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Kolmogorov laws for stratified turbulence

Abstract : Following the Kolmogorov technique, an exact relation for a vector third-order moment J is derived for three-dimensional incompressible stably stratified turbulence under the Boussinesq approximation. In the limit of a small Brunt-Vaisala frequency, isotropy may be assumed which allows us to find a generalized 4/3-law. For strong stratification, we make the ansatz that J is directed along axisymmetric surfaces parameterized by a scaling law relating horizontal and vertical coordinates. An integration of the exact relation under this hypothesis leads to a generalized Kolmogorov law which depends on the intensity of anisotropy parameterized by a single coefficient. By using a scaling relation between large horizontal and vertical length scales we fix this coefficient and propose a unique law.
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Pierre Augier, Sebastien Galtier, Paul Billant. Kolmogorov laws for stratified turbulence. Journal of Fluid Mechanics, 2012, 709, pp.659-670. ⟨10.1017/jfm.2012.379⟩. ⟨hal-00996508⟩

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