Spectral Analysis of a Three Dimensional Homogeneous Turbulence Submitted to a Solid Body Rotation
It is now well admitted that a solid body rotation acting on a three-dimensional and isotropic turbulence leads to the slowing of the kinetic energy decay of the fluctuating velocity field, together with a tendency to its bidimensionalisation. This last effect, which has been experimentally analysed |1|, justifies the theoretical (bi-dimensional) frame in which the turbulent flows submitted to a strong rotation have often been studied up to now. However starting from a three-dimensional state, no clear manifestation of a transition has been brought into light by direct numerical simulation |2|, |3| except in the case of initial conditions that already contained important two-dimensional structures |4|. Nevertheless these simulations reflect a clear change in the structure of the flow, primarily through the anisotropisation of the integral lengthscales, and as we have shown |5|, even in the case of a rigourously isotropic initial state, the behavior of the longitudinal length scales (separations parallel to the rotation axis) can be linked to a strong anisotropic structure of the second order spectral tensor, even if a quasi-spherical Reynolds tensor is maintained. These considerations illustrate the complexity of the problem of the transition, which has often been evaded by calling for the Batchelor-Proudman theorem, and it shows the necessity of a full three-dimensional spectral description in order to take into account the dependence on the orientation of the wave vector.
KeywordsDirect Numerical Simulation Equatorial Plane Isotropic Turbulence Solid Body Rotation Small Wave Number
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