INSTABILITIES IN 3-DIMENSIONAL DIFFERENTIALLY-HEATED CAVITIES WITH ADIABATIC HORIZONTAL WALLS

Considered are the transitional instabilities of the flow inside three -dimensional rectangular cavities that are differentially heated over two opposing vertical walls. The horizontal and lateral walls are adia batic. Emphasis is on (though not restricted to) the nir-filled, cubic al cavity. For this configuration, it was found that the occurrence of unsteady oscillations in the flow was preceded by a steady instabilit y (i.e. an instability resulting in a steady solution of the Navier-St okes equations for large time) which originated in an internal, strati fied shear layer that separates from the adiabatic horizontal walls of the cavity. This instability is inherently three-dimensional and char acterized by the presence of streamwise-oriented, counterrotating vort ices. It is probably caused by centrifugal forces. The subsequent, low -frequency, unsteady instability is strongly influenced by this steady instability and as a result its frequency differs strongly from its c ounterpart in the two-dimensional, square cavity. For larger Prandtl n umbers, however, the frequencies in the two- and three-dimensional cav ities are almost equal since no prior steady instability occurs. The i nstability mechanism responsible for the unsteady instability is there fore the same in both configurations even though the instability in th e three-dimensional cavity shows a distinct wave-like modulation in th e third direction. (C) 1996 American Institute of Physics.