## 1. Introduction

Diapycnal mixing is a key component to the large-scale ocean thermohaline overturning circulation (Saenko 2006; Kuhlbrodt et al. 2007; Jayne 2009). Numerical simulations reveal that the deep overturning cell and abyssal circulation (Samelson 1998; Hasumi and Suginohara 1999; Huang and Jin 2002; Saenko and Merryfield 2005; Katsman 2006), water-mass properties (Simmons et al. 2004b; Koch-Larrouy et al. 2007; Jochum 2009), air–sea interactions (Jochum 2009), abyssal ventilation, and the Southern Hemisphere westerlies (Friedrich et al. 2011) all depend, not only on the average mixing, but also on its vertical and horizontal distributions. Direct microstructure and inferred diffusivity estimates are sparse but find turbulent diffusivities to be highly heterogeneous and intermittent. Diffusivities are weak *O*(10^{−5} m^{2} s^{−1}) 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 rough topography (Polzin et al. 1997; Ledwell et al. 2000; St. Laurent et al. 2001; Toole et al. 1997; Naveira Garabato et al. 2004; Kunze et al. 2006; Stöber et al. 2008). Even over sloping topography, turbulence can be extremely variable (Moum et al. 2002; Carter et al. 2005; Nash et al. 2007; Klymak et al. 2006). Strong mixing at a few locales, mediated by rough topography, will impact the abyssal basin-scale circulation (McDougall 1989) and provide narrow pathways of exchange between deep and shallow water (Kunze et al. 2002, 2006), implying shorter local exchange times than bulk budget inferences.

The energy for mixing of the stratified ocean interior comes from tides (Munk and Wunsch 1998; Egbert and Ray 2003), wind-generated internal waves (Wunsch and Ferrari 2004), and abyssal subinertial currents (Weatherly and Martin 1978; Bryden and Nurser 2003; Nikurashin and Ferrari 2010a,b). The bulk of the internal-wave energy flux appears to radiate away from its sources as low-mode internal waves (Ray and Mitchum 1997; Morozov 1995; Althaus et al. 2003; Lee et al. 2006; Simmons et al. 2004a; Alford 2003; Klymak et al. 2006; Zhao et al. 2010; Dushaw et al. 2011), its fate as yet unknown. This implies that turbulent mixing parameterizations based only on local forcing will fall short. In a global assessment of internal-wave-driven turbulence in the ocean inferred from a finescale parameterization, Kunze et al. (2006) could not account for surface tide losses (Egbert and Ray 2003) by more than a factor of 3. In their data, the bulk of the turbulent dissipation was associated with rough bathymetry, but such topography was only poorly covered, with continental slopes particularly undersampled. Evidence has been found for low-mode internal tides breaking on continental slopes (Moum et al. 2002; Nash et al. 2004, 2007; Martini et al. 2011; Klymak et al. 2011) and in shelf canyons (Carter and Gregg 2002; Gregg et al. 2011; Lee et al. 2009).

One argument against near-boundary turbulence contributing to global ocean mixing is that it only stirs already-mixed waters (Phillips 1970; Phillips et al. 1986; Garrett 1990, 1991, 2001; Garrett et al. 1993) so will have low mixing efficiency. However, observations frequently find ~*O*(100 m)-thick well-stratified intensely turbulent layers overlying sloping topography (Toole et al. 1997; Lueck and Mudge 1997; Eriksen 1998; Carter and Gregg 2002; McPhee-Shaw et al. 2004; Nash et al. 2004, 2007; Carter et al. 2006; Klymak et al. 2006). Based on a 1D bottom-normal model, Garrett (1990) showed that sloping near-bottom isopycnals will drive a two-layer counterflow to reestablish the stratification, which would restore higher mixing efficiency. Numerical simulations with variations only normal to the bottom (e.g., Ramsden 1995; Umlauf and Burchard 2011) have confirmed many of these theoretical results. Such 1D bottom-normal boundary layer models disallow internal-wave radiation, reflection, and interaction. In addition, they permit no exchange of fluid between the bottom boundary layer (BBL) and stratified interior.

However, these arguments assume the bottom slope extends to infinity; that is, uniform mixing along the slope induces uniform flow parallel to the bottom. In a finite body of water, mixing necessarily raises the available potential energy of the fluid (Condie 1999) and, for a steady state, there has to be exchange with the interior at some depth. Moreover, ocean slopes, topographic roughness (Goff and Jordan 1988), along-isobath flows, stratification, internal-wave forcing, and near-bottom turbulence are all nonuniform (Nash et al. 2004, 2007). Resulting 2D and 3D convergences and divergences of upslope turbulence-driven transports will drive exchanges between the turbulent near-bottom boundary layer and the interior (Ivey 1987; Imberger and Ivey 1993; McPhee-Shaw and Kunze 2002; McPhee-Shaw 2006; Inall 2009). Armi (1978, 1979, 1980) provides incontrovertible if anecdotal evidence for exchange between boundary and interior waters, though his mean-flow generation argument was challenged on energetic grounds (Garrett 1979). Further evidence for such exchange comes from observations of intermediate nepheloid layers (INLs) extending seaward from continental margins. Studies have linked intermediate nepheloid layers to topographic slopes critical at semidiurnal frequencies (Cacchione and Drake 1986; Dickson and McCave 1986; Thorpe and White 1988; McPhee-Shaw et al. 2004; McPhee-Shaw 2006), presumed to be regions associated with energetic turbulent shear.

Bottom boundary mixing has been found to dominate in smaller lakes (Goudsmit et al. 1997), where interior mixing is also weak (Wüest et al. 1996; MacIntyre et al. 1999; Lorke et al. 2008), and in small coastal basins (Ledwell and Bratkovich 1995; Ledwell and Hickey 1995; Gregg and Kunze 1991). In fjords, where turbulent mixing is largely associated with internal tides generated at the sill, which then dissipate at sloping topography within the fjord, Stigebrandt and Aure (1989) inferred bulk mixing efficiencies of 0.04–0.11 (20%–50% of canonical 0.2 value). In a lake boundary layer dye-injection study, Wain and Rehmann (2010) found that 60% of the dye injected on the slope moved into the interior in under a day. Inall (2009) reported entrainment of dye into the boundary layer in 2 days, followed by detrainment along interior isopycnals 2 days later, also finding net mixing efficiencies of 0.044. However, boundary layers make up a much larger fraction of isopycnal surface area in these basins than in the deep ocean. In general, the magnitudes of boundary mixing’s contribution to the ocean total and exchange between bottom boundary and ocean interior waters remain unquantified.

In this paper, the effect of near-bottom turbulent mixing on slopes will be further explored using fine- and microstructure profile time series of temperature, salinity, transmissivity, and turbulent dissipation rate collected along the axes of Monterey and Soquel Submarine Canyons in water depths 370–1200 m. These data will be used to establish a link between boundary mixing nonuniformity and along-isopycnal exchange with less turbulent interior waters. Canyons are typified by extremely energetic internal tides (Shepard et al. 1974, 1979; Gordon and Marshall 1976; Hotchkiss and Wunsch 1982; Hunkins 1988; Matsuyama et al. 1993; Petruncio et al. 1998; Lafuente et al. 1999; Kunze et al. 2002; Lee et al. 2009) and turbulence (Lueck and Osborn 1985; Carter and Gregg 2002; Lee et al. 2009). By blocking alongslope geostrophic flow (MacCready and Rhines 1991, 1993; Trowbridge and Lentz 1991), narrow canyons can also enhance upwelling and exchange with the interior (Freeland and Denman 1982; Hickey 1995; Allen 1996; Allen and de Madron 2009). In section 2, pertinent previous work in Monterey Submarine Canyon is reviewed. The relevant fine- and microstructure measurements are described in section 3. Section 4 shows that turbulent boundary layers on the sloping axis are well stratified and much thicker than well-mixed bottom boundary layers. The implications of these stratified turbulent bottom layers for ocean mixing and their nonuniformity on exchange with the ocean interior are discussed in section 5. Finally, in section 6, these results are summarized, and their implications for mixing dynamics on slopes and possible global impacts are assessed.

## 2. Background: Internal tides and turbulence in Monterey Submarine Canyon

Previous measurements in Monterey Submarine Canyon (Petruncio et al. 1998; Kunze et al. 2002; Carter and Gregg 2002) found its internal-wave field dominated by semidiurnal internal tides, consistent with past measurements in numerous other canyons (Shepard et al. 1974, 1979), particularly in a 200–300-m-thick bottom-hugging beam along the canyon axis. This is explicable from the reflection behavior of internal waves by canyon topography (Cacchione and Wunsch 1974; Eriksen 1982; Hotchkiss and Wunsch 1982).

For 2D (normal) incidence, internal waves encountering a bottom slope steeper than their characteristics (supercritical) will reflect horizontally as if from a vertical wall back into deeper water, while internal waves encountering a gentler (subcritical) slope will be reflected upward as if from a flat bottom, preserving their horizontal direction of propagation. Internal waves encountering near-critical slopes will reflect to higher wavenumber and amplitude, both changes conducive to breaking and turbulence production. For oblique (nonnormal) incidence, supercritical slopes tend to turn internal waves toward shallower water like beaching surface waves rather than reflect them back into deeper water (Eriksen 1982; Thorpe 1999; Martini et al. 2011) so that more low-frequency energy is transmitted into shallow water than for normal incidence. Typically, canyon walls are supercritical and their thalwegs near critical for semidiurnal frequencies, so internal tides are focused into intense near-bottom beams running parallel to the axes’ bottoms. The axis of Monterey Submarine Canyon is subcritical at the semidiurnal frequency so will transmit internal tides toward its head. The axis of Soquel Canyon is supercritical so will reflect internal tides back into the main canyon. Regional numerical models (Jachec et al. 2006; Rosenfeld et al. 2009; Wang et al. 2009; Carter 2010; Hall and Carter 2011) suggest that the primary source for internal tides in Monterey Canyon is Sur Platform on the continental margin south of Monterey Bay. These internal waves radiate north before being funneled into the canyon by topographic interactions.

As would be expected with elevated internal-wave levels, intense turbulence with *ε* ~ *O*(10^{−6} W kg^{−1}) has been reported in Monterey Canyon in the near-bottom layers along the canyon axis (Lueck and Osborn 1985; Carter and Gregg 2002). These turbulence levels are roughly a factor of 6 higher than predictions from a finescale parameterization based on weakly nonlinear internal-wave/wave interactions cascading energy toward 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 by transforming incoming low modes directly into unstable waves. Kunze et al. reported the vertically integrated energy flux diminishing from 5 kW m^{−1} at the shelf break to 1 kW m^{−1} toward the head, consistent with observed turbulent kinetic energy dissipation rates *ε* as a sink.

Although fine sediments drape the walls of the canyon, the thalweg is characterized by sandy substrate to depths of at least 1500 m, indicative of an energetic flow environment (Paull et al. 2005; Xu and Noble 2009). The processes responsible for transport of fine sediments differ from those transporting coarse sand (Paull et al. 2005). It is thought that fine mud and silts do not settle because of continuous erosion by internal tidal currents (Xu and Noble 2009), whereas coarser material is delivered by episodic gravity currents (Xu et al. 2004).

## 3. Measurements

During 18–30 August 2008, spanning the spring tide of 21 August, 77 fine- and microstructure profiles were collected using a Rockland Scientific vertical microstructure profiler (VMP; http://www.rocklandscientific.com) rated to 2000-m depth at seven stations along the axes of Monterey Submarine Canyon and its branch, Soquel Canyon (Fig. 1). Water depths of 370–1200 m were sampled. Finescale pressure, temperature, and conductivity, as well as microscale shear and temperature gradient, were measured. The deepest microstructure station (42) was up canyon of San Gregorio Bend near the shelf break (Fig. 1), while the shallowest within Monterey Canyon (7) was just up canyon of Gooseneck Bend. Profiles sampled to within 0–262 m above the bottom (mab), on average 30 (±60) mab. Each station included a 12-h time series of repeated VMP casts, except the deepest station (42), where a combination of problems with the data tether cable, long cast time, and inclement weather prevented collecting a time series during a single day; at this station, profiles were collected on three separate days to gather adequate statistics. At shallow stations, 12–13 profiles could be collected in 12 h (sampling interval *δt* ~ 1 h or 2 buoyancy periods), while, at deeper stations, at least 8 profiles were collected (*δt* ~ 3 buoyancy periods). In the early part of the cruise, problems were experienced with a new data tether, which subsequently reduced data rates by a factor of 2. Estimated dissipation rates were not impacted. Dissipation rates *ε* = 15*ν**u _{z}*

^{2}/2, where the kinematic molecular viscosity

*ν*= 1.1 × 10

^{−6}m

^{2}s

^{−1}is the kinematic molecular viscosity and

*u*= ∂

_{z}*u*/∂

*z*is a single component of the transverse microscale shear, were computed by fitting half-overlapping 4-m binned shear spectra to the Nasmyth (1970) model spectrum (Oakey 1982) over the resolved wavenumber range, which typically includes neither the Ozmidov nor Kolmogorov scales, then integrating over the model spectrum. Uncertainties are a factor of 2 for 10

^{−10}<

*ε*< 10

^{−6}W kg

^{−1}based on fitting over different resolved wavenumber ranges. A SeaBird thermistor cable also failed and was replaced after the first 2 days. For impacted stations 22, 27, and 42, the tight water-property relations observed at other stations were used to infer temperature, salinity, and density from conductivity.

Additional 12-h time series of lowered ADCP–CTD–transmissometer (CTD–LADCP) profiling were collected before or after each VMP time series (except at station 42), as well as at five other axis locations (Fig. 1), to produce 24-h-long time series of isopycnal heaving at the stations with both VMP and CTD–LADCP profiles. Also on this cruise, expendable current profiler (XCP) surveys were collected near Monterey Bend and an ADCP–thermistor chain mooring placed near the canyon axis 1100-m isobath between San Gregorio and Monterey Bends for 2 months; these data will be used to examine the internal-wave climatology and energy budget elsewhere. This paper will focus on the microstructure, CTD, and transmissivity [beam attenuation coefficient (BAC)] profiles. XCP temperature profiles were used to estimate the thickness of the well-mixed bottom boundary layer. The beam attenuation coefficient is linearly related to the concentration of suspended particulate matter (SPM) for the fine-size particles and low concentrations (1–5 mg L^{−1}) found over continental margins (Baker and Lavelle 1984; Gardner 1989; McPhee-Shaw et al. 2004). Where density bands of suspended particulate matter are elevated compared to waters above and below that could be traced through multiple stations back to the canyon seafloor, these features are identified as INLs. Persistent INLs (those seen over many days) were used to infer regions of persistent offshore transport.

## 4. Results

Profile time series at the four shallowest stations in Soquel and Monterey Canyons (Fig. 2) are illustrative of the signals at all seven VMP stations. Semidiurnal and longer periods dominated 50–100-m isopycnal displacement *ξ* variability in the bottom one- to two-thirds of the water column, although unresolved time scales shorter than the profiling rate were also apparent. Mode 1 dominated in the two Monterey time series, whereas higher modes were evident in Soquel. Elevated turbulent dissipation rates *ε* in the bottom 200–300 m extended well into the stratified water column. The near-bottom layer of elevated turbulent dissipation rate *ε* changed its strength, thickness, and vertical distribution during the course of a tidal cycle, but sampling was too coarse (2–3 buoyancy periods) to identify the internal tidal bores that have been implicated in strong turbulence production on slopes (Key 1999; Rosenfeld et al. 1999; Carter and Gregg 2002; Klymak and Moum 2003). Midwater *ε* extrema may be due to topographic focusing of internal waves (Hotchkiss and Wunsch 1982), but we have insufficient data to establish their cause.

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 *ε* (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 *ξ* (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.

Citation: Journal of Physical Oceanography 42, 6; 10.1175/JPO-D-11-075.1

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 *ε* (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 *ξ* (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.

Citation: Journal of Physical Oceanography 42, 6; 10.1175/JPO-D-11-075.1

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 *ε* (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 *ξ* (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.

Citation: Journal of Physical Oceanography 42, 6; 10.1175/JPO-D-11-075.1

Optical attenuation was also elevated in a near-bottom layer a few hundred meters thick, particularly at station 12 (Fig. 2c). Elevated optical attenuation near 100-m depth in Soquel Canyon was likely a signature of intermediate nepheloid layers originating from the branch canyon’s nearby rim (Carter et al. 2005).

The two stations in Soquel Canyon (stations 17 and 19) were sampled 5 days apart with the shallowest station (Fig. 2b) sampled 1 day after neap and station 19 sampled 2 days after spring tide. The two stations in Monterey Canyon proper (stations 7 and 12) were collected one day apart near neap. The mooring (Fig. 1) exhibited a fortnightly cycle of near-bottom-intensified flows not more than a day out of phase with the local surface tide, suggesting a local source. Although internal tides in Monterey Canyon are generated remotely on the California continental margin to the south (Jachec et al. 2006; Carter 2010), with group velocities *O*(100 km day^{−1}) for mode-one internal tides, little spring–neap phase lag is expected.

Averaging over the station time series reveals *h _{ε}* = 200–300-m-thick turbulent layers (Fig. 3) above the bottom with average dissipation rates 〈

*ε*〉 = 4 × 10

^{−8}W kg

^{−1}(Fig. 4) at all seven stations. This is an order of magnitude above the

*O*(4 × 10

^{−9}W kg

^{−1}) dissipation rates (Figs. 3, 4) in the overlying 300–400 mab of the water column. Scatterplots of instantaneous 1-m dissipation rates

*ε*and buoyancy frequencies

*N*(Fig. 5) show no preference for high dissipation rates in low stratification or vice versa, so these averages are not biased; unstable instantaneous 1-m stratifications (

*N*

^{2}< 0) cluster toward higher dissipation rates and lower |

*N*

^{2}|. This near-bottom layer of elevated turbulence (Fig. 3) is well stratified with the 0–200-mab average buoyancy frequency 〈

*N*〉 = 3.5 × 10

^{−3}rad s

^{−1}compared to the 300–400-mab 〈

*N*〉 = 4.5 × 10

^{−3}rad s

^{−1}(Fig. 4) in overlying waters. We define these bottom few hundred meters as the “stratified turbulent layer” to distinguish them from any well-mixed bottom boundary layers arising from bottom stress or the diffusive bottom boundary condition (Phillips 1970). The buoyancy Reynolds number Re

*=*

_{b}*ε*/(

*ν*

*N*

^{2}) is 3000 in the stratified turbulent layer and 200 in the overlying water column. Maximum Ozmidov lengths

*ε*and buoyancy frequencies

*N*so the bulk of the stratified turbulent layer has no direct interaction with the bottom. The stratified turbulent layer is likely due to break down of large-amplitude internal waves after reflection from canyon topography (e.g., Hotchkiss and Wunsch 1982; Thorpe 1998; Eriksen 1998) or formation of hydraulic internal lee waves at topographic irregularities (Klymak et al. 2008). In support of this interpretation, isopycnal displacements

*ξ*are 50–100 m in the bottom one- to two-thirds of the water column (Fig. 2), a substantial fraction of the water depth.

Sections of tidally averaged dissipation rate log(*ε*) (red) and (negative) buoyancy frequency log(*N*) (green) profiles along the axes of (top) Soquel and (bottom) Monterey Canyons. Also shown are profiles of the horizontal upcanyon transport *ε* = 10^{−8} to 10^{−7} W kg^{−1} 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.

Citation: Journal of Physical Oceanography 42, 6; 10.1175/JPO-D-11-075.1

Sections of tidally averaged dissipation rate log(*ε*) (red) and (negative) buoyancy frequency log(*N*) (green) profiles along the axes of (top) Soquel and (bottom) Monterey Canyons. Also shown are profiles of the horizontal upcanyon transport *ε* = 10^{−8} to 10^{−7} W kg^{−1} 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.

Citation: Journal of Physical Oceanography 42, 6; 10.1175/JPO-D-11-075.1

Sections of tidally averaged dissipation rate log(*ε*) (red) and (negative) buoyancy frequency log(*N*) (green) profiles along the axes of (top) Soquel and (bottom) Monterey Canyons. Also shown are profiles of the horizontal upcanyon transport *ε* = 10^{−8} to 10^{−7} W kg^{−1} 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.

Citation: Journal of Physical Oceanography 42, 6; 10.1175/JPO-D-11-075.1

Depth-average dissipation rates *ε* (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 × 10^{−8} W kg^{−1}, eddy diffusivity *K* = 16 × 10^{−4} m^{2} s^{−1}, and Ozmidov length scale *L _{O}* = 1.6 m) compared to overlying waters (4 × 10

^{−9}W kg

^{−1}), whereas buoyancy frequencies differ by only 25% (3.5 × 10

^{−3}vs 4.5 × 10

^{−3}rad s

^{−1}).

Citation: Journal of Physical Oceanography 42, 6; 10.1175/JPO-D-11-075.1

Depth-average dissipation rates *ε* (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 × 10^{−8} W kg^{−1}, eddy diffusivity *K* = 16 × 10^{−4} m^{2} s^{−1}, and Ozmidov length scale *L _{O}* = 1.6 m) compared to overlying waters (4 × 10

^{−9}W kg

^{−1}), whereas buoyancy frequencies differ by only 25% (3.5 × 10

^{−3}vs 4.5 × 10

^{−3}rad s

^{−1}).

Citation: Journal of Physical Oceanography 42, 6; 10.1175/JPO-D-11-075.1

Depth-average dissipation rates *ε* (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 × 10^{−8} W kg^{−1}, eddy diffusivity *K* = 16 × 10^{−4} m^{2} s^{−1}, and Ozmidov length scale *L _{O}* = 1.6 m) compared to overlying waters (4 × 10

^{−9}W kg

^{−1}), whereas buoyancy frequencies differ by only 25% (3.5 × 10

^{−3}vs 4.5 × 10

^{−3}rad s

^{−1}).

Citation: Journal of Physical Oceanography 42, 6; 10.1175/JPO-D-11-075.1

Scatterplots of 1-m dissipation rate log(*ε*) vs stratification log(|*N*^{2}|)/2 in (a) the stratified turbulent near-bottom layer and (b) overlying waters. Red dots correspond to *N*^{2} > 0 and Ozmidov lengths *L _{O}* < 1 m, red circles correspond to

*N*

^{2}> 0 and

*L*> 1 m, and blue dots correspond to

_{O}*N*

^{2}< 0. Dotted vertical and horizontal lines correspond to total averages for

*N*

^{2}> 0 (red) and

*N*

^{2}< 0 (blue). Red (

*N*

^{2}> 0) and blue (

*N*

^{2}< 0) horizontal bars represent log(|

*N*

^{2}|) bin averages. The number of points for each stratification condition and the few that had to be rejected are indicated in the top left of each panel. Black diagonal dotted lines correspond to Ozmidov lengths

*L*= (

_{O}*ε*/

*N*

^{3})

^{1/2}of 1, 2, and 5 m as indicated along the upper axis. Unstable 1-m

*N*

^{2}(<0) are mostly found to the left of

*L*= 1 m.

_{O}Citation: Journal of Physical Oceanography 42, 6; 10.1175/JPO-D-11-075.1

Scatterplots of 1-m dissipation rate log(*ε*) vs stratification log(|*N*^{2}|)/2 in (a) the stratified turbulent near-bottom layer and (b) overlying waters. Red dots correspond to *N*^{2} > 0 and Ozmidov lengths *L _{O}* < 1 m, red circles correspond to

*N*

^{2}> 0 and

*L*> 1 m, and blue dots correspond to

_{O}*N*

^{2}< 0. Dotted vertical and horizontal lines correspond to total averages for

*N*

^{2}> 0 (red) and

*N*

^{2}< 0 (blue). Red (

*N*

^{2}> 0) and blue (

*N*

^{2}< 0) horizontal bars represent log(|

*N*

^{2}|) bin averages. The number of points for each stratification condition and the few that had to be rejected are indicated in the top left of each panel. Black diagonal dotted lines correspond to Ozmidov lengths

*L*= (

_{O}*ε*/

*N*

^{3})

^{1/2}of 1, 2, and 5 m as indicated along the upper axis. Unstable 1-m

*N*

^{2}(<0) are mostly found to the left of

*L*= 1 m.

_{O}Citation: Journal of Physical Oceanography 42, 6; 10.1175/JPO-D-11-075.1

Scatterplots of 1-m dissipation rate log(*ε*) vs stratification log(|*N*^{2}|)/2 in (a) the stratified turbulent near-bottom layer and (b) overlying waters. Red dots correspond to *N*^{2} > 0 and Ozmidov lengths *L _{O}* < 1 m, red circles correspond to

*N*

^{2}> 0 and

*L*> 1 m, and blue dots correspond to

_{O}*N*

^{2}< 0. Dotted vertical and horizontal lines correspond to total averages for

*N*

^{2}> 0 (red) and

*N*

^{2}< 0 (blue). Red (

*N*

^{2}> 0) and blue (

*N*

^{2}< 0) horizontal bars represent log(|

*N*

^{2}|) bin averages. The number of points for each stratification condition and the few that had to be rejected are indicated in the top left of each panel. Black diagonal dotted lines correspond to Ozmidov lengths

*L*= (

_{O}*ε*/

*N*

^{3})

^{1/2}of 1, 2, and 5 m as indicated along the upper axis. Unstable 1-m

*N*

^{2}(<0) are mostly found to the left of

*L*= 1 m.

_{O}Citation: Journal of Physical Oceanography 42, 6; 10.1175/JPO-D-11-075.1

The inferred turbulent layer eddy diffusivity *K* = *γ*〈*ε*〉/〈*N*^{2}〉 is 16 × 10^{−4} m^{2} s^{−1}, assuming a mixing efficiency *γ* = 0.2 (Osborn 1980). The use of this mixing efficiency is justified because the stratified turbulent layer is much thicker than the Ozmidov length scale *L _{O}* so that its turbulence is not affected by the bottom boundary. Although recent numerical and laboratory experiments (Shih et al. 2005; Barry et al. 2001) have reported lower mixing efficiencies at high Reynolds numbers, these suffered from domain sizes that could not simultaneously resolve the Ozmidov and Kolmogorov length scales at high Reynolds number. Microstructure observations collected multiple Ozmidov lengths from boundaries in the ocean consistently find high-Reynolds-number turbulent mixing efficiencies

*γ*= 0.20 ±0.05 (Oakey 1982; Gargett et al. 1984; Moum 1996; St. Laurent and Schmitt 1999).

Similar diffusivities were reported in stratified turbulent layers near the bottom at shallower locations along the canyon axis by Carter and Gregg (2002). Microstructure profiles collected near station 31 during a spring tide of August 2006 reveal even higher near-bottom dissipation rates 〈*ε*〉 ~ 2 × 10^{−7} W kg^{−1} and eddy diffusivities *K* in excess of 10^{−3} m^{2} s^{−1}. Because this sampling was not synoptic with the 2008 data and was collected closer to the spring tide, it is not included in the following analysis but provides support for consistently elevated *ε* along the canyon axis. At similar water depths on the continental margin south of Monterey Bay, distant from the canyon, average dissipation rates did not exceed 10^{−8} W kg^{−1} during 2006 sampling and inferred eddy diffusivities were ~*O*(10^{−4} m^{2} s^{−1}).

Estimates of the well-mixed bottom boundary layer thickness *h _{N}* span 0–60 m based on

*T*< 5 × 10

_{z}^{−4}°C m

^{−1}(equivalent to

*N*< 10

^{−3}rad s

^{−1}) and visual inspection of 97 XCP profiles, which measured into the bottom, with roughly 50% less than 5 m thick and 90% less than 30 m thick (Fig. 6), an order of magnitude thinner than the stratified turbulent layer thicknesses

*h*(Fig. 3). Because the 2008 XCP measurements were largely confined to the vicinity of Monterey Bend, we also examined more wide-ranging 129 XCP and 129 XCTD profiles collected in the canyon and on the continental slope to the north during 1997 (Kunze et al. 2002). These exhibit similar statistics, though two XCTD profiles had well-mixed bottom boundary layers thicker than 100 m. CTD bottom boundary layer thicknesses range over 17–57 m (Morrice et al. 2010) but are upper bounds because the CTD profiles did not reach the bottom. No attempt to infer well-mixed bottom boundary layer thicknesses from VMP profiles was made because these rarely reached the bottom and were not accompanied by an altimeter.

_{ε}Cumulative probability distribution functions of well-mixed bottom boundary layer thicknesses *h _{N}* in Monterey Canyon from 2008 XCP (thick solid), 1997 XCP (thin solid), and 1997 XCTD (dotted) profiles into the bottom (based on

*T*< 5 × 10

_{z}^{−4}°C m

^{−1}). Well-mixed boundary layer thicknesses

*h*range over 0–60 m, with 50% less than 5 m thick and 90% less than 30 m thick, an order of magnitude thinner than the stratified turbulent layer thicknesses

_{N}*h*

_{ε}(Fig. 3).

Citation: Journal of Physical Oceanography 42, 6; 10.1175/JPO-D-11-075.1

Cumulative probability distribution functions of well-mixed bottom boundary layer thicknesses *h _{N}* in Monterey Canyon from 2008 XCP (thick solid), 1997 XCP (thin solid), and 1997 XCTD (dotted) profiles into the bottom (based on

*T*< 5 × 10

_{z}^{−4}°C m

^{−1}). Well-mixed boundary layer thicknesses

*h*range over 0–60 m, with 50% less than 5 m thick and 90% less than 30 m thick, an order of magnitude thinner than the stratified turbulent layer thicknesses

_{N}*h*

_{ε}(Fig. 3).

Citation: Journal of Physical Oceanography 42, 6; 10.1175/JPO-D-11-075.1

Cumulative probability distribution functions of well-mixed bottom boundary layer thicknesses *h _{N}* in Monterey Canyon from 2008 XCP (thick solid), 1997 XCP (thin solid), and 1997 XCTD (dotted) profiles into the bottom (based on

*T*< 5 × 10

_{z}^{−4}°C m

^{−1}). Well-mixed boundary layer thicknesses

*h*range over 0–60 m, with 50% less than 5 m thick and 90% less than 30 m thick, an order of magnitude thinner than the stratified turbulent layer thicknesses

_{N}*h*

_{ε}(Fig. 3).

Citation: Journal of Physical Oceanography 42, 6; 10.1175/JPO-D-11-075.1

## 5. Implications for turbulent mixing and exchange with the interior

*h*=

*z*−

*z*is positive upward. Assuming a mixing efficiency

_{b}*γ*= 0.2 and the observed stratified turbulent layer dissipation rate 〈

*ε*〉 = 4 × 10

^{−8}W kg

^{−1}implies mixing times Δ

*t*= ΔAPE/(

*γ*〈

*ε*〉

*h*) = 2–5 months so that restratification processes, such as exchange with the interior (McPhee-Shaw and Kunze 2002) or upslope flow

_{ε}*U*

_{‖}(Garrett 1990; 1991), must operate on similar time scales.

### a. Upcanyon transports

*ℓ*(

_{y}*x*,

*z*) of cross-sectional area

*δ*

*x*δ

*z*(Fig. 7),

*x*is the upchannel coordinate and a Reynolds decomposition has been employed (

*u*=

*U*+

*u*′,

*w*=

*W*+

*w*′, and

*b*=

*B*+

*b*′),

*U*the time-mean horizontal velocity oriented along the canyon axis,

*B*= −

*g*[

*ρ*(

*z*) −

*ρ*

_{0}]/

*ρ*

_{0}the mean buoyancy anomaly, 〈

*u*′

*b*′〉 the upchannel perturbation buoyancy flux oriented up the canyon axis,

*W*the time-mean vertical velocity, and 〈

*w*′

*b*′〉 the turbulent diapycnal buoyancy flux. From mean continuity

*ℓ*(

_{y}*z*) ~ 4

*h*, assuming a triangular canyon cross section with wall slopes ∂

*H*/∂

*y*~ 0.5 and

*h*= 0 at the canyon axis bottom. From Fig. 3, isopycnal slopes ∂

*ξ*/∂

*x*are much gentler than the along-axis bathymetric slope

*s*= ∂

*H*/∂

*x*in the stratified turbulent layer so the upcanyon mean buoyancy gradient

*B*≡

_{x}*N*

^{2}∂

*ξ*/∂

*x*is small [i.e.,

*UB*/

_{x}*WB*~ (∂

_{z}*ξ*/∂

*x*)/

*s*≪ 1], justifying neglect of the first left-hand term in (3); this will not hold in any well-mixed bottom boundary layer where ∂

*ξ*/∂

*x*~

*s*

^{−1}, but, because the well-mixed BBL is thin and the canyon narrows as

*h*approaches zero, there will be little transport associated with this well-mixed bottom boundary layer (Fig. 3). The upcanyon horizontal buoyancy-flux divergence ∂〈

*u*′

*b*′〉/∂

*x*represents fluctuating exchange between the stratified turbulent layer and interior but cannot be quantified at this point; as will be seen, it is not measurable by conventional means. Dropping this term also neglects narrowing of the channel up-canyon ∂

*ℓ*/∂

_{y}*x*.

Schematic illustrating flow geometry in a canyon channel. (a) Along-axis section showing upchannel horizontal flow *U* through cross-sectional area *W* through flat surface *ℓ _{y}*(

*h*)

*δxδz*extending across the canyon, where height above canyon axis bottom

*h*=

*z*−

*z*and

_{b}*z*is the canyon axis bottom depth.

_{b}Citation: Journal of Physical Oceanography 42, 6; 10.1175/JPO-D-11-075.1

Schematic illustrating flow geometry in a canyon channel. (a) Along-axis section showing upchannel horizontal flow *U* through cross-sectional area *W* through flat surface *ℓ _{y}*(

*h*)

*δxδz*extending across the canyon, where height above canyon axis bottom

*h*=

*z*−

*z*and

_{b}*z*is the canyon axis bottom depth.

_{b}Citation: Journal of Physical Oceanography 42, 6; 10.1175/JPO-D-11-075.1

Schematic illustrating flow geometry in a canyon channel. (a) Along-axis section showing upchannel horizontal flow *U* through cross-sectional area *W* through flat surface *ℓ _{y}*(

*h*)

*δxδz*extending across the canyon, where height above canyon axis bottom

*h*=

*z*−

*z*and

_{b}*z*is the canyon axis bottom depth.

_{b}Citation: Journal of Physical Oceanography 42, 6; 10.1175/JPO-D-11-075.1

*w*′

*b*′〉 = −

*γ*〈

*ε*〉, where

*γ*is the mixing efficiency. The diapycnal velocity in (4) can be recast as

*ℓ*depends linearly on

_{y}*h*. We have used the observation that 〈

*ε*〉 and

*N*

^{2}are more or less constant in the stratified turbulent layer (Fig. 3) in the second equality, though this is not strictly true, and assume the same for the mixing efficiency

*γ*. In this layer,

*W*(

*h*) > 0 (upwelling) arises from narrowing of the canyon with depth ∂

*ℓ*/∂

_{y}*z*(hypsometry) rather than the vertical structure of stratification

*N*

^{2}or dissipation rate

*ε*; over sloping topography not so constrained (e.g., continental slopes, ridges, or seamounts), increased turbulent mixing toward the bottom will cause downwelling because then

*W*= (

*γ*/

*N*

^{2})∂

*ε*/∂

*z*with ∂

*ε*/∂

*z*< 0. As will be seen, 1D balances (4) and (5) are not the whole story because they cannot sustain the stratification in the presence of the bottom boundary and do not account for along-axis variability. As

*h*→ 0, canyon narrowing causes the left-hand side of (5) to blow up because the assumption of small

*B*no longer holds in the well-mixed bottom boundary layer. However, we will confine our use of (5) to the thicker overlying stratified turbulent layer.

_{x}Plugging 〈*ε*〉 = 4 × 10^{−8} W kg^{−1} and 〈*N*^{2}〉 = 1.2 × 10^{−5} s^{−2} into (5) produces *W*(*h*) ~ (4 × 10^{−4} m^{2} s^{−1})/*h* ranging from 1 m day^{−1} at *h* = 40 mab (which may be intermittently in a well-mixed bottom boundary layer; e.g., White 1994) to 0.2 m day^{−1} at the top of the stratified turbulent layer (*h*_{ε} = 300 mab). These are two to three orders of magnitude larger than the diapycnal velocity of *O*(1 cm day^{−1}) inferred for the ocean interior (Munk 1966).

*U*

_{‖}= (

*U*=

*W*/

*s*, 0,

*W*), where

*s*= ∂

*H*/∂

*x*= 0.027 is the along-axis bottom slope. We will assume that this relation holds in the stratified turbulent layer in keeping with (4) and previous bottom-normal 1D models to estimate

*U*. This does not contradict dropping of up-canyon mean advection

*U*∂

*B*/∂

*x*in (4) and (5), because this term was deemed small based on near-zero ∂

*B*/∂

*x*=

*N*

^{2}∂

*ξ*/∂

*x*, not

*U*, as will be verified shortly. The mean up-canyon flow is then

^{−1}at

*h*= 40 mab (which again may be intermittently in a well-mixed bottom boundary layer) to 10 m day

^{−1}at the top of the stratified turbulent layer (

*h*

_{ε}= 300 mab), so they are not measurable. Similar magnitudes have been previously inferred in Monterey Canyon (Kunze et al. 2002), on the flanks of the Mid-Atlantic Ridge (St. Laurent et al. 2001), and along the Hawaiian Ridge (Klymak et al. 2006). If these flows are supported by either cross-canyon geostrophic or accelerating up-canyon pressure gradients, corresponding isopycnal displacements are

*O*(1 cm) over kilometers across or along the canyon, which are also not measurable. With these magnitudes, we can infer the ratio of the neglected mean horizontal advection to the inferred vertical advection terms in (3),

*UB*/

_{x}*WN*

^{2}= (

*U*/

*W)*(∂

*ξ*/∂

*x*) < 10

^{−3}, justifying neglect of the mean horizontal advection term in (4) for the stratified turbulent layer.

*dA*=

_{x}*ℓ*(

_{y}*h*)

*dh*= 4

*hdh*because of the assumed triangular cross section of the canyon and canyon wall slope of 0.5. Numerically integrating the fourth term (7) at each station over the stratified turbulent near-bottom layer (Fig. 3) without assuming constant

*ε*and

*N*

^{2}produces upcanyon transports

*T*= 3–15 m

_{U}^{3}s

^{−1}(Fig. 8) in the bottom 300 m in Monterey Canyon; estimates in Soquel Canyon were not stable to small changes in integration bounds so are not included here. This transport can be interpreted as either (i) an area integral over

*dA*=

_{x}*ℓ*(

_{y}*h*)

*dh*= 4

*hdh*of time-mean up-canyon flow

*U*or (ii) an area integral

*dA*=

_{z}*ℓ*(

_{y}*h*)

*dx =*4

*hdx*of the diapycnal velocity

*W*. Thus, in much the same way that global upwelling and stratification can be used to quantify basin-average diapycnal diffusivities (Munk 1966; Munk and Wunsch 1998), turbulent mixing, stratification, and topography reported here can be used to infer mean mixing-driven diapycnal and upcanyon velocities. We caution that only one term, (∂〈

*w*′

*b*′〉/∂

*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, ∂〈

*u*′

*b*′〉/∂

*x*= −∂〈

*w*′

*b*′〉/∂

*z*=

*γ*∂(〈

*ε*〉

*ℓ*)/∂

_{y}*z*.

Inferred upcanyon transports *T _{U}* (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*= 32–34.5 km) implies entrainment from the interior to satisfy continuity, and convergence between stations 22 and 12 (

*r*= 24–32 km) implies injection of boundary water into the interior.

Citation: Journal of Physical Oceanography 42, 6; 10.1175/JPO-D-11-075.1

Inferred upcanyon transports *T _{U}* (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*= 32–34.5 km) implies entrainment from the interior to satisfy continuity, and convergence between stations 22 and 12 (

*r*= 24–32 km) implies injection of boundary water into the interior.

Citation: Journal of Physical Oceanography 42, 6; 10.1175/JPO-D-11-075.1

Inferred upcanyon transports *T _{U}* (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*= 32–34.5 km) implies entrainment from the interior to satisfy continuity, and convergence between stations 22 and 12 (

*r*= 24–32 km) implies injection of boundary water into the interior.

Citation: Journal of Physical Oceanography 42, 6; 10.1175/JPO-D-11-075.1

### 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 m^{3} s^{−1} range (Fig. 8), the transport *T _{U}* at station 22 (Fig. 1) is twice as large at 15 m

^{3}s

^{−1}; this is because the vertical gradient of

*ε*is weaker, so it competes less with ∂

*ℓ*/∂

_{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 convergences must be balanced by entrainment from the interior and injection of boundary layer fluid into the interior (McDougall 1989), respectively (see Fig. 10, which is discussed in detail in section 6), likely along isopycnals. The resulting exchange transport will be comparable in magnitude to the upslope transports [though the small magnitude inferred for

*UB*compared to

_{x}*WN*

^{2}suggests that the neglected perturbation (bolus) transport 〈

*u*′

*b*′〉 may dominate exchange along isopycnals; e.g., Gemmrich and van Haren 2002]. Despite these limitations, inferences about the locations and directions of exchange flows can be used to predict depth ranges where one might expect (i) clear water due to shoreward entrainment of offshore waters driven by upslope transport divergence and (ii) turbid water due to offshore injection of boundary water containing suspended particulate matter driven by convergence of boundary layer transports. Based on inferences from the microstructure measurements, we predict clear water between 1000- and 1100- (±100) m depth and turbid water between 700 and 1000 (±100) m.

Because bottom layers of suspended particulate matter are at least 200 m thick (Fig. 2), only stations deeper than 1200 m can be examined for evidence of detached INLs, which would be signatures of offshore transport associated with transport convergence between 600 and 1000 m in stations 22 and 12 (Figs. 1, 3, 8). Because internal-wave vertical displacements exceed 100 m (Fig. 2), distinct regions of elevated suspended particulate matter and clear water are difficult to discern in plots of beam attenuation coefficient versus depth. However, in density coordinates, a distinct INL is evident between *σ*_{θ} = 27.18 and 27.33 sandwiched by clear layers above and below (Fig. 9) at stations 32, 42, and 45 (Fig. 1). This INL remained on roughly the same isopycnals for all three stations and persisted for more than 4 days, indicating negligible diapycnal sediment flux or settling. The average depth 〈*z*(*σ*_{θ})〉 for these isopycnals is 740–900 (±100) m, consistent with the prediction of offshore transport of waters carrying elevated suspended sediment associated with convergent transport between stations 22 and 12 (Fig. 8). The layers of clear water above and below occupied 〈*z*(*σ*_{θ})〉 = 660–740 m and 900–1020 m, respectively. The 900–1020-m depth band of clear water is consistent with shoreward transport of clear waters from offshore predicted from the transport divergence between stations 27 and 22. There is no evidence of elevated beam attenuation coefficient for stations 22 and 12 within the stratified turbulent layer convergence region compared with the other stations. This indicates that the INL is not due to a particularly strong sediment source but arises from the convergent upcanyon transport.

Beam attenuation coefficient profiles as a function of density *σ*_{θ} at stations 45, 42, and 32 (Fig. 1) offshore of the water depths predicted to have divergent and convergent up-canyon transport (Fig. 8). Average depths of isopycnals 〈*z*(*σ*_{θ})〉 are shown along the right axis. Optical attenuation is elevated near the bottom and in an INL in *σ*_{θ} = 27.17–27.31 (〈*z*〉 = 740–900 m) sandwiched between clear water in *σ*_{θ} = 27.08–27.17 (〈*z*〉 = 660–740 m) and *σ*_{θ} = 27.31–27.38 (〈*z*〉 = 900–1020 m).

Citation: Journal of Physical Oceanography 42, 6; 10.1175/JPO-D-11-075.1

Beam attenuation coefficient profiles as a function of density *σ*_{θ} at stations 45, 42, and 32 (Fig. 1) offshore of the water depths predicted to have divergent and convergent up-canyon transport (Fig. 8). Average depths of isopycnals 〈*z*(*σ*_{θ})〉 are shown along the right axis. Optical attenuation is elevated near the bottom and in an INL in *σ*_{θ} = 27.17–27.31 (〈*z*〉 = 740–900 m) sandwiched between clear water in *σ*_{θ} = 27.08–27.17 (〈*z*〉 = 660–740 m) and *σ*_{θ} = 27.31–27.38 (〈*z*〉 = 900–1020 m).

Citation: Journal of Physical Oceanography 42, 6; 10.1175/JPO-D-11-075.1

Beam attenuation coefficient profiles as a function of density *σ*_{θ} at stations 45, 42, and 32 (Fig. 1) offshore of the water depths predicted to have divergent and convergent up-canyon transport (Fig. 8). Average depths of isopycnals 〈*z*(*σ*_{θ})〉 are shown along the right axis. Optical attenuation is elevated near the bottom and in an INL in *σ*_{θ} = 27.17–27.31 (〈*z*〉 = 740–900 m) sandwiched between clear water in *σ*_{θ} = 27.08–27.17 (〈*z*〉 = 660–740 m) and *σ*_{θ} = 27.31–27.38 (〈*z*〉 = 900–1020 m).

Citation: Journal of Physical Oceanography 42, 6; 10.1175/JPO-D-11-075.1

## 6. Discussion and conclusions

The two major observational conclusions are illustrated schematically in Fig. 10. Well-stratified near-bottom layers with elevated turbulent dissipation rates *ε* are an order of magnitude thicker than well-mixed bottom boundary layers (*h*_{ε} ≫ *h _{N}*; Figs. 2–6, 10a) along the sloping canyon axis. Turbulent near-bottom layers with 〈

*ε*〉 = 4 × 10

^{−8}W kg

^{−1}were found at all stations spanning canyon axis depths of 370–1200 m (Fig. 3). Similar dissipation rates were previously reported for Monterey Canyon axis depths shallower than 500 m (Carter and Gregg 2002). Turbulence dissipation rates

*ε*in the order of magnitude thinner well-mixed bottom boundary layers are not obviously different from those in overlying stratified turbulent waters (Fig. 2).

Schematic illustrating well-mixed (*h _{N}*) and stratified turbulent (

*h*) bottom layers on a slope based on observations. (a) Profiles of buoyancy frequency

_{ε}*N*(thin solid line) and dissipation rate

*ε*(thick solid line) with the heights above bottom of the well-mixed and stratified turbulent layers labeled

*h*and

_{N}*h*, respectively. (b) An across-isobath section showing isopycnals (thin solid lines) and the heights above bottom of the two layers (dotted diagonal lines). Isopycnals dip only in the well-mixed BBL (

_{ε}*h*<

*h*). Mixing-driven flow is parallel to the slope unless there is convergence (divergence) in the upslope flow

_{N}*U*

_{‖}to drive injection of near-bottom fluid (entrainment of ocean interior water) through either mean

*U*or fluctuating

*u*′ flows. Light gray stippling depicts turbid boundary layers and intermediate nepheloid layers.

Citation: Journal of Physical Oceanography 42, 6; 10.1175/JPO-D-11-075.1

Schematic illustrating well-mixed (*h _{N}*) and stratified turbulent (

*h*) bottom layers on a slope based on observations. (a) Profiles of buoyancy frequency

_{ε}*N*(thin solid line) and dissipation rate

*ε*(thick solid line) with the heights above bottom of the well-mixed and stratified turbulent layers labeled

*h*and

_{N}*h*, respectively. (b) An across-isobath section showing isopycnals (thin solid lines) and the heights above bottom of the two layers (dotted diagonal lines). Isopycnals dip only in the well-mixed BBL (

_{ε}*h*<

*h*). Mixing-driven flow is parallel to the slope unless there is convergence (divergence) in the upslope flow

_{N}*U*

_{‖}to drive injection of near-bottom fluid (entrainment of ocean interior water) through either mean

*U*or fluctuating

*u*′ flows. Light gray stippling depicts turbid boundary layers and intermediate nepheloid layers.

Citation: Journal of Physical Oceanography 42, 6; 10.1175/JPO-D-11-075.1

Schematic illustrating well-mixed (*h _{N}*) and stratified turbulent (

*h*) bottom layers on a slope based on observations. (a) Profiles of buoyancy frequency

_{ε}*N*(thin solid line) and dissipation rate

*ε*(thick solid line) with the heights above bottom of the well-mixed and stratified turbulent layers labeled

*h*and

_{N}*h*, respectively. (b) An across-isobath section showing isopycnals (thin solid lines) and the heights above bottom of the two layers (dotted diagonal lines). Isopycnals dip only in the well-mixed BBL (

_{ε}*h*<

*h*). Mixing-driven flow is parallel to the slope unless there is convergence (divergence) in the upslope flow

_{N}*U*

_{‖}to drive injection of near-bottom fluid (entrainment of ocean interior water) through either mean

*U*or fluctuating

*u*′ flows. Light gray stippling depicts turbid boundary layers and intermediate nepheloid layers.

Citation: Journal of Physical Oceanography 42, 6; 10.1175/JPO-D-11-075.1

Near-bottom stratified turbulent layers are by no means unique to Monterey Canyon. Similar features have been observed over other sloping topography including seamounts (Toole et al. 1997; Lueck and Mudge 1997; Eriksen 1998), ridges (Polzin et al. 1997; Lien and Gregg 2001; Thurnherr et al. 2005; Carter et al. 2006; Aucan et al. 2006; Kunze et al. 2006; Klymak et al. 2008), and the continental slope (Moum et al. 2002; Gemmrich and van Haren 2002; Nash et al. 2004, 2007). Thus, oft-repeated arguments that turbulence on slopes should be ineffective at mixing because it stirs already-mixed waters (Garrett 1990, 1991, 2001; Garrett et al. 1993) do not always hold and we will argue do not hold for the most intense turbulence.

At sites where energetic breaking internal waves are the principal source of near-boundary turbulence, as where either internal-wave generation or interactions with the topography are strong, 1D modeling (e.g., Mellor and Yamada 1982; Ramsden 1995; Umlauf and Burchard 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. 2004) and scattering (St. Laurent and Garrett 2002; Polzin 2009) of low-mode internal waves by topography, as well as generation of internal tide (Klymak et al. 2008; Legg and Klymak 2008) and internal lee waves (Nikurashin and Ferrari 2010a,b). These topographic interactions produce unstable internal-wave shears and overturns in the stratified water column (e.g., Slinn and Riley 1996; Eriksen 1998; Thorpe 1998; Gayen and Sarkar 2011) because of the flux of internal-wave energy into and out of the boundary supplying energy for water-column turbulence. By excluding across- and along-isobath variability, 1D bottom boundary layer modeling cannot induce the lateral buoyancy and pressure gradients associated with internal-wave radiation. Therefore, in situations where internal waves are the primary energy source for turbulence, a 2D or higher-dimension closure is necessary. Weak internal-wave fields that only break because of bottom stress may confine their turbulence to well-mixed bottom boundary layers, but, even under these conditions, overturning has been reported because of the advection of heavy over light water (Slinn and Riley 1996), an inherently 2D process.

Near-bottom turbulence can also be caused by mean along-isobath flows inducing up- or downslope Ekman flows (Trowbridge and Lentz 1991; MacCready and Rhines 1991, 1993; Middleton and Ramsden 1996). Xing and Davies (1999) report that flows of finite cross-isobath width induce transport convergences and divergences in the bottom Ekman layer as well. Condie (1999) found high mixing efficiencies associated with downslope Ekman flows caused by along-isobath flow with shallow water on the right (in the sense of deep western boundary currents).

A global assessment of diapycnal transport in canyons can be obtained from the ratio of mixing in canyons *r* = 0.2 is the fraction of continental slope incised by canyons based on the Pacific North American continental slope between the equator and Alaska (Hickey 1995), *n* = 100 is the number of Earth radii *ℓ _{x}* =

*h*

_{ε}/

*s*= 10 km is the length of canyon intersecting the stratified turbulent layer,

*h*

_{ε}= 300 m is the thickness of the turbulent stratified layer, and

*s =*∂

*H/*∂

*x*= 0.027 is the along-axis bottom slope. The ratio

^{−4}m

^{2}s

^{−1}(Gregg 1987; Ledwell et al. 1993; Kunze and Sanford 1996; Kunze et al. 2006), which in turn accounts for about 10% of the transport based on the bottom-water formation rate (Munk 1966; Munk and Wunsch 1998). We caution that it is not known whether most canyons are as turbulent as Monterey Canyon. However, intensified internal tide signals appear to be a universal feature of canyons (Shepard et al. 1974, 1979), and recent measurements have found intensified turbulence in Gaoping (Lee et al. 2009), as well as more typical continental slope Ascension (Gregg et al. 2011), Barrow (Shroyer 2012), and Barkley Canyons. A similar global integration of the layer dissipation rate

The along-axis section (Figs. 8, 10b) demonstrates our second challenge to the applicability of 1D boundary layer theory (4) over sloping topography: that is, that turbulence-driven upslope transports *T _{U}* need not be uniform. Other theoretical and laboratory studies have addressed convergence and exchange associated with nonuniform buoyancy flux theoretically and in the laboratory (Phillips et al. 1986; McDougall 1989; McPhee-Shaw and Kunze 2002). Nonuniform upcanyon transport was posed as a proof by contradiction in that the derived balance (4) is 1D. Although a 1D balance might hold between stations 42 and 27 and between stations 12 and 7 (Fig. 8), the anomalously high transport at station 22 will drive 2D flows and exchange with the interior. Inferred turbulence-driven upcanyon flows

*U*range from 50 m day

^{−1}(0.05 cm s

^{−1}) at

*h*= 40 mab to 10 m day

^{−1}at the top of the near-bottom turbulent layer (

*h*

_{ε}= 300 mab) so would not be directly measurable by conventional current meters (Xu and Noble 2009) even if such mean flows were not biased by topographic steering hysteresis (Rosenfeld et al. 1999). Upcanyon transports in Monterey Canyon are 3–8 m

^{3}s

^{−1}(Fig. 8). Higher upslope transport at station 22 (15 m

^{3}s

^{−1}) compared to deeper station 27 and shallower station 12 implies divergent boundary transport between 1000- and 1100- (±100) m depths, which should entrain water from the interior into the boundary layer, and convergent boundary transport between 700 and 1000 (±100) m, which should inject turbid boundary fluid into the interior. In the case of converging upslope transports, injection of sediment-laden bottom-layer water into the interior will result in intermediate nepheloid layers as confirmed by measured beam attenuation coefficients (Fig. 9). In the case of diverging upslope transports, clear interior flow will be entrained into the stratified turbulent near-bottom layer.

In general, variability of slope topography, stratification (Imberger and Ivey 1993), and internal-wave fields will all create turbulent heterogeneity, which will in turn drive convergences and divergences of turbulence-driven cross-isobath transports, leading to exchange with the interior to impact the ocean as a whole (McDougall 1989; McPhee-Shaw 2006). For example, Nash et al. (2004) described a turbulence hotspot on the semidiurnally near-critical part of the Virginia continental slope between 1000- and 1300-m depths. Nash et al. (2007) reported two isolated turbulent hotspots on the Oregon slope, both associated with the semidiurnal tide. Turbulent hotspots are often found over slopes that are near-critical for semidiurnal frequencies (Levine and Boyd 2006; Aucan and Merrifield 2008), often at continental shelf breaks (Cacchione and Drake 1986) and on ridge crests (Nash et al. 2006; Klymak et al. 2008). In the absence of converging canyon walls, increasing turbulent mixing toward the bottom over unrestricted slopes will produce downwelling rather than upwelling. More observations are needed over the undersampled continental margins to better characterize the spatial and temporal variability of turbulence in this environment and determine its role in mixing the World Ocean.

The measurements made here only allowed reliable quantification of the diapycnal mixing term ∂〈*w*′*b*′〉/∂*z* in (3), which could be balanced by any of the remaining three terms. The vertical balance inferred between diapycnal mixing and upwelling (4) required neglect of mean and perturbation horizontal flux terms. However, the inferred upcanyon transport divergence (Fig. 8) requires at least one of the horizontal terms not to vanish. Although we were able to justify neglect of mean advection, the perturbation horizontal flux cannot be quantified with conventional instruments and cannot be complete ruled out as a primary balancing term (e.g., Gemmrich and van Haren 2002). Future work might be better able to close this budget using dye injections to quantify the vertical mixing and offshore isopycnal transport.

## Acknowledgments

Invaluable assistance in the data collection was provided by Kevin Bartlett. Danielle Wain provided guidance into the lake literature. Additional helpful comments came from Jody Klymak, Trevor McDougall, and an anonymous reviewer. The captain and crew of *Point Sur* are commended for their able seamanship. Funding for this research came from NSF Grant OCE-0728341, ONR Grants N00014-05-1-0332 and N00014-08-1-0983, and NSERC Canada Research Chair funds.

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