Nature and dynamics of pseudo- and shear-Alfven waves overreflection in incompressible MHD shear flows
Wave overreflection – that is a shear flow non-normality induced phenomenon – often determines the dynamics of flow systems. We proposed new route of the overreflection dynamics analysis on an example of incompressible MHD constant shear flow containing pseudo- and shear-Alfven waves (PAW and SAW): introduced separate/normal variables for each counter propagating wave (that is, Elsasser variables in MHD flows) and, reduced the perturbation equations to two first-order ordinary differential equations for each counter propagating wave. The proposed analysis allows us to separate from each other basic physical processes, to follow their interplay and to gain new insights into the physics of the overreflection. Specifically, our study grasps and describes intrinsic linear coupling of counter propagating waves – the root of the overreflection. It is shown that: (1) PAW with long stream wise wavelength exhibit stronger growth and become more balanced, (2) PAW and SAW branches are not coupled (in the linear limit) with each other, (3) counter propagating SAW are coupled with each other, like counter propagating PAW, (4) the growth and balance degree of SAW are small compared with those of PAW waves. The proposed route is canonical/optimal and is easily applicable to widely discussed cases of the overreflection of spiral-density waves in astrophysical discs and of internal-gravity waves in stably stratified atmospheres.