Influence of permeability anisotropy and boundary conditions on thermal convection in seabed sediments

Abstract

We study how the surface boundary condition and permeability anisotropy influence the convective instability in seabed sediments. The sediments are modeled as a horizontal two-layer system consisting of an upper porous layer saturated with water (impurities are neglected) and a lower impermeable semi-infinite massif. Two types of boundary conditions for the filtration flow at the upper surface (the bottom of the water body) are considered: an open boundary and an impermeable boundary. A linear stability analysis is performed within the adjoint problem of convection in the porous layer and the heat transfer in the impermeable massif below. The stream function and the temperature of convective instability are calculated depending on the values of the permeability anisotropy parameter. It is shown that the stagnation point within the convective roll shifts down to the lower boundary of the porous layer in a medium with greater anisotropy. The temperature field penetrates deeper into the impermeable massif with increasing permeability anisotropy. We obtained equations defining the neutral stability curves for different values of the anisotropy parameter and under different upper boundary conditions. The convective threshold increases with the decreasing permeability of the upper boundary. An increase in anisotropy significantly lowers the convective instability threshold and decreases the critical wave number. In the limit of strong permeability anisotropy, when the liquid flows through the porous medium in the horizontal direction almost without resistance, convection becomes longwave, the convective threshold is an order of magnitude lower compared to an isotropic medium.