Galtier Sébastien
Institut d'Astrophysique Spatiale, CNRS-Université de Paris XI, Bâtiment 121, 91405 Orsay Cedex, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Jul;68(1 Pt 2):015301. doi: 10.1103/PhysRevE.68.015301. Epub 2003 Jul 15.
A weak wave turbulence theory is established for incompressible fluids under rapid rotation using a helicity decomposition, and the kinetic equations for energy E and helicity H are derived for three-wave coupling. As expected, nonlinear interactions of inertial waves lead to two-dimensional behavior of the turbulence with a transfer of energy and helicity mainly in the direction perpendicular to the rotation axis. For such a turbulence, we find, analytically, the anisotropic spectra E approximately k(-5/2)(perpendicular)k(-1/2)(parallel), H approximately k(-3/2)(perpendicular)k(-1/2)(parallel), and we prove that the energy cascade is to small scales. At lowest order, the wave theory does not describe the dynamics of two-dimensional (2D) modes which decouples from 3D waves.
利用螺旋度分解，为快速旋转下的不可压缩流体建立了弱波湍流理论，并推导了三波耦合的能量E和螺旋度H的动力学方程。正如预期的那样，惯性波的非线性相互作用导致湍流的二维行为，能量和螺旋度主要在垂直于旋转轴的方向上转移。对于这种湍流，我们通过解析得到了各向异性谱E近似为k^(-5/2)(垂直)k^(-1/2)(平行)，H近似为k^(-3/2)(垂直)k^(-1/2)(平行)，并且证明了能量级联是向小尺度的。在最低阶，波动理论没有描述与三维波解耦的二维（2D）模式的动力学。
