Inertial and kinetic-Alfv'en wave turbulences have a priori little in common: indeed, the first one concerns rotating hydrodynamics in the limit of a small Rossby number (with $\bol$ the rotating rate) while the second describes high frequency plasmas in the limit of a strong uniform magnetic field $B_0$. In this paper we show analytically that in the limit of local interactions in the perpendicular direction to $\bol$, the inertial wave turbulence equation converges towards the same nonlinear diffusion equation as for kinetic-Alfv'en waves when the same limit is taken; the only difference resides in the constants in front of the equations. Therefore, both systems share the same physical properties with for the stationary phase an energy spectrum in $\kpn^{-5/2}$; it is preceded by a self-similar solution of the second kind during the non-stationary phase with a spectrum proportional to $\kpn^{-8/3}$ which propagates explosively towards small scales. It is suggested that the proximity between these two problems may be used to better understand inertial or kinetic-Alfv'en wave turbulence.

中文翻译：

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惯性/运动Alfvén波湍流：局域相互作用极限中的一个孪生问题

惯性和动力学Alfv'en波湍流具有先验的共同点：确实，第一个涉及在较小Rossby数（旋转速率为\ bol $）的范围内的旋转流体动力学，而第二个则描述了高频等离子体。强均匀磁场的极限${乙}_0$。在本文中，我们分析地表明，在垂直于$ \ bol $的局部相互作用的极限中，当采用相同的极限时，惯性波湍流方程朝着与动力学Alfv'en波相同的非线性扩散方程收敛。唯一的区别在于方程式前面的常数。因此，两个系统都具有相同的物理特性，其中固定相的能谱为$ \ kpn ^ {-5/2} $。它在非平稳阶段之前具有第二种自相似解，其频谱与$ \ kpn ^ {-8/3} $成比例爆炸性地向小规模传播。建议将这两个问题之间的接近度用于更好地理解惯性或动力学Alfv'en波湍流。