Salhi A, Jacobitz F G, Schneider K, Cambon C
Département de Physique, Faculté des Sciences de Tunis, 1060, Tunis, Tunisia and Laboratoire de Mécanique des Fluides et d'Acoustique, Ecole Centrale de Lyon, UMR 5509, CNRS, INSA, UCB, 69134 Ecully Cedex, France.
Mechanical Engineering Department, Shiley-Marcos School of Engineering, University of San Diego, 5998 Alcalá Park, San Diego, California 92110, USA and M2P2 - UMR 7340 - CNRS & CMI, Aix-Marseille Université, 38 rue Joliot-Curie, 13451 Marseille Cedex 20, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Jan;89(1):013020. doi: 10.1103/PhysRevE.89.013020. Epub 2014 Jan 27.
Homogeneous turbulence in rotating shear flows is studied by means of pseudospectral direct numerical simulation and analytical spectral linear theory (SLT). The ratio of the Coriolis parameter to shear rate is varied over a wide range by changing the rotation strength, while a constant moderate shear rate is used to enable significant contributions to the nonlinear interscale energy transfer and to the nonlinear intercomponental redistribution terms. In the destabilized and neutral cases, in the sense of kinetic energy evolution, nonlinearity cannot saturate the growth of the largest scales. It permits the smallest scale to stabilize by a scale-by-scale quasibalance between the nonlinear energy transfer and the dissipation spectrum. In the stabilized cases, the role of rotation is mainly nonlinear, and interacting inertial waves can affect almost all scales as in purely rotating flows. In order to isolate the nonlinear effect of rotation, the two-dimensional manifold with vanishing spanwise wave number is revisited and both two-component spectra and single-point two-dimensional energy components exhibit an important effect of rotation, whereas the SLT as well as the purely two-dimensional nonlinear analysis are unaffected by rotation as stated by the Proudman theorem. The other two-dimensional manifold with vanishing streamwise wave number is analyzed with similar tools because it is essential for any shear flow. Finally, the spectral approach is used to disentangle, in an analytical way, the linear and nonlinear terms in the dynamical equations.
