K. Hutter et B. Straughan, Models for convection in thawing porous media in support for the subsea permafrost equations, J GEO R-SOL, 104(B12), 1999, pp. 29249-29260
When permafrost becomes submerged because of shore line erosion, the coveri
ng ocean acts as a thermal insulator, and the submerged permafrost starts t
o melt. The thawed layer is bounded above by the ocean bed through which sa
lt may intrude and by the phase boundary which for a fixed offshore positio
n is known to progress with the square root of time. This situation gives r
ise to nonsteady double-diffusion coupling Benard convection and liquefacti
on which can be described by the Darcy-Oberbeck-Boussinesq equations. The b
oundary value problem is formulated, and scalings are introduced which orie
nt themselves on the relative magnitudes of phase boundary and convective b
ulk 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 pertur
bative equations such as the double-diffusion Benard problem, the associate
d eigenvalue problem, its corrections and possible convective flows induced
by the various possible currents induced by the ocean circulation overlyin
g the thawed permafrost layer. The demonstration of this systematic approac
h is the main purpose of this paper.