Skewness of Spatial Gradients of Turbulent Dissipation Rates in the Mixed Layer

S. A. Thorpe School of Ocean Sciences, Menai Bridge, Anglesey, United Kingdom

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T. R. Osborn Department of Earth and Planetary Sciences, The Johns Hopkins University, Baltimore, Maryland

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Abstract

Temperature ramps or microfronts are coherent tilted structures in the oceanic and atmospheric boundary layers at which there are small, but detectable, changes in mean temperature. Their presence contributes to a nonzero skewness, ST(θ), of the spatial derivatives of temperature, dT/dx, at constant depth within the ocean mixed layer. The skewness ST(θ) has a roughly sinusoidal variation with θ, the direction in which the derivatives are measured relative to the wind. The magnitude of the skewness, |ST(0)|, measured in a direction into the wind (θ = 0) is of order unity, and the sign of ST(0) depends on the heat flux from the air to the water through the sea surface, being positive if the heat flux is positive. Recent observations using an AUV, Autosub, have shown that the mean values of ε, the rate of dissipation of turbulent kinetic energy per unit mass, change as temperature ramps are crossed. This observation raises the questions: Is the skewness of the gradient of logε, Slogε(θ), nonzero in the mixed layer even though ε is observed to be lognormal? If so, is Slogε(θ) related to ST(θ)? The answer to both of the questions appears to be “yes,” although the magnitude of Slogε(θ) is small, of order 5 × 10−2, and no clearly detectable variation with θ is found in the available data.

Corresponding author address: Dr. Steve A. Thorpe, Bodfryn, Glanrafon, Llangoed, Anglesey, LL58 8PH, United Kingdom. Email: oss413@sos.bangor.ac.uk

Abstract

Temperature ramps or microfronts are coherent tilted structures in the oceanic and atmospheric boundary layers at which there are small, but detectable, changes in mean temperature. Their presence contributes to a nonzero skewness, ST(θ), of the spatial derivatives of temperature, dT/dx, at constant depth within the ocean mixed layer. The skewness ST(θ) has a roughly sinusoidal variation with θ, the direction in which the derivatives are measured relative to the wind. The magnitude of the skewness, |ST(0)|, measured in a direction into the wind (θ = 0) is of order unity, and the sign of ST(0) depends on the heat flux from the air to the water through the sea surface, being positive if the heat flux is positive. Recent observations using an AUV, Autosub, have shown that the mean values of ε, the rate of dissipation of turbulent kinetic energy per unit mass, change as temperature ramps are crossed. This observation raises the questions: Is the skewness of the gradient of logε, Slogε(θ), nonzero in the mixed layer even though ε is observed to be lognormal? If so, is Slogε(θ) related to ST(θ)? The answer to both of the questions appears to be “yes,” although the magnitude of Slogε(θ) is small, of order 5 × 10−2, and no clearly detectable variation with θ is found in the available data.

Corresponding author address: Dr. Steve A. Thorpe, Bodfryn, Glanrafon, Llangoed, Anglesey, LL58 8PH, United Kingdom. Email: oss413@sos.bangor.ac.uk

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