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Measurement of Scalar Variance Dissipation from Lagrangian Floats

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  • 1 Applied Physics Laboratory and School of Oceanography, University of Washington, Seattle, Washington
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Abstract

Simultaneous measurements of temperature, salinity, their vertical gradients, and the vertical gradient of velocity across a 1.4-m-long Lagrangian float were used to investigate the accuracy with which the dissipation of scalar variance χ can be computed using inertial subrange methods from such a neutrally buoyant float. The float was deployed in a variety of environments in Puget Sound; χ varied by about 3.5 orders of magnitude. A previous study used an inertial subrange method to yield accurate measurements of ɛ, the rate of dissipation of kinetic energy, from this data. Kolmogorov scaling predicts a Lagrangian frequency spectrum for the rate of change of a scalar as ΦDσ/Dt(ω) = βsχ, where βs is a universal Kolmogorov constant. Measured spectra of the rate of change of potential density σ were nearly white at frequencies above N, the buoyancy frequency. Deviations at higher frequency could be modeled quantitatively using the measured deviations of the float from perfect Lagrangian behavior, yielding an empirical nondimensional form ΦDσ/Dt = βsχH(ω/ωL) for the measured spectra, where L is half the float length, ω3L = ɛ/L2, and H is a function describing the deviations of the spectrum from Kolmogorov scaling. Using this empirical form, estimates of χ were computed and compared with estimates derived from ɛ. The required mixing efficiency was computed from the turbulent Froude number ω0/N, where ω0 is the large-eddy frequency. The results are consistent over a range of ɛ from 10−8 to 3 × 10−5 W kg−1 implying that χ can be estimated from float data to an accuracy of least a factor of 2. These methods for estimating ɛ, χ, and the Froude number from Lagrangian floats appear to be unbiased and self-consistent for ɛ > 10−8 W kg−1. They are expected to fail in less energetic turbulence both for instrumental reasons and because the Reynolds number typically becomes too small to support an inertial subrange. The value of βs is estimated at 0.6 to within an uncertainty of less than a factor of 2.

Corresponding author address: Eric D’Asaro, Applied Physics Laboratory, University of Washington, 1013 NE 40th St., Seattle, WA 98115. Email: dasaro@apl.washington.edu

Abstract

Simultaneous measurements of temperature, salinity, their vertical gradients, and the vertical gradient of velocity across a 1.4-m-long Lagrangian float were used to investigate the accuracy with which the dissipation of scalar variance χ can be computed using inertial subrange methods from such a neutrally buoyant float. The float was deployed in a variety of environments in Puget Sound; χ varied by about 3.5 orders of magnitude. A previous study used an inertial subrange method to yield accurate measurements of ɛ, the rate of dissipation of kinetic energy, from this data. Kolmogorov scaling predicts a Lagrangian frequency spectrum for the rate of change of a scalar as ΦDσ/Dt(ω) = βsχ, where βs is a universal Kolmogorov constant. Measured spectra of the rate of change of potential density σ were nearly white at frequencies above N, the buoyancy frequency. Deviations at higher frequency could be modeled quantitatively using the measured deviations of the float from perfect Lagrangian behavior, yielding an empirical nondimensional form ΦDσ/Dt = βsχH(ω/ωL) for the measured spectra, where L is half the float length, ω3L = ɛ/L2, and H is a function describing the deviations of the spectrum from Kolmogorov scaling. Using this empirical form, estimates of χ were computed and compared with estimates derived from ɛ. The required mixing efficiency was computed from the turbulent Froude number ω0/N, where ω0 is the large-eddy frequency. The results are consistent over a range of ɛ from 10−8 to 3 × 10−5 W kg−1 implying that χ can be estimated from float data to an accuracy of least a factor of 2. These methods for estimating ɛ, χ, and the Froude number from Lagrangian floats appear to be unbiased and self-consistent for ɛ > 10−8 W kg−1. They are expected to fail in less energetic turbulence both for instrumental reasons and because the Reynolds number typically becomes too small to support an inertial subrange. The value of βs is estimated at 0.6 to within an uncertainty of less than a factor of 2.

Corresponding author address: Eric D’Asaro, Applied Physics Laboratory, University of Washington, 1013 NE 40th St., Seattle, WA 98115. Email: dasaro@apl.washington.edu

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