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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.

## 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.

## 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.

## 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.