PENETRATIVE CONVECTION IN THAWING SUBSEA PERMAFROST

Penetrative convection is investigated in a porous medium bounded abov e by the ocean bed and below by the interface of the thawing permafros t ground. The thermal equation of state relating the density, temperat ure and salinity is assumed to be that of ocean water as proposed by t he UNESCO formula. Employing the Boussinesq approximated Darcy-flow eq uations with such a realistic density formula in the buoyancy term, th e problem of convective motion of brine is studied. Such convection fl ow is observed off the coast of Alaska. The field variables in questio n are the brine-velocity field, the temperature and the salinity, alth ough we simplify the problem by imposing a temperature field that is l inear in the depth variable. For this simplified system we study the c ontinuous dependence of the velocity and salinity on the initial data, develop a linear instability analysis and, additionally, present a fu lly nonlinear three-dimensional stability analysis. This nonlinear ana lysis necessitates the introduction of a generalised energy (or Lyapun ov function) due to the extra terms present in the realistic equation of state. Numerical results indicate that values of the critical Rayle igh numbers are smaller than when these extra terms are omitted.