Growing pseudo-eigenmodes and positive logarithmic norms in rotating shear flows

Abstract

Rotating shear flows, when angular momentum increases and angular velocity decreases as functions of radiation coordinate, are hydrodynamically stable under linear perturbation. The Keplerian flow is an example of such systems which appears in astrophysical context. Although decaying eigenmodes exhibit large transient energy growth of perturbation which could govern nonlinearity into the system, the feedback of inherent instability to generate turbulence seems questionable. We show that such systems exhibiting growing pseudo-eigenmodes easily reach an upper bound of growth rate in terms of the logarithmic norm of the involved nonnormal operators, thus exhibiting feedback of inherent instability. This supports the existence of turbulence of hydrodynamic origin in the Keplerian accretion disc in astrophysics. Hence, this enlightens the mismatch between the linear theory and experimental/observed data and helps in resolving the outstanding question of origin of turbulence therein.

12 pages including 4 figures; to appear in New Journal of Physics

References in corpus (3)

• A weakly nonlinear analysis of the magnetorotational instability in a model channel flow
• Growing hydrodynamic modes in Keplerian accretion disks during secondary perturbations: Elliptical vortex effects
• Possible origin of viscosity in the Keplerian accretion disks due to secondary perturbation: Turbulent transport without magnetic field

Cited by in corpus (10)

• Stability of quasi-Keplerian shear flow in a laboratory experiment
• Stochastically driven instability in rotating shear flows
• Cross-correlation Aided Transport in Stochastically Driven Accretion Flows
• Hydromagnetics of advective accretion flows around black holes: Removal of angular momentum by large scale magnetic stresses
• Magnetohydrodynamic stability of stochastically driven accretion flows
• A pure hydrodynamic instability in shear flows and its application to astrophysical accretion disks
• Origin of hydrodynamic instability from noise: from laboratory flow to accretion disk
• Forced linear shear flows with rotation: rotating Couette-Poiseuille flow, its stability and astrophysical implications
• Hydrodynamical instability with noise in the Keplerian accretion discs: Modified Landau equation
• The competition between the hydrodynamic instability from noise and magnetorotational instability in the Keplerian disks