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## Abstract

Ocean lee waves occur on length scales that are smaller than the grid scale of global circulation models (GCMs). Therefore, such models must parameterize the drag associated with launching lee waves. This paper compares the lee wave drag predicted by existing parameterizations with the drag measured in high-resolution nonhydrostatic numerical simulations of a lee wave over periodic sinusoidal bathymetry. The simulations afford a time-varying glimpse at the nonlinear and nonhydrostatic oceanic lee wave spinup process and identify a characteristic time scale to reach steady state. The maximum instantaneous lee wave drag observed during the spinup period is found to be well predicted by linear lee wave theory for all hill heights. In steady state, the simulations demonstrate the applicability of parameterizing the drag based on applying linear theory to the lowest overtopping streamline of the flow (LOTS), as is currently employed in GCMs. However, because existing parameterizations are based only on the height of the LOTS, they implicitly assume hydrostatic flow. For hills tall enough to trap water in their valleys, the simulations identify a set of nonhydrostatic processes that can result in a reduction of the lee wave drag from that given by hydrostatic parameterizations. The simulations suggest implementing a time-dependent nonhydrostatic version of the LOTS-based parameterization of lee wave drag and demonstrate the remarkable applicability of linear lee wave theory to oceanic lee waves.

## Abstract

Ocean lee waves occur on length scales that are smaller than the grid scale of global circulation models (GCMs). Therefore, such models must parameterize the drag associated with launching lee waves. This paper compares the lee wave drag predicted by existing parameterizations with the drag measured in high-resolution nonhydrostatic numerical simulations of a lee wave over periodic sinusoidal bathymetry. The simulations afford a time-varying glimpse at the nonlinear and nonhydrostatic oceanic lee wave spinup process and identify a characteristic time scale to reach steady state. The maximum instantaneous lee wave drag observed during the spinup period is found to be well predicted by linear lee wave theory for all hill heights. In steady state, the simulations demonstrate the applicability of parameterizing the drag based on applying linear theory to the lowest overtopping streamline of the flow (LOTS), as is currently employed in GCMs. However, because existing parameterizations are based only on the height of the LOTS, they implicitly assume hydrostatic flow. For hills tall enough to trap water in their valleys, the simulations identify a set of nonhydrostatic processes that can result in a reduction of the lee wave drag from that given by hydrostatic parameterizations. The simulations suggest implementing a time-dependent nonhydrostatic version of the LOTS-based parameterization of lee wave drag and demonstrate the remarkable applicability of linear lee wave theory to oceanic lee waves.

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## Abstract

Turbulent mixing adjacent to the Velasco Reef and Kyushu–Palau Ridge, off northern Palau in the western equatorial Pacific Ocean, is examined using shipboard and moored observations. The study focuses on a 9-day-long, ship-based microstructure and velocity survey, conducted in November–December 2016. Several sections (9–15 km in length) of microstructure, hydrographic, and velocity fields were acquired over and around the reef, where water depths ranged from 50 to 3000 m. Microstructure profiles were collected while steaming slowly either toward or away from the reef, and underway current surveys were conducted along quasi-rectangular boxes with side lengths of 5–10 km. Near the reef, both tidal and subtidal motions were important, while subtidal motions were stronger away from the reef. Vertical shears of currents and mixing were stronger on the northern and eastern flanks of the reef than on the western flanks. High turbulent kinetic energy dissipation rates, 10^{−6}–10^{−4} W kg^{−1}, and large values of eddy diffusivities, 10^{−4}–10^{−2} m^{2} s^{−1}, with strong turbulent heat fluxes, 100–500 W m^{−2}, were found. Currents flowing along the eastern side separated at the northern tip of the reef and generated submesoscale cyclonic vorticity of about 2–4 times the planetary vorticity. The analysis suggests that a torque, imparted by the turbulent bottom stress, generated the cyclonic vorticity at the northern boundary. The northern reef is associated with high vertical transports resulting from both submesoscale flow convergences and energetic mixing. Even though the area around Palau represents a small footprint of the ocean, vertical velocities and mixing rates are several orders magnitude larger than in the open ocean.

## Abstract

Turbulent mixing adjacent to the Velasco Reef and Kyushu–Palau Ridge, off northern Palau in the western equatorial Pacific Ocean, is examined using shipboard and moored observations. The study focuses on a 9-day-long, ship-based microstructure and velocity survey, conducted in November–December 2016. Several sections (9–15 km in length) of microstructure, hydrographic, and velocity fields were acquired over and around the reef, where water depths ranged from 50 to 3000 m. Microstructure profiles were collected while steaming slowly either toward or away from the reef, and underway current surveys were conducted along quasi-rectangular boxes with side lengths of 5–10 km. Near the reef, both tidal and subtidal motions were important, while subtidal motions were stronger away from the reef. Vertical shears of currents and mixing were stronger on the northern and eastern flanks of the reef than on the western flanks. High turbulent kinetic energy dissipation rates, 10^{−6}–10^{−4} W kg^{−1}, and large values of eddy diffusivities, 10^{−4}–10^{−2} m^{2} s^{−1}, with strong turbulent heat fluxes, 100–500 W m^{−2}, were found. Currents flowing along the eastern side separated at the northern tip of the reef and generated submesoscale cyclonic vorticity of about 2–4 times the planetary vorticity. The analysis suggests that a torque, imparted by the turbulent bottom stress, generated the cyclonic vorticity at the northern boundary. The northern reef is associated with high vertical transports resulting from both submesoscale flow convergences and energetic mixing. Even though the area around Palau represents a small footprint of the ocean, vertical velocities and mixing rates are several orders magnitude larger than in the open ocean.

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## Abstract

Towed shipboard and moored observations show internal gravity waves over a tall, supercritical submarine ridge that reaches to 1000 m below the ocean surface in the tropical western Pacific north of Palau. The lee-wave or topographic Froude number, *Nh*
_{0}/*U*
_{0} (where *N* is the buoyancy frequency, *h*
_{0} the ridge height, and *U*
_{0} the farfield velocity), ranged between 25 and 140. The waves were generated by a superposition of tidal and low-frequency flows and thus had two distinct energy sources with combined amplitudes of up to 0.2 m s^{−1}. Local breaking of the waves led to enhanced rates of dissipation of turbulent kinetic energy reaching above 10^{−6} W kg^{−1} in the lee of the ridge near topography. Turbulence observations showed a stark contrast between conditions at spring and neap tide. During spring tide, when the tidal flow dominated, turbulence was approximately equally distributed around both sides of the ridge. During neap tide, when the mean flow dominated over tidal oscillations, turbulence was mostly observed on the downstream side of the ridge relative to the mean flow. The drag exerted by the ridge on the flow, estimated to

## Abstract

Towed shipboard and moored observations show internal gravity waves over a tall, supercritical submarine ridge that reaches to 1000 m below the ocean surface in the tropical western Pacific north of Palau. The lee-wave or topographic Froude number, *Nh*
_{0}/*U*
_{0} (where *N* is the buoyancy frequency, *h*
_{0} the ridge height, and *U*
_{0} the farfield velocity), ranged between 25 and 140. The waves were generated by a superposition of tidal and low-frequency flows and thus had two distinct energy sources with combined amplitudes of up to 0.2 m s^{−1}. Local breaking of the waves led to enhanced rates of dissipation of turbulent kinetic energy reaching above 10^{−6} W kg^{−1} in the lee of the ridge near topography. Turbulence observations showed a stark contrast between conditions at spring and neap tide. During spring tide, when the tidal flow dominated, turbulence was approximately equally distributed around both sides of the ridge. During neap tide, when the mean flow dominated over tidal oscillations, turbulence was mostly observed on the downstream side of the ridge relative to the mean flow. The drag exerted by the ridge on the flow, estimated to

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## Abstract

The effects of topography on the linear stability of both barotropic vortices and two-layer, baroclinic vortices are examined by considering cylindrical topography and vortices with stepwise relative vorticity profiles in the quasigeostrophic approximation. Four vortex configurations are considered, classified by the number of relative vorticity steps in the horizontal and the number of layers in the vertical: barotropic one-step vortex (Rankine vortex), barotropic two-step vortex, and their two-layer, baroclinic counterparts with the vorticity steps in the upper layer. In the barotropic calculation, the vortex is destabilized by topography having an oppositely signed potential vorticity jump while stabilized by topography of same-signed jump, that is, anticyclones are destabilized by seamounts while stabilized by depressions. Further, topography of appropriate sign and magnitude can excite a mode-1 instability for a two-step vortex, especially relevant for topographic encounters of an otherwise stable vortex. The baroclinic calculation is in general consistent with the barotropic calculation except that the growth rate weakens and, for a two-step vortex, becomes less sensitive to topography (sign and magnitude) as baroclinicity increases. The smaller growth rate for a baroclinic vortex is consistent with previous findings that vortices with sufficient baroclinic structure could cross the topography relatively easily. Nonlinear contour dynamics simulations are conducted to confirm the linear stability analysis and to describe the subsequent evolution.

## Abstract

The effects of topography on the linear stability of both barotropic vortices and two-layer, baroclinic vortices are examined by considering cylindrical topography and vortices with stepwise relative vorticity profiles in the quasigeostrophic approximation. Four vortex configurations are considered, classified by the number of relative vorticity steps in the horizontal and the number of layers in the vertical: barotropic one-step vortex (Rankine vortex), barotropic two-step vortex, and their two-layer, baroclinic counterparts with the vorticity steps in the upper layer. In the barotropic calculation, the vortex is destabilized by topography having an oppositely signed potential vorticity jump while stabilized by topography of same-signed jump, that is, anticyclones are destabilized by seamounts while stabilized by depressions. Further, topography of appropriate sign and magnitude can excite a mode-1 instability for a two-step vortex, especially relevant for topographic encounters of an otherwise stable vortex. The baroclinic calculation is in general consistent with the barotropic calculation except that the growth rate weakens and, for a two-step vortex, becomes less sensitive to topography (sign and magnitude) as baroclinicity increases. The smaller growth rate for a baroclinic vortex is consistent with previous findings that vortices with sufficient baroclinic structure could cross the topography relatively easily. Nonlinear contour dynamics simulations are conducted to confirm the linear stability analysis and to describe the subsequent evolution.

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## Abstract

Microstructure measurements in Drake Passage and on the flanks of Kerguelen Plateau find turbulent dissipation rates *ε* on average factors of 2–3 smaller than linear lee-wave generation predictions, as well as a factor of 3 smaller than the predictions of a well-established parameterization based on finescale shear and strain. Here, the possibility that these discrepancies are a result of conservation of wave action *E*/*ω*
_{
L
} = *E*/|*kU*| is explored. Conservation of wave action will transfer a fraction of the lee-wave radiation back to the mean flow if the waves encounter weakening currents *U*, where the intrinsic or Lagrangian frequency *ω*
_{
L
} = |*kU*| ↓ |*f*| and *k* the along-stream horizontal wavenumber, where *kU* ≡ **k** ⋅ **V**. The dissipative fraction of power that is lost to turbulence depends on the Doppler shift of the intrinsic frequency between generation and breaking, hence on the topographic height spectrum and bandwidth *N*/*f*. The partition between dissipation and loss to the mean flow is quantified for typical topographic height spectral shapes and *N*/*f* ratios found in the abyssal ocean under the assumption that blocking is local in wavenumber. Although some fraction of lee-wave generation is always dissipated in a rotating fluid, lee waves are not as large a sink for balanced energy or as large a source for turbulence as previously suggested. The dissipative fraction is 0.44–0.56 for topographic spectral slopes and buoyancy frequencies typical of the deep Southern Ocean, insensitive to flow speed *U* and topographic splitting. Lee waves are also an important mechanism for redistributing balanced energy within their generating bottom current.

## Abstract

Microstructure measurements in Drake Passage and on the flanks of Kerguelen Plateau find turbulent dissipation rates *ε* on average factors of 2–3 smaller than linear lee-wave generation predictions, as well as a factor of 3 smaller than the predictions of a well-established parameterization based on finescale shear and strain. Here, the possibility that these discrepancies are a result of conservation of wave action *E*/*ω*
_{
L
} = *E*/|*kU*| is explored. Conservation of wave action will transfer a fraction of the lee-wave radiation back to the mean flow if the waves encounter weakening currents *U*, where the intrinsic or Lagrangian frequency *ω*
_{
L
} = |*kU*| ↓ |*f*| and *k* the along-stream horizontal wavenumber, where *kU* ≡ **k** ⋅ **V**. The dissipative fraction of power that is lost to turbulence depends on the Doppler shift of the intrinsic frequency between generation and breaking, hence on the topographic height spectrum and bandwidth *N*/*f*. The partition between dissipation and loss to the mean flow is quantified for typical topographic height spectral shapes and *N*/*f* ratios found in the abyssal ocean under the assumption that blocking is local in wavenumber. Although some fraction of lee-wave generation is always dissipated in a rotating fluid, lee waves are not as large a sink for balanced energy or as large a source for turbulence as previously suggested. The dissipative fraction is 0.44–0.56 for topographic spectral slopes and buoyancy frequencies typical of the deep Southern Ocean, insensitive to flow speed *U* and topographic splitting. Lee waves are also an important mechanism for redistributing balanced energy within their generating bottom current.

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## Abstract

In this study, a 2-yr time series of velocity profiles to 1000 m from meridional glider surveys is used to characterize the wake in the lee of a large island in the western tropical North Pacific Ocean, Palau. Surveys were completed along sections to the east and west of the island to capture both upstream and downstream conditions. Objectively mapped in time and space, mean sections of velocity show the incident westward North Equatorial Current accelerating around the island of Palau, increasing from 0.1 to 0.2 m s^{−1} at the surface. Downstream of the island, elevated velocity variability and return flow in the lee are indicative of boundary layer separation. Isolating for periods of depth-average westward flow reveals a length scale in the wake that reflects local details of the topography. Eastward flow is shown to produce an asymmetric wake. Depth-average velocity time series indicate that energetic events (on time scales from weeks to months) are prevalent. These events are associated with mean vorticity values in the wake up to 0.3*f* near the surface and with instantaneous values that can exceed *f* (the local Coriolis frequency) during periods of sustained, anomalously strong westward flow. Thus, ageostrophic effects become important to first order.

## Abstract

In this study, a 2-yr time series of velocity profiles to 1000 m from meridional glider surveys is used to characterize the wake in the lee of a large island in the western tropical North Pacific Ocean, Palau. Surveys were completed along sections to the east and west of the island to capture both upstream and downstream conditions. Objectively mapped in time and space, mean sections of velocity show the incident westward North Equatorial Current accelerating around the island of Palau, increasing from 0.1 to 0.2 m s^{−1} at the surface. Downstream of the island, elevated velocity variability and return flow in the lee are indicative of boundary layer separation. Isolating for periods of depth-average westward flow reveals a length scale in the wake that reflects local details of the topography. Eastward flow is shown to produce an asymmetric wake. Depth-average velocity time series indicate that energetic events (on time scales from weeks to months) are prevalent. These events are associated with mean vorticity values in the wake up to 0.3*f* near the surface and with instantaneous values that can exceed *f* (the local Coriolis frequency) during periods of sustained, anomalously strong westward flow. Thus, ageostrophic effects become important to first order.

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## Abstract

Drag and turbulence in steady stratified flows over “abyssal hills” have been parameterized using linear theory and rates of energy cascade due to wave–wave interactions. Linear theory has no drag or energy loss due to large-scale bathymetry because waves with intrinsic frequency less than the Coriolis frequency are evanescent. Numerical work has tested the theory by high passing the topography and estimating the radiation and turbulence. Adding larger-scale bathymetry that would generate evanescent internal waves generates nonlinear and turbulent flow, driving a dissipation approximately twice that of the radiating waves for the topographic spectrum chosen. This drag is linear in the forcing velocity, in contrast to atmospheric parameterizations that have quadratic drag. Simulations containing both small- and large-scale bathymetry have more dissipation than just adding the large- and small-scale dissipations together, so the scales couple. The large-scale turbulence is localized, generally in the lee of large obstacles. Medium-scale regional models partially resolve the “nonpropagating” wavenumbers, leading to the question of whether they need the large-scale energy loss to be parameterized. Varying the resolution of the simulations indicates that if the ratio of gridcell height to width is less than the root-mean-square topographic slope, then the dissipation is overestimated in coarse models (by up to 25%); conversely, it can be underestimated by up to a factor of 2 if the ratio is greater. Most regional simulations are likely in the second regime and should have extra drag added to represent the large-scale bathymetry, and the deficit is at least as large as that parameterized for abyssal hills.

## Abstract

Drag and turbulence in steady stratified flows over “abyssal hills” have been parameterized using linear theory and rates of energy cascade due to wave–wave interactions. Linear theory has no drag or energy loss due to large-scale bathymetry because waves with intrinsic frequency less than the Coriolis frequency are evanescent. Numerical work has tested the theory by high passing the topography and estimating the radiation and turbulence. Adding larger-scale bathymetry that would generate evanescent internal waves generates nonlinear and turbulent flow, driving a dissipation approximately twice that of the radiating waves for the topographic spectrum chosen. This drag is linear in the forcing velocity, in contrast to atmospheric parameterizations that have quadratic drag. Simulations containing both small- and large-scale bathymetry have more dissipation than just adding the large- and small-scale dissipations together, so the scales couple. The large-scale turbulence is localized, generally in the lee of large obstacles. Medium-scale regional models partially resolve the “nonpropagating” wavenumbers, leading to the question of whether they need the large-scale energy loss to be parameterized. Varying the resolution of the simulations indicates that if the ratio of gridcell height to width is less than the root-mean-square topographic slope, then the dissipation is overestimated in coarse models (by up to 25%); conversely, it can be underestimated by up to a factor of 2 if the ratio is greater. Most regional simulations are likely in the second regime and should have extra drag added to represent the large-scale bathymetry, and the deficit is at least as large as that parameterized for abyssal hills.