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This paper reports on a direct measurement of the turbulent heat flux. The sampling was from a submarine that used a conventional airfoil probe to measure the vertical component of turbulent velocity and a thermistor probe to measure the temperature fluctuations in a well-defined, shear-driven, turbulent weakly stratified layer. Error analyses indicate that these heat flux estimates are the first statistically significant results. A comparison between the direct measurements and an eddy diffusivity model shows that the flux Richardson number in the shear layer is about 0.05. The dominant heat flux contribution is in the neighborhood of 0.7-cpm wavenumber.
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Yamazaki et al. (1993) studied this question.
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