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

Citation
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
Citations number
16
Categorie Soggetti
Earth Sciences
Journal title
JOURNAL OF GEOPHYSICAL RESEARCH-SOLID EARTH
ISSN journal
21699313 → ACNP
Volume
104
Issue
B12
Year of publication
1999
Pages
29249 - 29260
Database
ISI
SICI code
0148-0227(199912)104:B12<29249:MFCITP>2.0.ZU;2-O
Abstract
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.