An optimal transient growth of small perturbations in thin gaseous discs

TL;DR

This paper demonstrates that even spectrally stable thin gaseous discs can experience significant transient growth of linear perturbations, which has implications for understanding disc stability and dynamics.

Contribution

It introduces a model showing substantial transient growth of perturbations in nearly Keplerian thin discs, highlighting a mechanism for instability despite spectral stability.

Findings

Transient growth can be significant in stable discs

Perturbations are modeled as neutral modes with corotational radius

Implications for disc stability and evolution

Abstract

A thin gaseous disc with an almost keplerian angular velocity profile, bounded by a free surface and rotating around point-mass gravitating object is nearly spectrally stable. Despite that the substantial transient growth of linear perturbations measured by the evolution of their acoustic energy is possible. This fact is demonstrated for the simple model of a non-viscous polytropic thin disc of a finite radial size where the small adiabatic perturbations are considered as a linear combination of neutral modes with a corotational radius located beyond the outer boundary of the flow.