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

Abstract

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 doublediffusion coupling B•nard 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 B•nard 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.

Methane oxidation following submarine permafrost degradation: Measurements from a central Laptev Sea shelf borehole

“…Pore water is comparatively saline (10–17) from the seabed down to the position of the freeze/thaw transition, which suggests that the transport of seawater through the overlying unfrozen sediment to the thaw front is dominantly convective rather than diffusive [ Harrison and Osterkamp , ; Chuvilin et al ., ] and that seawater is not limited at the freezing front. Such convection may be driven by density and temperature differences between seawater at the sediment‐water interface and freshwater from the thaw front [ Hutter and Straughan , ]. The greater sulfate concentration variability in segment III than in segment II is not reflected in the overall salinity of pore water but follows the stable isotope ratios closely, with the exception of the sample closest to the seafloor (at 2 m bsf).…”

Effect of property variation and modelling on convection in a fluid overlying a porous layer

“…Then, we substitute from the di!erential equations (10) and (11) for @ and @ . Upon using Equations (26) we derive, in non-dimensional form, the following "nal interface condition:…”

“…Speci"c applications of convection in the porous}#uid layer system include the curious formation of stones into regular hexagonal patterns on the lake bed near the edge of certain alpine lakes (cf., Reference [9]). Thawing subsea permafrost is another (e.g., Reference [10]), salt ponds represent yet another if #ow of saline solution into the soil bed of the pond is considered (e.g., References [11}13]). Flow of water under the Earth's surface is a topic of much concern to geotechnical engineers and the #ow between a #uid and a porous medium is very important in this context (cf., References [14,15]).…”

Nearshore arctic subsea permafrost in transition

“…In C2 this drop is less abrupt and occurs a few meters above the boundary, in the absence of a change in sediment texture. This could be the result of mixing between downward moving saline pore water and upward moving freshwater from the thawing permafrost below, or indicate a transition from convective to molecular diffusion (Hutter and Straughan 1999).…”