P. S. Joarder | Searcharxiv

arXiv1997

On the absence of dissipative instability of negative energy waves in hydrodynamic shear flows

Stability criterion for the surface gravity capillary waves in a flowing two-layered fluid system with viscous dissipation is investigated. It is seen that the dissipative instability of negative energy waves is absent,- contrary to what earlier authors have concluded. Their error is identified to arise from an erroneous choice of the dissipation law, in which the wave profile velocity is wrongly equated to the particle velocity. Our corrected dissipation law is also shown to restore Galilean invariance to the stability condition of the system.

physics.flu-dyn↗

arXiv1997

Energy Calculation of Magnetohydrodynamic Waves and Their Stability For Viscous Shearing Flows

A self-consistent, thermodynamic approach is employed to derive the wave energy of a magnetohydrodynamic system within the harmonic approximation and to obtain the familiar dispersion relation from the resulting equation of motion. The evolution of the system due to an external perturbation is studied by a linear response formalism, that also gives the energy absorbed by the magnetohydrodynamic system from the external field. The calculated wave energy reveals the presence of positive and negative energy waves, that coalesce together to give rise to Kelvin - Helmholtz instability of the system. The threshold value of this instability changes only slightly in the presence of a small amount of viscosity, thus precluding the dissipative instability of the negative energy waves. The prediction of such a dissipative instability by earlier authors turns out to be the result of an erroneous choice of the viscous drag force, that violates the fundamental law of Galilean invariance.

physics.plasm-ph↗