We highlight a noncanonical yet natural choice of variables for an efficient derivation of a kinetic equation for the energy density in nonisotropic systems, including internal gravity waves on a vertical plane, inertial, and Rossby waves. The existence of a second quadratic invariant simplifies the kinetic equation and leads to extra conservation laws for resonant interactions. We analytically determine the scaling of the radial turbulent energy spectrum. Our findings suggest the existence of an inverse energy cascade of internal gravity waves, from small to large scales, in practically relevant scenarios.

中文翻译：

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符号不定不变量塑造湍流级联


我们强调了非规范但自然的变量选择，用于有效推导非各向同性系统中能量密度的动力学方程，包括垂直平面上的内部重力波、惯性波和罗斯贝波。第二个二次不变量的存在简化了动力学方程并导致了共振相互作用的额外守恒定律。我们通过分析确定了径向湍流能谱的比例。我们的研究结果表明，在实际相关的场景中，存在从小尺度到大尺度的内部重力波的逆能量级联。