THERMOCAPILLARY AND BUOYANT FLOWS WITH LOW-FREQUENCY JITTER - II - SPANWISE JITTER

A temperature gradient is applied along a fluid filled slot. A basic s tate is considered where the slot is subject to thermocapillary forces and vertical mean gravity, each of which produces a parallel flow and a vertical advected temperature gradient, and is also subject to stre amwise mean gravity, which will make the applied temperature stratific ation either stable or unstable. When this basic state is perturbed by jitter imposed in the spanwise direction, normal to the plane of the basic flow, the resulting fluid motion is three dimensional. The flow and temperature fields are found to have a simple functional dependenc e on streamwise and spanwise coordinates, but retain a complicated dep endence on vertical coordinate. Perturbation equations describing the vertical variation of these fields are derived when the jitter is weak . At first order in the spanwise jitter, there is a time periodic span wise-streamwise circulation around the slot. As this circulation also advects heat, it produces spanwise temperature gradients, enabling the rmocapillarity and vertical gravity to generate subsidiary spanwise fl ows. At next order in the weak spanwise jitter, parallel streamwise fl ows are encountered, along with streamwise and vertical temperature gr adients. In most parameter regimes these are opposed to the flow and t emperature fields in the basic state. A thorough parametric investigat ion is performed where the weak spanwise jitter equations are solved, assuming for simplicity that streamwise gravity is absent. This leads to comparatively simple polynomial solutions in vertical coordinate fo r the various fields. A large number of parameters can still affect th e solutions, however, and a detailed parametric investigation is perfo rmed. Interesting behavior is found at small Blot number, with trappin g of heat producing large temperatures in the slot and large subsidiar y flows. The spanwise to streamwise aspect ratio is another influentia l parameter, since geometric constraints encountered at extreme values of this ratio suppress certain velocity components of the flow and en hance others, thereby suppressing or enhancing temperature advection. These advected temperature fields themselves produce subsidiary veloci ties and subsidiary temperatures, which can exhibit a subtle and often counterintuitive dependence on the spanwise-streamwise aspect ratio. (C) 1998 American Institute of Physics.