Non-exponential hydrodynamical growth in density-stratified thin Keplerian discs

TL;DR

This paper investigates the short-term evolution of small perturbations in thin, density-stratified Keplerian discs, revealing non-modal hydrodynamical growth mechanisms that could lead to turbulence despite spectral stability.

Contribution

It identifies and analyzes two non-modal growth mechanisms in thin discs, providing new insights into potential turbulence pathways beyond classical stability analysis.

Findings

Non-resonant excitation causes linear growth of perturbations.

Resonant coupling leads to quadratic growth of initial disturbances.

Non-modal growth may trigger secondary instabilities and turbulence.

Abstract

The short time evolution of three dimensional small perturbations is studied. Exhibiting spectral asymptotic stability, thin discs are nonetheless shown to host intensive hydrodynamical activity in the shape of non modal growth of initial small perturbations. Two mechanisms that lead to such behavior are identified and studied, namely, non-resonant excitation of vertically confined sound waves by stable planar inertia-coriolis modes that results in linear growth with time, as well as resonant coupling of those two modes that leads to a quadratic growth of the initial perturbations. It is further speculated that the non modal growth can give rise to secondary strato-rotational instabilities and thus lead to a new route to turbulence generation in thin discs.