for more than 4 days, indicating negligible di- inferences about the locations and directions of exchange apycnal sediment flux or settling. The average depth flows can be used to predict depth ranges where one might hz(su)i for these isopycnals is 740–900 (6100) m, con- expect (i) clear water due to shoreward entrainment of sistent with the prediction of offshore transport of waters offshore waters driven by upslope transport divergence carrying elevated suspended sediment associated with and (ii) turbid water due to offshore injection of boundary convergent transport between stations 22 and 12 (Fig. 8). water containing suspended particulate matter driven by The layers of clear water above and below occupied convergence of boundary layer transports. Based on in- hz(su)i 5 660–740 m and 900–1020 m, respectively. ferences from the microstructure measurements, we pre- The 900–1020-m depth band of clear water is consistent dict clear water between 1000- and 1100- (6100) m depth with shoreward transport of clear waters from offshore and turbid water between 700 and 1000 (6100) m. predicted from the transport divergence between stations Because bottom layers of suspended particulate matter 27 and 22. There is no evidence of elevated beam at- are at least 200 m thick (Fig. 2), only stations deeper than tenuationcoefficientforstations22and12withinthe 1200 m can be examined for evidence of detached INLs, stratified turbulent layer convergence region compared which would be signatures of offshore transport associ- with the other stations. This indicates that the INL is not ated with transport convergence between 600 and 1000 m due to a particularly strong sediment source but arises in stations 22 and 12 (Figs. 1, 3, 8). Because internal-wave from the convergent upcanyon transport. vertical displacements exceed 100 m (Fig. 2), distinct regions of elevated suspended particulate matter and clear 6. Discussion and conclusions water are difficult to discern in plots of beam attenuation coefficient versus depth. However, in density coordinates, The two major observational conclusions are illustrated a distinct INL is evident between su 5 27.18 and 27.33 schematically in Fig. 10. Well-stratified near-bottom layers sandwiched by clear layers above and below (Fig. 9) at with elevated turbulent dissipation rates « are an order of

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2011) will not capture the essential physics. Because these appear to be the locations of the strongest near-bottom turbulence, instances where thin well-mixed bottom boundary layers driven by bottom stress or the diffusive bottom boundary condition may not be important globally. Stratified turbulent layers are not produced by 1D numerical simulations on slopes. Their physics is inherently 2D or 3D (e.g., Klymak et al. 2008; Scotti 2011; Gayen and Sarkar 2011). Such dynamics includes reflection (Eriksen 1982, 1985; Slinn and Riley 1996, 1998; Toole et al. 1997; Thorpe 1997; Eriksen 1998; Nash et al. FIG. 10. Schematic illustrating well-mixed (h ) and stratified N 2004) and scattering (St. Laurent and Garrett 2002; turbulent (h«) bottom layers on a slope based on observations. (a) Profiles of buoyancy frequency N (thin solid line) and dissipation Polzin 2009) of low-mode internal waves by topography, rate « (thick solid line) with the heights above bottom of the well- as well as generation of internal tide (Klymak et al. mixed and stratified turbulent layers labeled hN and h«, re- 2008; Legg and Klymak 2008) and internal lee waves spectively. (b) An across-isobath section showing isopycnals (thin (Nikurashin and Ferrari 2010a,b). These topographic in- solid lines) and the heights above bottom of the two layers (dotted diagonal lines). Isopycnals dip only in the well-mixed BBL (h , teractions produce unstable internal-wave shears and hN). Mixing-driven flow is parallel to the slope unless there is overturns in the stratified water column (e.g., Slinn and convergence (divergence) in the upslope flow Uk to drive injection Riley 1996; Eriksen 1998; Thorpe 1998; Gayen and Sarkar of near-bottom fluid (entrainment of ocean interior water) through 2011) because of the flux of internal-wave energy into and 9 either mean U or fluctuating u flows. Light gray stippling depicts out of the boundary supplying energy for water-column turbid boundary layers and intermediate nepheloid layers. turbulence. By excluding across- and along-isobath variability, 1D bottom boundary layer modeling cannot magnitude thicker than well-mixed bottom boundary induce the lateral buoyancy and pressure gradients asso- layers (h« hN; Figs. 2–6, 10a) along the sloping canyon ciated with internal-wave radiation. Therefore, in situa- axis. Turbulent near-bottom layers with h«i 5 4 3 1028 tions where internal waves are the primary energy Wkg21 were found at all stations spanning canyon axis source for turbulence, a 2D or higher-dimension closure depths of 370–1200 m (Fig. 3). Similar dissipation rates is necessary. Weak internal-wave fields that only break were previously reported for Monterey Canyon axis because of bottom stress may confine their turbulence to depths shallower than 500 m (Carter and Gregg 2002). well-mixed bottom boundary layers, but, even under these Turbulence dissipation rates « in the order of magnitude conditions, overturning has been reported because of the thinner well-mixed bottom boundary layers are not ob- advection of heavy over light water (Slinn and Riley 1996), viously different from those in overlying stratified tur- an inherently 2D process. bulent waters (Fig. 2). Near-bottom turbulence can also be caused by mean Near-bottom stratified turbulent layers are by no along-isobath flows inducing up- or downslope Ekman means unique to Monterey Canyon. Similar features have flows (Trowbridge and Lentz 1991; MacCready and been observed over other sloping topography including Rhines 1991, 1993; Middleton and Ramsden 1996). seamounts (Toole et al. 1997; Lueck and Mudge 1997; Xing and Davies (1999) report that flows of finite cross- Eriksen 1998), ridges (Polzin et al. 1997; Lien and Gregg isobath width induce transport convergences and di- 2001; Thurnherr et al. 2005; Carter et al. 2006; Aucan vergences in the bottom Ekman layer as well. Condie et al. 2006; Kunze et al. 2006; Klymak et al. 2008), and the (1999) found high mixing efficiencies associated with continental slope (Moum et al. 2002; Gemmrich and van downslope Ekman flows caused by along-isobath flow Haren 2002; Nash et al. 2004, 2007). Thus, oft-repeated with shallow water on the right (in the sense of deep arguments that turbulence on slopes should be inef- western boundary currents). fective at mixing because it stirs already-mixed waters A global assessment of diapycnal transport in can- (Garrett 1990, 1991, 2001; Garrett et al. 1993) do not yons can be obtained from the ratio of mixing in can- always hold and we will argue do not hold for the most yons KcAc ffi KcrnR4‘x to that in the ocean interior 2 intense turbulence. KoAo ffi Ko2R4,wherer 5 0.2 is the fraction of con- At sites where energetic breaking internal waves are tinental slope incised by canyons based on the Pacific the principal source of near-boundary turbulence, as North American continental slope between the equa- where either internal-wave generation or interactions tor and Alaska (Hickey 1995), n 5 100 is the number of with the topography are strong, 1D modeling (e.g., Mellor Earth radii R4 of continental shelf break, ‘x 5 h«/s 5 and Yamada 1982; Ramsden 1995; Umlauf and Burchard 10 km is the length of canyon intersecting the stratified

Unauthenticated | Downloaded 09/24/21 04:52 PM UTC JUNE 2012 K U N Z E E T A L . 923 turbulent layer, h« 5 300 m is the thickness of the the case of converging upslope transports, injection of turbulent stratified layer, and s 5 ›H/›x 5 0.027 is the sediment-laden bottom-layer water into the interior will along-axis bottom slope. The ratio KcAc/(KoAo) 5 result in intermediate nepheloid layers as confirmed by (Kc/Ko)[rn‘x/(2R4)] ; (16/0.1)(1/60) ; 2.7. Thus, measured beam attenuation coefficients (Fig. 9). In the worldwide, canyons might produce 2–3 times as much case of diverging upslope transports, clear interior flow diapycnal transport as the basin-average interior diffu- will be entrained into the stratified turbulent near-bottom sivity of 0.1 3 1024 m2 s21 (Gregg 1987; Ledwell et al. layer. 1993; Kunze and Sanford 1996; Kunze et al. 2006), which In general, variability of slope topography, stratifica- in turn accounts for about 10% of the transport based on tion (Imberger and Ivey 1993), and internal-wave fields the bottom-water formation rate (Munk 1966; Munk and will all create turbulent heterogeneity, which will in turn Wunsch 1998). We caution that it is not known whether drive convergences and divergences of turbulence-driven most canyons are as turbulent as Monterey Canyon. cross-isobath transports, leading to exchange with the in- However, intensified internal tide signals appear to be a terior to impact the ocean as a whole (McDougall 1989; universal feature of canyons (Shepard et al. 1974, 1979), McPhee-Shaw 2006). For example, Nash et al. (2004) de- and recent measurements have found intensified turbu- scribed a turbulence hotspot on the semidiurnally near- lence in Gaoping (Lee et al. 2009), as well as more typical critical part of the Virginia continental slope between continental slope Ascension (Gregg et al. 2011), Barrow 1000- and 1300-m depths. Nash et al. (2007) reported two (Shroyer 2012), and Barkley Canyons. A similar global isolated turbulent hotspots on the Oregon slope, both integration of the layer dissipation rate r«h«rnR4L yields associated with the semidiurnal tide. Turbulent hotspots 10 GW, assuming dissipation along a 10-km canyon are often found over slopes that are near-critical for length, comparable to the 3 GW along a 200-km length semidiurnal frequencies (Levine and Boyd 2006; Aucan of the Hawaiian Ridge (Klymak et al. 2006) and about and Merrifield 2008), often at continental shelf breaks 1% of the deep-ocean surface tide loss (Egbert and Ray (Cacchione and Drake 1986) and on ridge crests (Nash 2003). et al. 2006; Klymak et al. 2008). In the absence of con- The along-axis section (Figs. 8, 10b) demonstrates verging canyon walls, increasing turbulent mixing toward our second challenge to the applicability of 1D bound- the bottom over unrestricted slopes will produce down- ary layer theory (4) over sloping topography: that is, that welling rather than upwelling. More observations are turbulence-driven upslope transports TU need not be needed over the undersampled continental margins to uniform. Other theoretical and laboratory studies have better characterize the spatial and temporal variability of addressed convergence and exchange associated with turbulence in this environment and determine its role in nonuniform buoyancy flux theoretically and in the lab- mixing the World Ocean. oratory (Phillips et al. 1986; McDougall 1989; McPhee- The measurements made here only allowed reliable Shaw and Kunze 2002). Nonuniform upcanyon transport quantification of the diapycnal mixing term ›hw9b9i/›z in was posed as a proof by contradiction in that the derived (3), which could be balanced by any of the remaining balance (4) is 1D. Although a 1D balance might hold three terms. The vertical balance inferred between di- between stations 42 and 27 and between stations 12 and apycnal mixing and upwelling (4) required neglect of 7 (Fig. 8), the anomalously high transport at station 22 mean and perturbation horizontal flux terms. However, will drive 2D flows and exchange with the interior. In- the inferred upcanyon transport divergence (Fig. 8) re- ferred turbulence-driven upcanyon flows U range from quires at least one of the horizontal terms not to vanish. 50 m day21 (0.05 cm s21)ath 5 40 mab to 10 m day21 at Although we were able to justify neglect of mean advec- the top of the near-bottom turbulent layer (h« 5 300 mab) tion, the perturbation horizontal flux cannot be quantified so would not be directly measurable by conventional with conventional instruments and cannot be complete current meters (Xu and Noble 2009) even if such mean ruled out as a primary balancing term (e.g., Gemmrich flows were not biased by topographic steering hystere- and van Haren 2002). Future work might be better able to sis (Rosenfeld et al. 1999). Upcanyon transports in close this budget using dye injections to quantify the ver- Monterey Canyon are 3–8 m3 s21 (Fig. 8). Higher up- tical mixing and offshore isopycnal transport. slope transport at station 22 (15 m3 s21) compared to deeper station 27 and shallower station 12 implies di- Acknowledgments. Invaluable assistance in the data vergent boundary transport between 1000- and 1100- collection was provided by Kevin Bartlett. Danielle (6100) m depths, which should entrain water from the Wain provided guidance into the lake literature. Ad- interior into the boundary layer, and convergent bound- ditional helpful comments came from Jody Klymak, ary transport between 700 and 1000 (6100) m, which Trevor McDougall, and an anonymous reviewer. The should inject turbid boundary fluid into the interior. In captain and crew of Point Sur are commended for their

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