Inertial/kinetic-Alfvén wave turbulence: A twin problem in the limit of local interactions
Résumé
Inertial and kinetic-Alfvén wave turbulences have a priori little in common: indeed, the first one concerns rotating hydrodynamics in the limit of a small Rossby number (with 0 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 0 , the inertial wave turbulence equation converges towards the same nonlinear diffusion equation as for kinetic-Alfvén 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 for the stationary phase with an energy spectrum in k −5/2 ⊥ ; it is preceded by a self-similar solution of the second kind during the nonstationary phase with a spectrum proportional to k −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-Alfvén wave turbulence.
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