Models for convection in thawing porous media in support for the subsea permafrost equations

Abstract

When permafrost becomes submerged because of shore line erosion, the covering ocean acts as a thermal insulator, and the submerged permafrost starts to melt. The thawed layer is bounded above by the ocean bed through which salt may intrude and by the phase boundary which for a fixed offshore position is known to progress with the square root of time. This situation gives rise to nonsteady double‐diffusion coupling Bénard convection and liquefaction which can be described by the Darcy‐Oberbeck‐Boussinesq equations. The boundary value problem is formulated, and scalings are introduced which orient themselves on the relative magnitudes of phase boundary and convective bulk velocities of the salt convective regime identified by Harrison [1982]. The multiscale perturbation analysis that is introduced not only verifies the observed thaw rates with a parabolic‐in‐time phase boundary retreat, it equally automatically generates the equations for the corresponding perturbative equations such as the double‐diffusion Bénard problem, the associated eigenvalue problem, its corrections and possible convective flows induced by the various possible currents induced by the ocean circulation overlying the thawed permafrost layer. The demonstration of this systematic approach is the main purpose of this paper.