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## Abstract

Modern surface drifters tracked by Argos are an attractive method for measuring the spatial structure of near-surface currents. This note discusses the accuracy to which velocity can be estimated from such data, assuming perfect drifters. The analysis concentrates on data from OCEAN STORMS centered at 47.5°N in the eastern North Pacific, a region of low mesoscale activity. The irregular, but nearly diurnally repeating, pattern of fixes leads to leakage between near-inertial (1.48 cpd) and subinertial (0.5 cpd) frequencies. Total spectral leakage for a naive spline interpolant of the fixes is about 2×10^{−3} in energy, or 5% in amplitude. Other interpolants can produce an order of magnitude more leakage. An algorithm that controls these errors is described. Only an inertial peak and frequencies well below 0.5 cpd can be resolved. The remaining noise can be described as the sum of a random fix error of 600 m rms and unresolved subinertial velocities with an rms displacement of about 550 m. The errors in the computed inertial and low-frequency velocities are 0.03 and 0.01 m s^{−1}, respectively. These can be reduced with further time averaging. Significantly better estimates of velocities would require both more accurate and more frequent position fixes.

## Abstract

Modern surface drifters tracked by Argos are an attractive method for measuring the spatial structure of near-surface currents. This note discusses the accuracy to which velocity can be estimated from such data, assuming perfect drifters. The analysis concentrates on data from OCEAN STORMS centered at 47.5°N in the eastern North Pacific, a region of low mesoscale activity. The irregular, but nearly diurnally repeating, pattern of fixes leads to leakage between near-inertial (1.48 cpd) and subinertial (0.5 cpd) frequencies. Total spectral leakage for a naive spline interpolant of the fixes is about 2×10^{−3} in energy, or 5% in amplitude. Other interpolants can produce an order of magnitude more leakage. An algorithm that controls these errors is described. Only an inertial peak and frequencies well below 0.5 cpd can be resolved. The remaining noise can be described as the sum of a random fix error of 600 m rms and unresolved subinertial velocities with an rms displacement of about 550 m. The errors in the computed inertial and low-frequency velocities are 0.03 and 0.01 m s^{−1}, respectively. These can be reduced with further time averaging. Significantly better estimates of velocities would require both more accurate and more frequent position fixes.

## 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 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

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

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

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

A truly Lagrangian float would follow all three components of oceanic velocity on all timescales. Progress toward this goal is reviewed by analyzing the performance of nearly Lagrangian floats deployed in a variety of oceanic flows. Two new float types, described in this paper, are autonomous with durations of months, can alternate between Lagrangian and profiling modes, relay data via satellite, and can carry a variety of sensors. A novel hull design is light, strong, and has a compressibility close to that of seawater.

The key to making floats accurately Lagrangian is an improved understanding of the factors that control float buoyancy and motion. Several insights are presented here. Anodized aluminum gains weight in seawater due to reactions between its surface and seawater. At low pressure the buoyancy of floats with O-ring seals varies as if attached bubbles of air were being compressed. The volume of “air” decays exponentially with a decay scale of a few days from 10 to 30 cc at deployment to an asymptotic value that depends on pressure. The drag of floats moving slowly through a stratified ocean is dominated by internal wave generation and is thus linear, not quadratic. Internal wave drag acting on an isopycnal-seeking float will cause the float to be Lagrangian for frequencies greater than about *N*/30, where *N* is the buoyancy frequency.

These floats have proven most useful in measuring the turbulence in ocean boundary layers and other regions of strong turbulence where the ability of the floats to be Lagrangian on short timescales matches the short timescale of the processes and where the size of the turbulent eddies exceeds the size of the float. On longer timescales, the floats successfully operate as isopycnal followers. Because truly Lagrangian floats are highly sensitive to minor perturbations, extension of the frequency band over which the floats are Lagrangian will require careful control of float buoyancy and thus a detailed understanding of the float's equation of state.

## Abstract

A truly Lagrangian float would follow all three components of oceanic velocity on all timescales. Progress toward this goal is reviewed by analyzing the performance of nearly Lagrangian floats deployed in a variety of oceanic flows. Two new float types, described in this paper, are autonomous with durations of months, can alternate between Lagrangian and profiling modes, relay data via satellite, and can carry a variety of sensors. A novel hull design is light, strong, and has a compressibility close to that of seawater.

The key to making floats accurately Lagrangian is an improved understanding of the factors that control float buoyancy and motion. Several insights are presented here. Anodized aluminum gains weight in seawater due to reactions between its surface and seawater. At low pressure the buoyancy of floats with O-ring seals varies as if attached bubbles of air were being compressed. The volume of “air” decays exponentially with a decay scale of a few days from 10 to 30 cc at deployment to an asymptotic value that depends on pressure. The drag of floats moving slowly through a stratified ocean is dominated by internal wave generation and is thus linear, not quadratic. Internal wave drag acting on an isopycnal-seeking float will cause the float to be Lagrangian for frequencies greater than about *N*/30, where *N* is the buoyancy frequency.

These floats have proven most useful in measuring the turbulence in ocean boundary layers and other regions of strong turbulence where the ability of the floats to be Lagrangian on short timescales matches the short timescale of the processes and where the size of the turbulent eddies exceeds the size of the float. On longer timescales, the floats successfully operate as isopycnal followers. Because truly Lagrangian floats are highly sensitive to minor perturbations, extension of the frequency band over which the floats are Lagrangian will require careful control of float buoyancy and thus a detailed understanding of the float's equation of state.

## 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

Pressure gradient measurements on a subsurface Lagrangian float are used to measure the spectrum of surface waves for 100 days of measurements at Ocean Weather Station *Papa*. Along Lagrangian trajectories of surface waves, the pressure is constant and the vertical pressure gradient fluctuations equal the Eulerian fluctuations at the mean float depth to second order in wave height. Measurement of the pressure difference between the top and the bottom of the float can thus be used to measure the waves. Corrections for the wave decay with depth, for the vertical motion of the float, for the finite sampling interval, and for the sampling noise (among others) are necessary to obtain accurate results. With these corrections, scalar spectra accurately match those from a nearby Waverider buoy for significant wave heights greater than about 3 m. For smaller wave heights, noise in the pressure measurements biases the float spectral measurements. Significant wave height is measured with an rms error of 0.37 m over the measured range of 1–9 m. This demonstrates that Lagrangian floats accurately follow the Lagrangian trajectories of surface waves. More detailed and quieter measurements of float motion could likely measure directional wave spectra from below the surface. Similar methods could be used to infer surface wave properties from other subsurface vehicles.

## Abstract

Pressure gradient measurements on a subsurface Lagrangian float are used to measure the spectrum of surface waves for 100 days of measurements at Ocean Weather Station *Papa*. Along Lagrangian trajectories of surface waves, the pressure is constant and the vertical pressure gradient fluctuations equal the Eulerian fluctuations at the mean float depth to second order in wave height. Measurement of the pressure difference between the top and the bottom of the float can thus be used to measure the waves. Corrections for the wave decay with depth, for the vertical motion of the float, for the finite sampling interval, and for the sampling noise (among others) are necessary to obtain accurate results. With these corrections, scalar spectra accurately match those from a nearby Waverider buoy for significant wave heights greater than about 3 m. For smaller wave heights, noise in the pressure measurements biases the float spectral measurements. Significant wave height is measured with an rms error of 0.37 m over the measured range of 1–9 m. This demonstrates that Lagrangian floats accurately follow the Lagrangian trajectories of surface waves. More detailed and quieter measurements of float motion could likely measure directional wave spectra from below the surface. Similar methods could be used to infer surface wave properties from other subsurface vehicles.