Transient Response and Disturbance Growth in Vertical Buoyancy-Driven Flows

The basic physical characteristics of flow response to a changed bounding-surface energy input is reviewed. Response regimes are delineated in terms of locally laminar, unstable, transition, and turbulent flows and dimensionality and regimes intermediate to the others. Very large transient heat transfer effects arise. A key general question is how such regimes become unstable and progress to turbulence. Transient disturbance growth analysis is very difficult and few results are available. This paper develops a general and purely numerical formulation for two-dimensional transient response and disturbance growth. It relies on imposed random flow and associated temperature and disturbance motion pressure disturbances. It applies to any boundary region regime and is specialized here to disturbance growth in a developing buoyancy-driven flow, as an example.