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Measurement of Turbulent Kinetic Energy Dissipation Rate with a Lagrangian Float

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  • 1 Applied Physics Laboratory, University of Washington, Seattle, Washington
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Abstract

This study tests the ability of a neutrally buoyant float to estimate the dissipation rate of turbulent kinetic energy ɛ from its vertical acceleration spectrum using an inertial subrange method. A Lagrangian float was equipped with a SonTek acoustic Doppler velocimeter (ADV), which measured the vector velocity 1 m below the float's center, and a pressure sensor, which measured the float's depth. Measurements were taken in flows where estimates of ɛ varied from 10−8 to 10−3 W kg−1. Previous observational and theoretical studies conclude that the Lagrangian acceleration spectrum is white within the inertial subrange with a level proportional to ɛ. The size of the Lagrangian float introduces a highly reproducible spectral attenuation at high frequencies. Estimates of the dissipation rate of turbulent kinetic energy using float measurements ɛfloat were obtained by fitting the observed spectra to a model spectrum that included the attenuation effect. The ADV velocity measurements were converted to a wavenumber spectrum using a variant of Taylor's hypothesis. The spectrum exhibited the expected −5/3 slope within an inertial subrange. The turbulent kinetic energy dissipation rate ɛADV was computed from the level of this spectrum. These two independent estimates, ɛADV and ɛfloat, were highly correlated. The ratio ɛfloat/ɛADV deviated from one by less than a factor of 2 over the five decades of ɛ measured. This analysis confirms that ɛ can be estimated reliably from Lagrangian float acceleration spectra in turbulent flows. For the meter-sized floats used here, the size of the float and the noise level of the pressure measurements sets a lower limit of ɛfloat > 10−8 W kg−1.

Corresponding author address: Dr. Ren-Chieh Lien, Applied Physics Laboratory and School of Oceanography, College of Ocean and Fishery Sciences, University of Washington, Seattle, WA 98105. Email: lien@apl.washington.edu

Abstract

This study tests the ability of a neutrally buoyant float to estimate the dissipation rate of turbulent kinetic energy ɛ from its vertical acceleration spectrum using an inertial subrange method. A Lagrangian float was equipped with a SonTek acoustic Doppler velocimeter (ADV), which measured the vector velocity 1 m below the float's center, and a pressure sensor, which measured the float's depth. Measurements were taken in flows where estimates of ɛ varied from 10−8 to 10−3 W kg−1. Previous observational and theoretical studies conclude that the Lagrangian acceleration spectrum is white within the inertial subrange with a level proportional to ɛ. The size of the Lagrangian float introduces a highly reproducible spectral attenuation at high frequencies. Estimates of the dissipation rate of turbulent kinetic energy using float measurements ɛfloat were obtained by fitting the observed spectra to a model spectrum that included the attenuation effect. The ADV velocity measurements were converted to a wavenumber spectrum using a variant of Taylor's hypothesis. The spectrum exhibited the expected −5/3 slope within an inertial subrange. The turbulent kinetic energy dissipation rate ɛADV was computed from the level of this spectrum. These two independent estimates, ɛADV and ɛfloat, were highly correlated. The ratio ɛfloat/ɛADV deviated from one by less than a factor of 2 over the five decades of ɛ measured. This analysis confirms that ɛ can be estimated reliably from Lagrangian float acceleration spectra in turbulent flows. For the meter-sized floats used here, the size of the float and the noise level of the pressure measurements sets a lower limit of ɛfloat > 10−8 W kg−1.

Corresponding author address: Dr. Ren-Chieh Lien, Applied Physics Laboratory and School of Oceanography, College of Ocean and Fishery Sciences, University of Washington, Seattle, WA 98105. Email: lien@apl.washington.edu

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