THERMOCAPILLARY AND BUOYANT FLOWS WITH LOW-FREQUENCY JITTER - I - JITTER CONFINED TO THE PLANE

A temperature gradient is applied along a fluid filled slot with a fla t upper interface, establishing how via thermocapillarity and/or buoya ncy. There is a known parallel. flow along the slot, in which the flui d velocity varies vertically, and there is a known convected temperatu re profile. This parallel flow is then subjected to gravitational modu lation or ''jitter'' which is applied at low frequency and in various directions. For gravity modulations in the plane of the basic flow, an alytic solutions for velocity and temperature profiles are obtained fo r jitter of arbitrary amplitude. These solutions involve modifications to the earlier parallel flow solutions. Jitter in the vertical direct ion generates vorticity due to coupling with the applied horizontal te mperature gradient. This alternately cooperates or competes with the s teady basic how over a cycle of the modulation, but does not qualitati vely change the flow or temperature profiles. Jitter applied along the slot produces vorticity only when coupled to vertical convected tempe rature gradients and so is important when the basic flow is sufficient ly strong (large Marangoni and/or Rayleigh number). Various cases are considered for the basic flow, which may be driven by thermocapillarit y alone, by vertical gravity alone or by a mixture of thermocapillarit y and Vertical gravity. When strong streamwise jitter is added to any of these cases, the flow profile alternates during the modulation cycl e between boundary layer structures and vertically stacked cells. The type of structure selected depends on the sense of the horizontal ther mal stratification with respect to the jitter, and in that part of the cycle where this stratification is unstable, there are particular amp litudes of jitter which can give strong cellular motions or runaways. These runaways represent a resonant interaction with stationary Raylei gh-Benard cells. (C) 1998 American Institute of Physics.