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Fluids 2017, 2(2), 28; doi:10.3390/fluids2020028

Anisotropic Wave Turbulence for Reduced Hydrodynamics with Rotationally Constrained Slow Inertial Waves

1
Department of Applied Mathematics, University of Colorado, Boulder, CO 80045, USA
2
Tata Institute of Fundamental Research, Hyderabad 500075, India
Academic Editors: Helena Margarida Ramos and Mehrdad Massoudi
Received: 8 March 2017 / Revised: 13 May 2017 / Accepted: 24 May 2017 / Published: 27 May 2017
(This article belongs to the Special Issue Advances in Hydrodynamics)
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Abstract

Kinetic equations for rapidly rotating flows are developed in this paper using multiple scales perturbation theory. The governing equations are an asymptotically reduced set of equations that are derived from the incompressible Navier-Stokes equations. These equations are applicable for rapidly rotating flow regimes and are best suited to describe anisotropic dynamics of rotating flows. The independent variables of these equations inherently reside in a helical wave basis that is the most suitable basis for inertial waves. A coupled system of equations for the two global invariants: energy and helicity, is derived by extending a simpler symmetrical system to the more general non-symmetrical helical case. This approach of deriving the kinetic equations for helicity follows naturally by exploiting the symmetries in the system and is different from the derivations presented in an earlier weak wave turbulence approach that uses multiple correlation functions to account for the asymmetry due to helicity. Stationary solutions, including Kolmogorov solutions, for the flow invariants are obtained as a scaling law of the anisotropic wave numbers. The scaling law solutions compare affirmatively with results from recent experimental and simulation data. Thus, anisotropic wave turbulence of the reduced hydrodynamic system is a weak turbulence model for strong anisotropy with a dominant k cascade where the waves aid the turbulent cascade along the perpendicular modes. The waves also enable an appropriate closure of the kinetic equation through averaging of their phases. View Full-Text
Keywords: multi-scale perturbation; slow helical waves; slow manifold; rapidly rotating turbulence multi-scale perturbation; slow helical waves; slow manifold; rapidly rotating turbulence
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Sen, A. Anisotropic Wave Turbulence for Reduced Hydrodynamics with Rotationally Constrained Slow Inertial Waves. Fluids 2017, 2, 28.

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