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- Author or Editor: Louis Goodman x

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## Abstract

The vertical motion of a neutrally buoyant float is determined from the solution to the nonlinear forced harmonic oscillator equation originally set forth by Voorhis. Float response to forced vertical oscillations is characterized by the response ratio, *r* = ξ_{r}/ξ_{w}, where ξ_{r}, is the vertical displacement of an isopycnal relative to the float, and ξ_{w} is the vertical displacement of an isopycnal relative to its initial equilibrium position. For isopycnal displacements with frequencies much less than the resonant frequency of the float, the goat can be considered to be in near dynamic equilibrium with the forcing, and *r* is a function of the relative compressibility between the float and seawater, *s* = γ_{f}/ γ_{w}, and the normalized buoyancy frequency *N* = *N*/Ω, where Ω is a characteristic float frequency defined by Ω^{2} = *g*ξ_{w}[1 − (α_{f}α_{w}
^{−1})]^{− 1}, where α_{f}, α_{w} are the coefficients of thermal expansion of the float and water, respectively. For the new dynamic equilibrium case, data obtained from a float deployment in a Gulf Stream meander result in an observed *r* value close to the predicted value. For the case of float response to an isopycnal displacement of frequency near the resonant frequency of the float, vertical motion depends on drag, in addition to the material properties of the float and seawater. The bandwidth over which resonance can occur is parametrized by the ‘*Q*’ factor, the inverse of the normalized bandwidth, which for cylindrical floats is predicted to be greater than 1, indicating sharp resonance. From a float deployment in the Gulf Stream region it was estimated that *Q* ≈ 5. For this case, the spectrum of float temperature, which was used as an indicator of the relative response between the float and a displaced isopycnal, and the spectrum of the float pressure, used as an indicator of float displacement, did scale according to that predicted by the condition of near equilibrium response, up to of order the resonant frequency of the float.

## Abstract

The vertical motion of a neutrally buoyant float is determined from the solution to the nonlinear forced harmonic oscillator equation originally set forth by Voorhis. Float response to forced vertical oscillations is characterized by the response ratio, *r* = ξ_{r}/ξ_{w}, where ξ_{r}, is the vertical displacement of an isopycnal relative to the float, and ξ_{w} is the vertical displacement of an isopycnal relative to its initial equilibrium position. For isopycnal displacements with frequencies much less than the resonant frequency of the float, the goat can be considered to be in near dynamic equilibrium with the forcing, and *r* is a function of the relative compressibility between the float and seawater, *s* = γ_{f}/ γ_{w}, and the normalized buoyancy frequency *N* = *N*/Ω, where Ω is a characteristic float frequency defined by Ω^{2} = *g*ξ_{w}[1 − (α_{f}α_{w}
^{−1})]^{− 1}, where α_{f}, α_{w} are the coefficients of thermal expansion of the float and water, respectively. For the new dynamic equilibrium case, data obtained from a float deployment in a Gulf Stream meander result in an observed *r* value close to the predicted value. For the case of float response to an isopycnal displacement of frequency near the resonant frequency of the float, vertical motion depends on drag, in addition to the material properties of the float and seawater. The bandwidth over which resonance can occur is parametrized by the ‘*Q*’ factor, the inverse of the normalized bandwidth, which for cylindrical floats is predicted to be greater than 1, indicating sharp resonance. From a float deployment in the Gulf Stream region it was estimated that *Q* ≈ 5. For this case, the spectrum of float temperature, which was used as an indicator of the relative response between the float and a displaced isopycnal, and the spectrum of the float pressure, used as an indicator of float displacement, did scale according to that predicted by the condition of near equilibrium response, up to of order the resonant frequency of the float.

## Abstract

The terms of the steady-state, homogeneous turbulent kinetic energy budgets are obtained from measurements of turbulence and fine structure from the small autonomous underwater vehicle (AUV) Remote Environmental Measuring Units (REMUS). The transverse component of Reynolds stress and the vertical flux of heat are obtained from the correlation of vertical and transverse horizontal velocity, and the correlation of vertical velocity and temperature fluctuations, respectively. The data were obtained using a turbulence package, with two shear probes, a fast-response thermistor, and three accelerometers. To obtain the vector horizontal Reynolds stress, a generalized eddy viscosity formulation is invoked. This allows the downstream component of the Reynolds stress to be related to the transverse component by the direction of the finescale vector vertical shear. The Reynolds stress and the vector vertical shear then allow an estimate of the rate of production of turbulent kinetic energy (TKE). Heat flux is obtained by correlating the vertical velocity with temperature fluctuations obtained from the FP-07 thermistor. The buoyancy flux term is estimated from the vertical flux of heat with the assumption of a constant temperature–salinity (T–S) relationship. Turbulent dissipation is obtained directly from the usage of shear probes.

A multivariate correction procedure is developed to remove vehicle motion and vibration contamination from the estimates of the TKE terms. A technique is also developed to estimate the statistical uncertainty of using this estimation technique for the TKE budget terms. Within the statistical uncertainty of the estimates herein, the TKE budget on average closes for measurements taken in the weakly stratified waters at the entrance to Long Island Sound. In the strongly stratified waters of Narragansett Bay, the TKE budget closes when the buoyancy Reynolds number exceeds 20, an indicator and threshold for the initiation of turbulence in stratified conditions. A discussion is made regarding the role of the turbulent kinetic energy length scale relative to the length of the AUV in obtaining these estimates, and in the TKE budget closure.

## Abstract

The terms of the steady-state, homogeneous turbulent kinetic energy budgets are obtained from measurements of turbulence and fine structure from the small autonomous underwater vehicle (AUV) Remote Environmental Measuring Units (REMUS). The transverse component of Reynolds stress and the vertical flux of heat are obtained from the correlation of vertical and transverse horizontal velocity, and the correlation of vertical velocity and temperature fluctuations, respectively. The data were obtained using a turbulence package, with two shear probes, a fast-response thermistor, and three accelerometers. To obtain the vector horizontal Reynolds stress, a generalized eddy viscosity formulation is invoked. This allows the downstream component of the Reynolds stress to be related to the transverse component by the direction of the finescale vector vertical shear. The Reynolds stress and the vector vertical shear then allow an estimate of the rate of production of turbulent kinetic energy (TKE). Heat flux is obtained by correlating the vertical velocity with temperature fluctuations obtained from the FP-07 thermistor. The buoyancy flux term is estimated from the vertical flux of heat with the assumption of a constant temperature–salinity (T–S) relationship. Turbulent dissipation is obtained directly from the usage of shear probes.

A multivariate correction procedure is developed to remove vehicle motion and vibration contamination from the estimates of the TKE terms. A technique is also developed to estimate the statistical uncertainty of using this estimation technique for the TKE budget terms. Within the statistical uncertainty of the estimates herein, the TKE budget on average closes for measurements taken in the weakly stratified waters at the entrance to Long Island Sound. In the strongly stratified waters of Narragansett Bay, the TKE budget closes when the buoyancy Reynolds number exceeds 20, an indicator and threshold for the initiation of turbulence in stratified conditions. A discussion is made regarding the role of the turbulent kinetic energy length scale relative to the length of the AUV in obtaining these estimates, and in the TKE budget closure.

## Abstract

Lateral stirring is a basic oceanographic phenomenon affecting the distribution of physical, chemical, and biological fields. Eddy stirring at scales on the order of 100 km (the mesoscale) is fairly well understood and explicitly represented in modern eddy-resolving numerical models of global ocean circulation. The same cannot be said for smaller-scale stirring processes. Here, the authors describe a major oceanographic field experiment aimed at observing and understanding the processes responsible for stirring at scales of 0.1–10 km. Stirring processes of varying intensity were studied in the Sargasso Sea eddy field approximately 250 km southeast of Cape Hatteras. Lateral variability of water-mass properties, the distribution of microscale turbulence, and the evolution of several patches of inert dye were studied with an array of shipboard, autonomous, and airborne instruments. Observations were made at two sites, characterized by weak and moderate background mesoscale straining, to contrast different regimes of lateral stirring. Analyses to date suggest that, in both cases, the lateral dispersion of natural and deliberately released tracers was O(1) m^{2} s^{–1} as found elsewhere, which is faster than might be expected from traditional shear dispersion by persistent mesoscale flow and linear internal waves. These findings point to the possible importance of kilometer-scale stirring by submesoscale eddies and nonlinear internal-wave processes or the need to modify the traditional shear-dispersion paradigm to include higher-order effects. A unique aspect of the Scalable Lateral Mixing and Coherent Turbulence (LatMix) field experiment is the combination of direct measurements of dye dispersion with the concurrent multiscale hydrographic and turbulence observations, enabling evaluation of the underlying mechanisms responsible for the observed dispersion at a new level.

## Abstract

Lateral stirring is a basic oceanographic phenomenon affecting the distribution of physical, chemical, and biological fields. Eddy stirring at scales on the order of 100 km (the mesoscale) is fairly well understood and explicitly represented in modern eddy-resolving numerical models of global ocean circulation. The same cannot be said for smaller-scale stirring processes. Here, the authors describe a major oceanographic field experiment aimed at observing and understanding the processes responsible for stirring at scales of 0.1–10 km. Stirring processes of varying intensity were studied in the Sargasso Sea eddy field approximately 250 km southeast of Cape Hatteras. Lateral variability of water-mass properties, the distribution of microscale turbulence, and the evolution of several patches of inert dye were studied with an array of shipboard, autonomous, and airborne instruments. Observations were made at two sites, characterized by weak and moderate background mesoscale straining, to contrast different regimes of lateral stirring. Analyses to date suggest that, in both cases, the lateral dispersion of natural and deliberately released tracers was O(1) m^{2} s^{–1} as found elsewhere, which is faster than might be expected from traditional shear dispersion by persistent mesoscale flow and linear internal waves. These findings point to the possible importance of kilometer-scale stirring by submesoscale eddies and nonlinear internal-wave processes or the need to modify the traditional shear-dispersion paradigm to include higher-order effects. A unique aspect of the Scalable Lateral Mixing and Coherent Turbulence (LatMix) field experiment is the combination of direct measurements of dye dispersion with the concurrent multiscale hydrographic and turbulence observations, enabling evaluation of the underlying mechanisms responsible for the observed dispersion at a new level.