Wave turbulence in a rotating channel: numerical implementation and results
Résumé
The analysis of Scott (2014) is implemented numerically. Decaying turbulence is confined toa channel between two infinite, parallel, rotating walls. The Rossby and Ekman numbers aresupposed small, the former condition making nonlinearity small, while the latter allows theturbulence to persist for the many rotational periods needed for the small nonlinearity to beeffective. The flow is expressed as a combination of inertial waveguide modes, indexed by atwo-dimensional wave vector k and an integer n. n=0 modes form a 2D component of theflow, whereas the remainder is the wave component, on which attention is focused in thisarticle. Assuming statistical axisymmetry and homogeneity in directions parallel to the walls,the second-order moments of the mode amplitudes yield a spectral matrix, A_nm(k,t) (wherek=|k|), of which the diagonal elements describe the distribution of energy over differentmodes. Wave-turbulence analysis provides an equation governing the time evolution of A_nn,(n non zero), the wave spectra, which forms the basis for the present work. The initial distribution of energy is Gaussian and depends on a parameter XI, the initial spectral width. The problem has two other parameters, beta_w and beta_v , which correspond to two distinct viscous dissipative mechanisms: wall damping due to boundary layers and volumetric damping by viscous effects throughout the flow. Results obtained by numerical solution include the timeevolution of the total wave energy, E, and the detailed description of its distribution over kand n provided by A_nn(k).
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