Stochastically driven instability in rotating shear flows

TL;DR

This paper investigates how stochastic noise can induce instability and turbulence in Rayleigh stable rotating shear flows, like those in astrophysical disks, by analyzing perturbation correlations and energy dissipation.

Contribution

It introduces the novel idea that additive stochastic noise can cause instability in Rayleigh stable flows, providing a new perspective on turbulence origin in astrophysical contexts.

Findings

Stochastic noise leads to large correlations and energy dissipation in perturbations.

All tested angular velocity profiles show similar growth and roughness exponents.

The results suggest a universal behavior in stochastically forced rotating shear flows.

Abstract

Origin of hydrodynamic turbulence in rotating shear flows is investigated. The particular emphasis is the flows whose angular velocity decreases but specific angular momentum increases with increasing radial coordinate. Such flows are Rayleigh stable, but must be turbulent in order to explain observed data. Such a mismatch between the linear theory and observations/experiments is more severe when any hydromagnetic/magnetohydrodynamic instability and then the corresponding turbulence therein is ruled out. The present work explores the effect of stochastic noise on such hydrodynamic flows. We essentially concentrate on a small section of such a flow which is nothing but a plane shear flow supplemented by the Coriolis effect. This also mimics a small section of an astrophysical accretion disk. It is found that such stochastically driven flows exhibit large temporal and spatial correlations of perturbation velocities, and hence large energy dissipations of perturbation, which presumably generate instability. A range of angular velocity (\Omega) profiles of background flow, starting from that of constant specific angular momentum (\lambda = \Omega r^2 ; r being the radial coordinate) to that of constant circular velocity (v_\phi = \Omega r), is explored. However, all the background angular velocities exhibit identical growth and roughness exponents of perturbations, revealing a unique universality class for the stochastically forced hydrodynamics of rotating shear flows. This work, to the best of our knowledge, is the first attempt to understand origin of instability and turbulence in the three-dimensional Rayleigh stable rotating shear flows by introducing additive noise to the underlying linearized governing equations. This has important implications to resolve the turbulence problem in astrophysical hydrodynamic flows such as accretion disks.