Skew Fluxes in Polarized Wave Fields

John F. Middleton Physical and Chemical Sceinces, Department of Fisheries and Oceans, Bedford Institute of Oceanography, Dartmouth, N.S., Canada

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John W. Loder Physical and Chemical Sceinces, Department of Fisheries and Oceans, Bedford Institute of Oceanography, Dartmouth, N.S., Canada

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Abstract

The scalar flux due to small amplitude waves that exhibit a preferred sense of rotation or polarization is shown to consist of a component. FS, that is skewed, being everywhere orthogonal to the mean scalar gradient, ∇Q. The skew flux is parameterized by FS = −D ∇Q where D, a vector diffusivity, is a measure of particle mean angular momentum. The skew flux may affect the evolution of mean scalar since its divergence, ∇·FS = US·∇Q, may be nonzero if the velocity US≈−∇ × D is up or down the mean gradient. For statistically steady waves, US corresponds to the Stokes velocity of particle drift. Integral theorems for new skew transport and the interpretation of fixed-point measurements are discussed, and the skew flux illustrated through several examples.

Abstract

The scalar flux due to small amplitude waves that exhibit a preferred sense of rotation or polarization is shown to consist of a component. FS, that is skewed, being everywhere orthogonal to the mean scalar gradient, ∇Q. The skew flux is parameterized by FS = −D ∇Q where D, a vector diffusivity, is a measure of particle mean angular momentum. The skew flux may affect the evolution of mean scalar since its divergence, ∇·FS = US·∇Q, may be nonzero if the velocity US≈−∇ × D is up or down the mean gradient. For statistically steady waves, US corresponds to the Stokes velocity of particle drift. Integral theorems for new skew transport and the interpretation of fixed-point measurements are discussed, and the skew flux illustrated through several examples.

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