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## Abstract

Velocity measurements in the outer part of the bottom boundary layer on the Hatteras Abyssal Plain are examined for indicators of boundary-layer turbulence. Velocity fluctuations in two frequency bands, near-inertial and high-frequency (1–4 cph), display mixed-layer signatures. The high-frequency velocities measure primarily boundary-layer turbulence. The turbulence, so measured, is modulated on inertial and tidal time scales and extends intermittently to the mixed layer top. The near-inertial velocities are less energetic within the mixed layer than above and, for the dominant clockwise component, the mixed layer leads the interior. Following D'Asaro (1982), this is attributed to turbulent stresses which, consequently, must fill the mixed layer. These observations suggest that the entire bottom mixed layer is at least inter-mittently turbulent.

## Abstract

Velocity measurements in the outer part of the bottom boundary layer on the Hatteras Abyssal Plain are examined for indicators of boundary-layer turbulence. Velocity fluctuations in two frequency bands, near-inertial and high-frequency (1–4 cph), display mixed-layer signatures. The high-frequency velocities measure primarily boundary-layer turbulence. The turbulence, so measured, is modulated on inertial and tidal time scales and extends intermittently to the mixed layer top. The near-inertial velocities are less energetic within the mixed layer than above and, for the dominant clockwise component, the mixed layer leads the interior. Following D'Asaro (1982), this is attributed to turbulent stresses which, consequently, must fill the mixed layer. These observations suggest that the entire bottom mixed layer is at least inter-mittently turbulent.

## Abstract

The interaction of near-inertial velocities with the benthic boundary layer above a flat bottom is investigated using a diagnostic model and a 3-month time series of velocity from a fixed array of current meters. The observed near-inertial motions are assumed to be due to internal waves and diurnal tides. If the vertical wavelength of the internal waves is much larger than the boundary-layer thickness, the turbulent stresses acting on the near-inertial motions and the work done by the stresses on these motions can be computed. The boundary layer is estimated to absorb –0.003 to 0.024 erg cm^{−2} s^{−1} from the near-inertial motions, with one-third coming from the K_{1} diurnal tide and the rest from the internal-wave field. This is far less than estimated by Leaman (1976) and suggests that the benthic boundary layer on a flat bottom plays a minor role in dissipating internal-wave energy. This is also much less than the total energy dissipation in the boundary layer, suggesting that the boundary layer is primarily driven by low-frequency motions, not internal waves. A simple slab model with a linearized quadratic drag law qualitatively explains the observed near-inertial velocity structure and energy flux.

## Abstract

The interaction of near-inertial velocities with the benthic boundary layer above a flat bottom is investigated using a diagnostic model and a 3-month time series of velocity from a fixed array of current meters. The observed near-inertial motions are assumed to be due to internal waves and diurnal tides. If the vertical wavelength of the internal waves is much larger than the boundary-layer thickness, the turbulent stresses acting on the near-inertial motions and the work done by the stresses on these motions can be computed. The boundary layer is estimated to absorb –0.003 to 0.024 erg cm^{−2} s^{−1} from the near-inertial motions, with one-third coming from the K_{1} diurnal tide and the rest from the internal-wave field. This is far less than estimated by Leaman (1976) and suggests that the benthic boundary layer on a flat bottom plays a minor role in dissipating internal-wave energy. This is also much less than the total energy dissipation in the boundary layer, suggesting that the boundary layer is primarily driven by low-frequency motions, not internal waves. A simple slab model with a linearized quadratic drag law qualitatively explains the observed near-inertial velocity structure and energy flux.

## Abstract

Upper ocean currents and temperature in the northeastern Pacific were measured during a 14-day period in November 1980 as part of STREX. Velocities in the upper ocean are dominated by near-inertial frequency oscillations. Thew oscillations are modified by wind stress variations associated with the passage of a strong cold front. The change in the inertial currents both in the mixed layer and below is qualitatively consistent with linear internal wave dynamics if turbulent stresses during the storm are assumed to extend 10–20 m below the mixed layer.

The ratio of mean squared buoyancy frequency *N*
^{2} and mean squared shear *S*
^{2} computed over a 10 m interval defines an average Richardson number *R*
_{0}=*N*
^{2}/*S*
^{2}; *R*
_{0} is approximately 2.5 except in regions of high inertial shear. In particular, values as low as 0.7 are obtained in a 20 m thick region immediately below the base of the mixed layer. The data are consistent with a model of the oecanic shear field consisting of a background shear, corresponding to a value of *R*
_{0}=2.5, plus a variable inertial frequency shear field. Variations in *R*
_{0}, and by implication the rate of mixing, are due primarily to variations in the inertial frequency shear.

The mixed layer deepened 3–5 m during the 15 November storm. The temperature profiles suggest that mixing due to the storm extended roughly 5 m below the mixed layer. The mixed layer model of Niiler successfully models the observed response of the mixed layer. The amount of deepening is sensitive to the preexisting inertial currents during the storm passage. Using this model the amount of deepening could have been up to 80% greater than observed, if the storm had occurred earlier in the measurements, when the preexisting inertial currents were larger.

## Abstract

Upper ocean currents and temperature in the northeastern Pacific were measured during a 14-day period in November 1980 as part of STREX. Velocities in the upper ocean are dominated by near-inertial frequency oscillations. Thew oscillations are modified by wind stress variations associated with the passage of a strong cold front. The change in the inertial currents both in the mixed layer and below is qualitatively consistent with linear internal wave dynamics if turbulent stresses during the storm are assumed to extend 10–20 m below the mixed layer.

The ratio of mean squared buoyancy frequency *N*
^{2} and mean squared shear *S*
^{2} computed over a 10 m interval defines an average Richardson number *R*
_{0}=*N*
^{2}/*S*
^{2}; *R*
_{0} is approximately 2.5 except in regions of high inertial shear. In particular, values as low as 0.7 are obtained in a 20 m thick region immediately below the base of the mixed layer. The data are consistent with a model of the oecanic shear field consisting of a background shear, corresponding to a value of *R*
_{0}=2.5, plus a variable inertial frequency shear field. Variations in *R*
_{0}, and by implication the rate of mixing, are due primarily to variations in the inertial frequency shear.

The mixed layer deepened 3–5 m during the 15 November storm. The temperature profiles suggest that mixing due to the storm extended roughly 5 m below the mixed layer. The mixed layer model of Niiler successfully models the observed response of the mixed layer. The amount of deepening is sensitive to the preexisting inertial currents during the storm passage. Using this model the amount of deepening could have been up to 80% greater than observed, if the storm had occurred earlier in the measurements, when the preexisting inertial currents were larger.

## Abstract

Time series of wind stress computed from long-term meteorological buoy data off North America are used to examine the forcing of surface inertial currents by the wind. A simple damped slab model of the mixed layer is used to compute 〈Π(*H*)〉, the average flux of energy from the wind to mixed layer inertial currents in a mixed layer of fixed depth *H*. The forcing of mixed layer inertial motions is highly intermittent. Most of the forcing occurs during the winter months, with a few dozen events accounting for typically over half the total energy flux. Major forcing events are usually associated with translating cold fronts or small lows with scales of about 100 km. The larger, synoptic scale features have little energy at the inertial frequency and thus result in only weak forcing of inertial currents. A strong seasonal signal exists in the inertial forcing. At OWS-P (50°N, 145°W), 〈Π(50 m)〉 is largest from October to February and is a factor of 12 above the June and July values. If seasonally varying mixed layer depths are used, 〈Π(*H*)〉 is largest in October, due to the combination of a shallow mixed layer and strong forcing. The forcing of inertial motions varies with location, although comprehensive geographical coverage is not obtained here. In these data the 1~ wintertime average 〈Π(50 m)〉 is found off the east coast of North America at about 35°N. The smallest value, in the Gulf of Mexico, is four times less. Although a strong correlation between 〈Π(50 m)〉 and 〈*u*
^{*3}〉 the parameterized flux of energy to mixed layer turbulence, is found at OWS-P, this correlation does not hold at all other locations. This suggests that climatological models that attempt to parameterize 〈Π〉 in terms of 〈*u*
^{*3}〉 will need to be tuned to local conditions.

## Abstract

Time series of wind stress computed from long-term meteorological buoy data off North America are used to examine the forcing of surface inertial currents by the wind. A simple damped slab model of the mixed layer is used to compute 〈Π(*H*)〉, the average flux of energy from the wind to mixed layer inertial currents in a mixed layer of fixed depth *H*. The forcing of mixed layer inertial motions is highly intermittent. Most of the forcing occurs during the winter months, with a few dozen events accounting for typically over half the total energy flux. Major forcing events are usually associated with translating cold fronts or small lows with scales of about 100 km. The larger, synoptic scale features have little energy at the inertial frequency and thus result in only weak forcing of inertial currents. A strong seasonal signal exists in the inertial forcing. At OWS-P (50°N, 145°W), 〈Π(50 m)〉 is largest from October to February and is a factor of 12 above the June and July values. If seasonally varying mixed layer depths are used, 〈Π(*H*)〉 is largest in October, due to the combination of a shallow mixed layer and strong forcing. The forcing of inertial motions varies with location, although comprehensive geographical coverage is not obtained here. In these data the 1~ wintertime average 〈Π(50 m)〉 is found off the east coast of North America at about 35°N. The smallest value, in the Gulf of Mexico, is four times less. Although a strong correlation between 〈Π(50 m)〉 and 〈*u*
^{*3}〉 the parameterized flux of energy to mixed layer turbulence, is found at OWS-P, this correlation does not hold at all other locations. This suggests that climatological models that attempt to parameterize 〈Π〉 in terms of 〈*u*
^{*3}〉 will need to be tuned to local conditions.

## Abstract

The three-dimensional structure of the near-inertial frequency internal wave field was measured at two open ocean sites using expendable velocity profilers. Both wave fields appear to be dominantly wind forced although their vertical structure and horizontal scales are quite different. The HYDRO-79 data were taken in the Sargasso Sea in September 1979. The internal wave field is predominantly downward propagating and vertically uniform, when WKB scaled, in the upper 800 m of the ocean. The energy density is roughly equal to Munk's (1981) universal value. The STKEX data were taken during a period of strong storms in the northeastern Pacific Ocean in November 1980. In the upper few hundred meters the wave field is five times larger horizontally and five times more energetic, when WKB scaled, than the HYDRO-79 wave field. Measurements made after the passage of a strong cold front show an even more energetic and larger scale wave field extending to 500 m. Comparison with the simulations of Price (1983a,b) suggests that this change may be due to the generation of near-inertial frequency internal waves by the wind stress variation associated with the cold front.

## Abstract

The three-dimensional structure of the near-inertial frequency internal wave field was measured at two open ocean sites using expendable velocity profilers. Both wave fields appear to be dominantly wind forced although their vertical structure and horizontal scales are quite different. The HYDRO-79 data were taken in the Sargasso Sea in September 1979. The internal wave field is predominantly downward propagating and vertically uniform, when WKB scaled, in the upper 800 m of the ocean. The energy density is roughly equal to Munk's (1981) universal value. The STKEX data were taken during a period of strong storms in the northeastern Pacific Ocean in November 1980. In the upper few hundred meters the wave field is five times larger horizontally and five times more energetic, when WKB scaled, than the HYDRO-79 wave field. Measurements made after the passage of a strong cold front show an even more energetic and larger scale wave field extending to 500 m. Comparison with the simulations of Price (1983a,b) suggests that this change may be due to the generation of near-inertial frequency internal waves by the wind stress variation associated with the cold front.

## Abstract

Vertical velocities in the ocean boundary layer were measured for two weeks at an open ocean, wintertime site using neutrally buoyant floats. Simultaneous measurements of the surface meteorology and surface waves showed a large variability in both wind and wave properties and only weak correlations between them. Buoyancy forcing was weak. The mean square vertical velocity in the boundary layer *σ*
^{2}
_{
w
}
*u*
^{2}
_{∗}
*σ*
^{2}
_{
w
}
*A*
*u*
^{2}
_{∗}
*ρ*
*u*
^{2}
_{∗}
*ρ* is the density of the water). The deviations from this relation can be attributed entirely to statistical variation and measurement error. The measured values of *σ*
^{2}
_{
w
}
*A*

## Abstract

Vertical velocities in the ocean boundary layer were measured for two weeks at an open ocean, wintertime site using neutrally buoyant floats. Simultaneous measurements of the surface meteorology and surface waves showed a large variability in both wind and wave properties and only weak correlations between them. Buoyancy forcing was weak. The mean square vertical velocity in the boundary layer *σ*
^{2}
_{
w
}
*u*
^{2}
_{∗}
*σ*
^{2}
_{
w
}
*A*
*u*
^{2}
_{∗}
*ρ*
*u*
^{2}
_{∗}
*ρ* is the density of the water). The deviations from this relation can be attributed entirely to statistical variation and measurement error. The measured values of *σ*
^{2}
_{
w
}
*A*

## Abstract

Three neutrally buoyant floats were air deployed ahead of Hurricane Dennis on 28 August 1999. These floats were designed to accurately follow three-dimensional water trajectories and measure pressure (i.e., their own depth) and temperature. The hurricane eye passed between two of the floats; both measured the properties of the ocean boundary layer beneath sustained 30 m s^{−1} winds. The floats repeatedly moved through a mixed layer 30–70 m deep at average vertical speeds of 0.03–0.06 m s^{−1}. The speed was roughly proportional to the friction velocity. Mixed layer temperature cooled about 2.8° and 0.75°C at the floats on the east and west sides of the northward-going storm, respectively. Much of the cooling occurred before the eye passage. The remaining terms in the horizontally averaged mixed layer heat budget, the vertical velocity–temperature covariance and the Lagrangian heating rate, were computed from the float data. Surface heat fluxes accounted for only a small part of the cooling. Most of the cooling was due to entrainment of colder water from below and, on the right-hand (east) side only, horizontal advection and mixing with colder water. The larger entrainment flux on this side of the hurricane was presumably due to the much larger inertial currents and shear. Although these floats can make detailed measurements of the heat transfer mechanisms in the ocean boundary layer under these severe conditions, accurate measurements of heat flux will require clusters of many floats to reduce the statistical error.

## Abstract

Three neutrally buoyant floats were air deployed ahead of Hurricane Dennis on 28 August 1999. These floats were designed to accurately follow three-dimensional water trajectories and measure pressure (i.e., their own depth) and temperature. The hurricane eye passed between two of the floats; both measured the properties of the ocean boundary layer beneath sustained 30 m s^{−1} winds. The floats repeatedly moved through a mixed layer 30–70 m deep at average vertical speeds of 0.03–0.06 m s^{−1}. The speed was roughly proportional to the friction velocity. Mixed layer temperature cooled about 2.8° and 0.75°C at the floats on the east and west sides of the northward-going storm, respectively. Much of the cooling occurred before the eye passage. The remaining terms in the horizontally averaged mixed layer heat budget, the vertical velocity–temperature covariance and the Lagrangian heating rate, were computed from the float data. Surface heat fluxes accounted for only a small part of the cooling. Most of the cooling was due to entrainment of colder water from below and, on the right-hand (east) side only, horizontal advection and mixing with colder water. The larger entrainment flux on this side of the hurricane was presumably due to the much larger inertial currents and shear. Although these floats can make detailed measurements of the heat transfer mechanisms in the ocean boundary layer under these severe conditions, accurate measurements of heat flux will require clusters of many floats to reduce the statistical error.

## Abstract

The evolution of near-inertial frequency currents is often thought to be controlled by the linear, inviscid equations of motion. This hypothesis is tested by simulating the near-inertial currents described in Part I using a two-dimensional, nearly inviscid, nonlinear layer model with realistic wind forcing and stratification. The β effect and mixing of momentum below the mixed layer during the storm are crucial to realistic modeling, whereas the nonlinear terms have only a minor effect. The model fails to simulate the observations in several ways. First, the mixed layer inertial currents decay more rapidly than predicted and propagate into the thermocline with a different pattern. Second, the shear at the base of the mixed layer decays much more rapidly than predicted. Third, mesoscale eddies modulate the evolution of the inertial currents much less than predicted. These differences are much larger than the errors in the observations and cannot be removed by reasonable variations of the forcing or stratification. The nearly linear and inviscid internal wave equations thus cannot accurately predict the observed evolution of the near-inertial currents; additional physical processes, perhaps nonlinear interactions with smaller-scale internal waves and/or fronts, are required in the equations.

## Abstract

The evolution of near-inertial frequency currents is often thought to be controlled by the linear, inviscid equations of motion. This hypothesis is tested by simulating the near-inertial currents described in Part I using a two-dimensional, nearly inviscid, nonlinear layer model with realistic wind forcing and stratification. The β effect and mixing of momentum below the mixed layer during the storm are crucial to realistic modeling, whereas the nonlinear terms have only a minor effect. The model fails to simulate the observations in several ways. First, the mixed layer inertial currents decay more rapidly than predicted and propagate into the thermocline with a different pattern. Second, the shear at the base of the mixed layer decays much more rapidly than predicted. Third, mesoscale eddies modulate the evolution of the inertial currents much less than predicted. These differences are much larger than the errors in the observations and cannot be removed by reasonable variations of the forcing or stratification. The nearly linear and inviscid internal wave equations thus cannot accurately predict the observed evolution of the near-inertial currents; additional physical processes, perhaps nonlinear interactions with smaller-scale internal waves and/or fronts, are required in the equations.

## Abstract

The interaction of strong near-inertial frequency currents generated by a storm with preexisting subinertial frequency currents is investigated. For 10 days after the storm, the near-inertial currents remain in the mixed layer and the subinertial currents are steady, so their interaction is particularly simple. Linearized models predict that the frequency of the near-inertial currents should be shifted by ½ζ where ζ is the subinertial vorticity. This theory, combined with values of ζ estimated either from velocity measurements or from the vorticity equation, produces frequency shifts in the inertial currents at least five times larger than the confidence limits on the observations. Possible explanations include the concentration of ζ in narrow frontal zones and nonlinear wave-wave interactions.

## Abstract

The interaction of strong near-inertial frequency currents generated by a storm with preexisting subinertial frequency currents is investigated. For 10 days after the storm, the near-inertial currents remain in the mixed layer and the subinertial currents are steady, so their interaction is particularly simple. Linearized models predict that the frequency of the near-inertial currents should be shifted by ½ζ where ζ is the subinertial vorticity. This theory, combined with values of ζ estimated either from velocity measurements or from the vorticity equation, produces frequency shifts in the inertial currents at least five times larger than the confidence limits on the observations. Possible explanations include the concentration of ζ in narrow frontal zones and nonlinear wave-wave interactions.

## Abstract

A three-dimensional nonhydrostatic numerical model is used to calculate nonlinear energy transfers within decaying Garrett–Munk internal wavefields. Inviscid wave interactions are calculated over horizontal scales from about 1 to 80 km and for vertical mode numbers less than about 40 in an exponentially stratified model ocean 2000 m deep. The rate of energy transfer from these scales to smaller, numerically damped scales is used to make predictions of the dissipation rate ε in the open ocean midlatitude thermocline. In agreement with the theoretical analyses based on resonant interaction and eikonal theories, the simulation results predict ε ∝ *Ē*
^{2}
*N*
^{2}, where *Ē* and *N* are the internal wave energy density and the ambient buoyancy frequency respectively. The magnitudes of the simulated dissipation rates are shown to be in good agreement with the dissipation measurements taken from six diverse sites in the midlatitude thermocline. The results suggest that the rates of dissipation and mixing in the ocean thermocline are controlled by the nonlinear dynamics of the large-scale energy-containing internal waves.

## Abstract

A three-dimensional nonhydrostatic numerical model is used to calculate nonlinear energy transfers within decaying Garrett–Munk internal wavefields. Inviscid wave interactions are calculated over horizontal scales from about 1 to 80 km and for vertical mode numbers less than about 40 in an exponentially stratified model ocean 2000 m deep. The rate of energy transfer from these scales to smaller, numerically damped scales is used to make predictions of the dissipation rate ε in the open ocean midlatitude thermocline. In agreement with the theoretical analyses based on resonant interaction and eikonal theories, the simulation results predict ε ∝ *Ē*
^{2}
*N*
^{2}, where *Ē* and *N* are the internal wave energy density and the ambient buoyancy frequency respectively. The magnitudes of the simulated dissipation rates are shown to be in good agreement with the dissipation measurements taken from six diverse sites in the midlatitude thermocline. The results suggest that the rates of dissipation and mixing in the ocean thermocline are controlled by the nonlinear dynamics of the large-scale energy-containing internal waves.