Linear coupling and overreflection phenomena of magnetohydrodynamic waves in smooth shear flows

Abstract

Special features of magnetohydrodynamic waves linear dynamics in smooth shear flows are studied. Quantitative asymptotic and numerical analysis are performed for wide range of system parameters when basic flow has constant shear of velocity and uniform magnetic field is parallel to the basic flow. The special features consist of magnetohydrodynamic wave mutual transformation and over-reflection phenomena. The transformation takes place for arbitrary shear rates and involves all magnetohydrodynamic wave modes. While the over-reflection occurs only for slow magnetosonic and Alfvén waves at high shear rates. Studied phenomena should be decisive in the elaboration of the self-sustaining model of magnetohydrodynamic turbulence in the shear flows.

Linear coupling of acoustic and cyclotron waves in plasma flows

“…From physical point of view this means, that there are no (over)reflection phenomena [18] and only the resonant coupling between different waves modes with the same sign of phase velocity can occur. From (11) we also learn that there are two pairs of complex conjugated resonant points of the first order 1 :…”

“…Generally, the time scale of resonant coupling ∆τ is of the order of ∆τ ∼ R −1/2 [18] and the evolution of the waves is adiabatic when…”

“…It is well known [24] that in this case components of T ± and T ∓ are exponentially small with respect to the large parameter 1/R and can be neglected. Consequently, (18) decomposes and reduces to:…”

“…In [18] these efficient mathematical tools were used, for the first time, for the study of the velocity shear induced coupling and transformation of MHD waves. The problem which we are studying now, also allows thorough probing by means of this asymptotic method.…”

“…First, it demonstrates that the shear-induced transformations in plasmas are not characteristic only to MHD systems but they exist and are efficient also for low-frequency electrostatic waves: the ion-sound waves (ISW) and the ion-cyclotron waves (ICW). Second, using recently developed method of the evaluation of the transformation coefficients [18], we give full quantitative and analytic description of the coupling efficiency for the case of low shearing rate flows. Third, we point out that the mathematical description of this particular sort of wave coupling is exactly analogous to the one in neutral fluid flows: coupling of sound waves with internal gravity waves [11]!…”