A Thermodynamic Lower Bound on Transition-Triggering Disturbances

Abstract

A clear distinction must be made, in the linear analysis of flow instabilities, between instabilities that behave as self-sustained oscillators, i.e. grow unceasingly in time from arbitrarily small initial disturbances even in an infinitely quiet environment, and those that behave as spatial amplifiers, i.e. amplify disturbances that come at one spatial location from the environment to a possibly large amplitude at another location, but cease if external disturbances are switched off. In slightly more mathematical terms, the former arise from initial conditions in time and the latter from boundary conditions (or other external sources) in space. This distinction, which applies without ambiguity to spatially bounded flows of any shape, transforms into the distinction between absolute and convective instabilities in the context of spatially infinite homogeneous flows.