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.
KeywordsVortex Anisotropy Boulder Cose
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