NUMERICAL STUDY OF INSTABILITY IN A HORIZONTAL POROUS CHANNEL WITH BOTTOM HEATING AND FORCED HORIZONTAL FLOW

We study the two-dimensional convective patterns in a long horizontal porous layer heated from below, where a nonzero cross-flow is imposed. Indeed experiments show that time-periodic planar flows are found at moderate values of the flow rate. Within the framework of the Darcy la w, above the absolute threshold, varied end-conditions lead to oscilla tory patterns, which are more or less similar to each other in the bul k of the device but present differences near the extremities. Dependin g on the boundary-conditions, the numerical simulation may produce pat terns which are space-periodic traveling rolls or waves of amplitude m odulated within a stationary region, with envelopes in the form of fro nts. Space-periodic boundary-conditions yield wavelengths linked to th e total length of the device, which sets: the frequency. Input boundar y-conditions breaking translational invariance along the direction of the main flow yield different structures and select the temporal perio d. Most attention is paid to inlet-conditions imposing a linear profil e of temperature (at the entrance of the device). We study the variati ons of the frequency vs the seeping flow rate and the filtration Rayle igh number. The length of the resulting front is also considered. (C) 1998 American Institute of Physics.