A local nonlinear solution as an approximation to low-frequency spanwise jitter in thermoconvective flows

Abstract

A shallow fluid-filled cavity with a longitudinal applied temperature gradient is subjected to spanwise accelerations (g-jitter) representing the space-based microgravity environment. A simplified slot model is introduced to describe the buoyancy-driven flow and advected temperature fields produced in the cavity. Numerical solutions indicate that boundary layer behaviour can manifest itself in the limit of strong g-jitter (large Rayleigh number Ra). However, boundary layer thicknesses do not obey the conventional Ra^−1/4 scaling that typically arises in free thermal convection problems. This anomalous scaling results from the three-dimensional complexity of the flow and advected temperature fields, which are not themselves produced by a single fixed applied temperature change. Three different regimes are identified at large Rayleigh number characterized by the shapes of the advected temperature profiles. These regimes are selected according to the values of the Biot number Bi and an aspect ratio parameter. Simple models are presented of the boundary layer behaviour which reproduce, in each regime, the numerically predicted scalings for boundary layer thickness and advected temperature. These models give a succinct overall picture of the slot behaviour in the buoyancy-dominated limit.