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- Author or Editor: Jody M. Klymak x

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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.

## Abstract

Two-dimensional simulations of stratified flow over an isolated ridge are used to evaluate energy dissipation associated with barotropic tidal flow over topography with critical or near-critical slope. In the midslope region, a shallow borelike flow forms along the bottom in a layer where dissipation rates are increased by several orders of magnitude, and the flow speed is about twice the barotropic background velocity. The height and turbulence in this layer depend on predictable functions of stratification, rotation, and the characteristic forcing speed. A physically sound power-law parameterization of the total energy dissipation associated with this turbulent layer is presented. This simple parameterization is also applicable to coarser-resolution models, where it may be included to compute energy dissipation above continental slopes, even for cases where the slope angle differs somewhat from criticality.

## Abstract

Two-dimensional simulations of stratified flow over an isolated ridge are used to evaluate energy dissipation associated with barotropic tidal flow over topography with critical or near-critical slope. In the midslope region, a shallow borelike flow forms along the bottom in a layer where dissipation rates are increased by several orders of magnitude, and the flow speed is about twice the barotropic background velocity. The height and turbulence in this layer depend on predictable functions of stratification, rotation, and the characteristic forcing speed. A physically sound power-law parameterization of the total energy dissipation associated with this turbulent layer is presented. This simple parameterization is also applicable to coarser-resolution models, where it may be included to compute energy dissipation above continental slopes, even for cases where the slope angle differs somewhat from criticality.

## Abstract

Horizontal tow measurements of internal waves are rare and have been largely supplanted in recent decades by vertical profile measurements. Here, estimates of isotherm displacements and turbulence dissipation rate from a towed vehicle deployed near Hawaii are presented. The displacement data are interpreted in terms of horizontal wavenumber spectra of isopycnal slope. The spectra span scales from 5 km to 0.1 m, encompassing both internal waves and turbulence. The turbulence subrange is identified using a standard turbulence fit, and the rest of the motions are deemed to be internal waves. The remaining subrange has a slightly red slope (*ϕ* ∼ *k*
^{−1/2}
_{
x
}) and vertical coherences compatible with internal waves, in agreement with previous towed measurements. However, spectral amplitudes in the internal wave subrange exhibit surprisingly little variation despite a four-order-of-magnitude change in turbulence dissipation rate observed at the site. The shape and amplitude of the horizontal spectra are shown to be consistent with observations and models of vertical internal wave spectra that consist of two subranges: a “linear” subrange (*ϕ* ∼ *k*
^{0}
_{
z
}) and a red “saturated” subrange (*ϕ* ∼ *k*
^{−1}
_{
z
}). These two subranges are blurred in the transformation to horizontal spectra, yielding slopes close to those observed. The saturated subrange does not admit amplitude variations in the spectra yet is an important component of the measured horizontal spectra, explaining the poor correspondence with the dissipation rate.

## Abstract

Horizontal tow measurements of internal waves are rare and have been largely supplanted in recent decades by vertical profile measurements. Here, estimates of isotherm displacements and turbulence dissipation rate from a towed vehicle deployed near Hawaii are presented. The displacement data are interpreted in terms of horizontal wavenumber spectra of isopycnal slope. The spectra span scales from 5 km to 0.1 m, encompassing both internal waves and turbulence. The turbulence subrange is identified using a standard turbulence fit, and the rest of the motions are deemed to be internal waves. The remaining subrange has a slightly red slope (*ϕ* ∼ *k*
^{−1/2}
_{
x
}) and vertical coherences compatible with internal waves, in agreement with previous towed measurements. However, spectral amplitudes in the internal wave subrange exhibit surprisingly little variation despite a four-order-of-magnitude change in turbulence dissipation rate observed at the site. The shape and amplitude of the horizontal spectra are shown to be consistent with observations and models of vertical internal wave spectra that consist of two subranges: a “linear” subrange (*ϕ* ∼ *k*
^{0}
_{
z
}) and a red “saturated” subrange (*ϕ* ∼ *k*
^{−1}
_{
z
}). These two subranges are blurred in the transformation to horizontal spectra, yielding slopes close to those observed. The saturated subrange does not admit amplitude variations in the spectra yet is an important component of the measured horizontal spectra, explaining the poor correspondence with the dissipation rate.

## Abstract

Isopycnal slope spectra were computed from thermistor data obtained using a microstructure platform towed through turbulence generated by internal tidal motions near the Hawaiian Ridge. The spectra were compared with turbulence dissipation rates *ε* that are estimated using shear probes. The turbulence subrange of isopycnal slope spectra extends to surprisingly large horizontal wavelengths (>100 m). A four-order-of-magnitude range in turbulence dissipation rates at this site reveals that isopycnal slope spectra ∝ *ε*
^{2/3}
*k*
^{1/3}
_{
x
}. The turbulence spectral subrange (*k _{x}
* > 0.4 cpm) responds to the dissipation rate as predicted by the Batchelor model spectrum, both in amplitude and towed vertical coherence. Scales between 100 and 1000 m are modeled by a linear combination of internal waves and turbulence while at larger scales internal waves dominate. The broad bandwidth of the turbulence subrange means that a fit of spectral amplitude to the Batchelor model yields reasonable estimates of

*ε*, even when applied at scales of tens of meters that in vertical profiles would be obscured by other fine structure.

## Abstract

Isopycnal slope spectra were computed from thermistor data obtained using a microstructure platform towed through turbulence generated by internal tidal motions near the Hawaiian Ridge. The spectra were compared with turbulence dissipation rates *ε* that are estimated using shear probes. The turbulence subrange of isopycnal slope spectra extends to surprisingly large horizontal wavelengths (>100 m). A four-order-of-magnitude range in turbulence dissipation rates at this site reveals that isopycnal slope spectra ∝ *ε*
^{2/3}
*k*
^{1/3}
_{
x
}. The turbulence spectral subrange (*k _{x}
* > 0.4 cpm) responds to the dissipation rate as predicted by the Batchelor model spectrum, both in amplitude and towed vertical coherence. Scales between 100 and 1000 m are modeled by a linear combination of internal waves and turbulence while at larger scales internal waves dominate. The broad bandwidth of the turbulence subrange means that a fit of spectral amplitude to the Batchelor model yields reasonable estimates of

*ε*, even when applied at scales of tens of meters that in vertical profiles would be obscured by other fine structure.

## Abstract

Observations and modeling simulations are presented that illustrate the importance of a density contrast and the upstream response to the time dependence of stratified flow over the Knight Inlet sill. Repeated sections of velocity and density show that the flow during ebb and flood tides is quite different: a large lee wave develops early in flood tide, whereas lee-wave growth is suppressed until the second half of ebb tide. There is a large upstream response that displaces as much water as accumulates in the lee wave, one that is large enough to also block the flow at a depth roughly consistent with simple dynamics. There is a large density contrast between the seaward and landward sides of the sill, and a “salty pool” of water is found in the seaward basin that is not found landward. The interface with this salty pool demarks the point of flow separation during ebb, initially suppressing the lee wave and then acting as its lower boundary. A simple two-dimensional numerical model of the inlet was used to explore the important factors governing the flow. A base simulation that included the landward–seaward asymmetry of the sill shape, but not the density difference, yielded a response that was almost symmetric with a large lee wave forming early during both flood and ebb tide. The simulation behaves more like the observations when a salty pool of water is added seaward of the sill. This salty pool induces flow separation in the model and suppresses growth of the lee wave until late in ebb. This effect is termed “density-forced” flow separation, a modification of “postwave” flow separation that allows for a density gradient across an obstacle.

## Abstract

Observations and modeling simulations are presented that illustrate the importance of a density contrast and the upstream response to the time dependence of stratified flow over the Knight Inlet sill. Repeated sections of velocity and density show that the flow during ebb and flood tides is quite different: a large lee wave develops early in flood tide, whereas lee-wave growth is suppressed until the second half of ebb tide. There is a large upstream response that displaces as much water as accumulates in the lee wave, one that is large enough to also block the flow at a depth roughly consistent with simple dynamics. There is a large density contrast between the seaward and landward sides of the sill, and a “salty pool” of water is found in the seaward basin that is not found landward. The interface with this salty pool demarks the point of flow separation during ebb, initially suppressing the lee wave and then acting as its lower boundary. A simple two-dimensional numerical model of the inlet was used to explore the important factors governing the flow. A base simulation that included the landward–seaward asymmetry of the sill shape, but not the density difference, yielded a response that was almost symmetric with a large lee wave forming early during both flood and ebb tide. The simulation behaves more like the observations when a salty pool of water is added seaward of the sill. This salty pool induces flow separation in the model and suppresses growth of the lee wave until late in ebb. This effect is termed “density-forced” flow separation, a modification of “postwave” flow separation that allows for a density gradient across an obstacle.

## Abstract

In high-latitude fjords and channels in the Canadian Arctic Archipelago, walls support radiating internal tides as Kelvin waves. Such waves allow for significant barotropic to baroclinic tidal energy conversion, which is otherwise small or negligible when poleward of the critical latitude. This fundamentally three-dimensional system of a subinertial channel is investigated with a suite of numerical simulations in rectangular channels of varying width featuring idealized, isolated ridges. Even in channels as wide as 5 times the internal Rossby radius, tidal conversion can remain as high as predicted by an equivalent two-dimensional, nonrotating system. Curves of tidal conversion as a function of channel width, however, do not vary monotonically. Instead, they display peaks and nulls owing to interference between the Kelvin waves along the wall and similar waves that propagate along the ridge flanks, the wavelengths of which can be estimated from linear theory to guide prediction. Because the wavelengths are comparable to width scales of Arctic channels and fjords, the interference will play a first-order role in tidal energy budgets and may consequently influence the stability of glaciers, the ventilation of deep layers, the locations of sediment deposition, and the fate of freshwater exiting the Arctic Ocean.

## Abstract

In high-latitude fjords and channels in the Canadian Arctic Archipelago, walls support radiating internal tides as Kelvin waves. Such waves allow for significant barotropic to baroclinic tidal energy conversion, which is otherwise small or negligible when poleward of the critical latitude. This fundamentally three-dimensional system of a subinertial channel is investigated with a suite of numerical simulations in rectangular channels of varying width featuring idealized, isolated ridges. Even in channels as wide as 5 times the internal Rossby radius, tidal conversion can remain as high as predicted by an equivalent two-dimensional, nonrotating system. Curves of tidal conversion as a function of channel width, however, do not vary monotonically. Instead, they display peaks and nulls owing to interference between the Kelvin waves along the wall and similar waves that propagate along the ridge flanks, the wavelengths of which can be estimated from linear theory to guide prediction. Because the wavelengths are comparable to width scales of Arctic channels and fjords, the interference will play a first-order role in tidal energy budgets and may consequently influence the stability of glaciers, the ventilation of deep layers, the locations of sediment deposition, and the fate of freshwater exiting the Arctic Ocean.

## Abstract

Barotropic to baroclinic conversion and attendant phenomena were recently examined at the Kaena Ridge as an aspect of the Hawaii Ocean Mixing Experiment. Two distinct mixing processes appear to be at work in the waters above the 1100-m-deep ridge crest. At middepths, above 400 m, mixing events resemble their open-ocean counterparts. There is no apparent modulation of mixing rates with the fortnightly cycle, and they are well modeled by standard open-ocean parameterizations. Nearer to the topography, there is quasi-deterministic breaking associated with each baroclinic crest passage. Large-amplitude, small-scale internal waves are triggered by tidal forcing, consistent with lee-wave formation at the ridge break. These waves have vertical wavelengths on the order of 400 m. During spring tides, the waves are nonlinear and exhibit convective instabilities on their leading edge. Dissipation rates exceed those predicted by the open-ocean parameterizations by up to a factor of 100, with the disparity increasing as the seafloor is approached. These observations are based on a set of repeated CTD and microconductivity profiles obtained from the research platform (R/P) *Floating Instrument Platform* (*FLIP*), which was trimoored over the southern edge of the ridge crest. Ocean velocity and shear were resolved to a 4-m vertical scale by a suspended Doppler sonar. Dissipation was estimated both by measuring overturn displacements and from microconductivity wavenumber spectra. The methods agreed in water deeper than 200 m, where sensor resolution limitations do not limit the turbulence estimates. At intense mixing sites new phenomena await discovery, and existing parameterizations cannot be expected to apply.

## Abstract

Barotropic to baroclinic conversion and attendant phenomena were recently examined at the Kaena Ridge as an aspect of the Hawaii Ocean Mixing Experiment. Two distinct mixing processes appear to be at work in the waters above the 1100-m-deep ridge crest. At middepths, above 400 m, mixing events resemble their open-ocean counterparts. There is no apparent modulation of mixing rates with the fortnightly cycle, and they are well modeled by standard open-ocean parameterizations. Nearer to the topography, there is quasi-deterministic breaking associated with each baroclinic crest passage. Large-amplitude, small-scale internal waves are triggered by tidal forcing, consistent with lee-wave formation at the ridge break. These waves have vertical wavelengths on the order of 400 m. During spring tides, the waves are nonlinear and exhibit convective instabilities on their leading edge. Dissipation rates exceed those predicted by the open-ocean parameterizations by up to a factor of 100, with the disparity increasing as the seafloor is approached. These observations are based on a set of repeated CTD and microconductivity profiles obtained from the research platform (R/P) *Floating Instrument Platform* (*FLIP*), which was trimoored over the southern edge of the ridge crest. Ocean velocity and shear were resolved to a 4-m vertical scale by a suspended Doppler sonar. Dissipation was estimated both by measuring overturn displacements and from microconductivity wavenumber spectra. The methods agreed in water deeper than 200 m, where sensor resolution limitations do not limit the turbulence estimates. At intense mixing sites new phenomena await discovery, and existing parameterizations cannot be expected to apply.

## Abstract

A simple parameterization for tidal dissipation near supercritical topography, designed to be applied at deep midocean ridges, is presented. In this parameterization, radiation of internal tides is quantified using a linear knife-edge model. Vertical internal wave modes that have nonrotating phase speeds slower than the tidal advection speed are assumed to dissipate locally, primarily because of hydraulic effects near the ridge crest. Evidence for high modes being dissipated is given in idealized numerical models of tidal flow over a Gaussian ridge. These idealized models also give guidance for where in the water column the predicted dissipation should be placed. The dissipation recipe holds if the Coriolis frequency *f* is varied, as long as *hN*/*W* ≫ *f*, where *N* is the stratification, *h* is the topographic height, and *W* is a width scale. This parameterization is not applicable to shallower topography, which has significantly more dissipation because near-critical processes dominate the observed turbulence. The parameterization compares well against simulations of tidal dissipation at the Kauai ridge but predicts less dissipation than estimated from observations of the full Hawaiian ridge, perhaps because of unparameterized wave–wave interactions.

## Abstract

A simple parameterization for tidal dissipation near supercritical topography, designed to be applied at deep midocean ridges, is presented. In this parameterization, radiation of internal tides is quantified using a linear knife-edge model. Vertical internal wave modes that have nonrotating phase speeds slower than the tidal advection speed are assumed to dissipate locally, primarily because of hydraulic effects near the ridge crest. Evidence for high modes being dissipated is given in idealized numerical models of tidal flow over a Gaussian ridge. These idealized models also give guidance for where in the water column the predicted dissipation should be placed. The dissipation recipe holds if the Coriolis frequency *f* is varied, as long as *hN*/*W* ≫ *f*, where *N* is the stratification, *h* is the topographic height, and *W* is a width scale. This parameterization is not applicable to shallower topography, which has significantly more dissipation because near-critical processes dominate the observed turbulence. The parameterization compares well against simulations of tidal dissipation at the Kauai ridge but predicts less dissipation than estimated from observations of the full Hawaiian ridge, perhaps because of unparameterized wave–wave interactions.

## Abstract

Very high turbulent dissipation rates (above ε = 10^{−4} W kg^{−1}) were observed in the nonlinear internal lee waves that form each tide over a sill in Knight Inlet, British Columbia. This turbulence was due to both shear instabilities and the jumplike adjustment of the wave to background flow conditions. Away from the sill, turbulent dissipation was significantly lower (ε = 10^{−7} to ε = 10^{−8} W kg^{−1}). Energy removed from the barotropic tide was estimated using a pair of tide gauges; a peak of 20 MW occurred during spring tide. Approximately two-thirds of the barotropic energy loss radiated away as internal waves, while the remaining one-third was lost to processes near the sill. Observed dissipation in the water column does not account for the near-sill losses, but energy lost to vortex shedding and near-bottom turbulence, though not measured, could be large enough to close the energy budget.

## Abstract

Very high turbulent dissipation rates (above ε = 10^{−4} W kg^{−1}) were observed in the nonlinear internal lee waves that form each tide over a sill in Knight Inlet, British Columbia. This turbulence was due to both shear instabilities and the jumplike adjustment of the wave to background flow conditions. Away from the sill, turbulent dissipation was significantly lower (ε = 10^{−7} to ε = 10^{−8} W kg^{−1}). Energy removed from the barotropic tide was estimated using a pair of tide gauges; a peak of 20 MW occurred during spring tide. Approximately two-thirds of the barotropic energy loss radiated away as internal waves, while the remaining one-third was lost to processes near the sill. Observed dissipation in the water column does not account for the near-sill losses, but energy lost to vortex shedding and near-bottom turbulence, though not measured, could be large enough to close the energy budget.

## Abstract

The downward propagation of near-inertial internal waves following winter storms is examined in the context of a 2-yr record of velocity in the upper 800 m at Ocean Station Papa. The long time series allow accurate estimation of wave frequency, whereas the continuous data in depth allow separation into upward- and downward-propagating components. Near-inertial kinetic energy (KE_{in}) dominates the record. At all measured depths, energy in downgoing motions exceeds that of upward-propagating motions by factors of 3–7, whereas KE_{in} is elevated by a factor of 3–5 in winter relative to summer. The two successive winters are qualitatively similar but show important differences in timing and depth penetration. Energy is seen radiating downward in a finite number of wave groups, which are tagged and catalogued to determine the vertical group velocity *c _{gz}
*, which has a mean of about 1.5 × 10

^{−4}m s

^{−1}(13 m day

^{−1}). Case studies of three of these are presented in detail.

Downward energy flux is estimated as *c _{gz}
* × KE

_{in}(i) by summing over the set of events, (ii) from time series near the bottom of the record, and (iii) from the wavenumber–frequency spectrum and the dispersion relationship. These estimates are compared to the work done on near-inertial motions in the mixed layer by the wind, which is directly estimated from mixed layer near-inertial currents and winds measured from a surface buoy 10 km away. All three methods yield similar values, indicating that 12%–33% of the energy input into the mixed layer transits 800 m toward the deep sea. This simple picture neglects lateral energy flux carried by the first few vertical modes, which was not measured. The substantial deep penetration implies that near-inertial motions may play a role in mixing the deep ocean, but the strong observed variability calls for a need to better understand the role of lateral mesoscale structures in modulating the vertical propagation.

## Abstract

The downward propagation of near-inertial internal waves following winter storms is examined in the context of a 2-yr record of velocity in the upper 800 m at Ocean Station Papa. The long time series allow accurate estimation of wave frequency, whereas the continuous data in depth allow separation into upward- and downward-propagating components. Near-inertial kinetic energy (KE_{in}) dominates the record. At all measured depths, energy in downgoing motions exceeds that of upward-propagating motions by factors of 3–7, whereas KE_{in} is elevated by a factor of 3–5 in winter relative to summer. The two successive winters are qualitatively similar but show important differences in timing and depth penetration. Energy is seen radiating downward in a finite number of wave groups, which are tagged and catalogued to determine the vertical group velocity *c _{gz}
*, which has a mean of about 1.5 × 10

^{−4}m s

^{−1}(13 m day

^{−1}). Case studies of three of these are presented in detail.

Downward energy flux is estimated as *c _{gz}
* × KE

_{in}(i) by summing over the set of events, (ii) from time series near the bottom of the record, and (iii) from the wavenumber–frequency spectrum and the dispersion relationship. These estimates are compared to the work done on near-inertial motions in the mixed layer by the wind, which is directly estimated from mixed layer near-inertial currents and winds measured from a surface buoy 10 km away. All three methods yield similar values, indicating that 12%–33% of the energy input into the mixed layer transits 800 m toward the deep sea. This simple picture neglects lateral energy flux carried by the first few vertical modes, which was not measured. The substantial deep penetration implies that near-inertial motions may play a role in mixing the deep ocean, but the strong observed variability calls for a need to better understand the role of lateral mesoscale structures in modulating the vertical propagation.