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Kolmogorov laws for stratified turbulence

Published online by Cambridge University Press:  31 August 2012

Pierre Augier
LadHyX, CNRS, École Polytechnique, 91128 Palaiseau CEDEX, France
Sébastien Galtier
Institut d’Astrophysique Spatiale, Université Paris-Sud, bâtiment 121, 91405 Orsay, France
Paul Billant
LadHyX, CNRS, École Polytechnique, 91128 Palaiseau CEDEX, France


Following the Kolmogorov technique, an exact relation for a vector third-order moment is derived for three-dimensional incompressible stably stratified turbulence under the Boussinesq approximation. In the limit of a small Brunt–Väisälä frequency, isotropy may be assumed which allows us to find a generalized -law. For strong stratification, we make the ansatz that 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.

Copyright © Cambridge University Press 2012

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