Instabilities in three-dimensional differentially-heated cavities with adiabatic horizontal walls

Abstract

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 adiabatic. Emphasis is on (though not restricted to) the air-filled, cubical cavity. For this configuration, it was found that the occurrence of unsteady oscillations in the flow was preceded by a steady instability (i.e. an instability resulting in a steady solution of the Navier-Stokes equations for large time) which originated in an internal, stratified shear layer that separates from the adiabatic horizontal walls of the cavity. This instability is inherently three-dimensional and characterized by the presence of streamwise-oriented, counterrotating vortices. 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 counterpart in the two-dimensional, square cavity. For larger Prandtl numbers, however, the frequencies in the two- and three-dimensional cavities are almost equal since no prior steady instability occurs. The instability mechanism responsible for the unsteady instability is therefore the same in both configurations even though the instability in the three-dimensional cavity shows a distinct wave-like modulation in the third direction. © 1996 American Institute of Physics.