BUOYANT FLOWS WITH LOW-FREQUENCY JITTER

A slot with applied temperature stratification is considered when mean gravity is directed along its length and weak quasistatic jitter is a pplied in the spanwise direction, but when there is no component of gr avity in the vertical. The behavior of the slot is governed by a numbe r of factors: The sense of the mean gravity with respect to the applie d stratification, the spanwise and lengthwise Rayleigh numbers, the Pr andtl and Blot numbers, and the spanwise-lengthwise aspect ratio of th e slot. A perturbation expansion of the governing equations is perform ed for weak spanwise jitter. At the first order of perturbation there is a circulation around the slot, producing an advected temperature fi eld with spanwise gradients. At second order there are inflows or outf lows in both the spanwise and lengthwise directions, along with a vert ical redistribution of fluid. There is also a temperature field with l engthwise gradients, which typically competes with the applied tempera ture gradient. Equations are derived governing the vertical structure of all these fields and are solved in terms of a set of special basis functions. A parametric study is performed for the solutions. When len gthwise buoyancy forces are absent (the lengthwise Rayleigh number is zero), it is comparatively easy to deduce the required fields. However , finite lengthwise Rayleigh numbers couple the momentum and thermal e quations thereby affecting the structure of the fields. Interesting be havior is predicted for small Blot numbers, when convected heat is eff ectively trapped in the slot: Infinitessimal flows can produce finite advected temperatures. The limits of small Blot number and small lengt hwise Rayleigh number are found to be noninterchangeable. At large len gthwise Rayleigh number, boundary layers occur for stable applied stra tification and layered cellular structures occur for unstable stratifi cation. For the stable case at moderately small Blot number, the tempe rature jump across the boundary layer is small compared with the depth independent temperature in the bulk. Then by exploiting the boundary layer nature of the solutions, it becomes simple to predict the bulk f luid temperatures, interfacial heat fluxes and the circulations associ ated with the buoyant flows. Turning to the unstably stratified case, it is demonstrated that runaways can occur at first order in the spanw ise jitter, and these correspond to resonant excitation of three-dimen sional, stationary, long wave Rayleigh-Benard modes. It is demonstrate d how the Blot number and the spanwise-lengthwise aspect ratio of the slot influence the lengthwise Rayleigh number at which these resonance s occur. There is in addition a set of two-dimensional Rayleigh-Benard modes, which can potentially become excited at second order. When the Blot number and the spanwise-lengthwise aspect ratio are not too larg e, the Rayleigh numbers corresponding to the two sets of modes are nea rly coincident. The second-order system will then be strongly forced n ear resonance, causing it to have a disproportionately large response. (C) 1998 American Institute of Physics.