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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* = Î¾_{r}/Î¾_{w}, where Î¾_{r}, is the vertical displacement of an isopycnal relative to the float, and Î¾_{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* = Î³_{f}/ Î³_{w}, and the normalized buoyancy frequency *N* = *N*/Î©, where Î© is a characteristic float frequency defined by Î©^{2} = *g*Î¾_{w}[1 âˆ’ (Î±_{f}Î±_{w}
^{âˆ’1})]^{âˆ’ 1}, where Î±_{f}, Î±_{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 â€˜*Q*â€™ 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* â‰ˆ 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* = Î¾_{r}/Î¾_{w}, where Î¾_{r}, is the vertical displacement of an isopycnal relative to the float, and Î¾_{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* = Î³_{f}/ Î³_{w}, and the normalized buoyancy frequency *N* = *N*/Î©, where Î© is a characteristic float frequency defined by Î©^{2} = *g*Î¾_{w}[1 âˆ’ (Î±_{f}Î±_{w}
^{âˆ’1})]^{âˆ’ 1}, where Î±_{f}, Î±_{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 â€˜*Q*â€™ 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* â‰ˆ 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 temperatureâ€“salinity (Tâ€“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 temperatureâ€“salinity (Tâ€“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.