Nonlinear physics of double-diffusive convection in geological systems

Double-diffusive convection (D.D.C.) is a nonlinear fluid-dynamical phenomenon, driven by thermal and compositional effects on the density. We discuss the nature of subcritical, finite-amplitude, double-diffusive convection for infinite Prandtl number and large Lewis number, Le, which have applications in magma chambers and at the D″-layer at the core-mantle boundary (CMB). Numerical solutions by two-dimensional, finite-element method are presented to portray the nature of time-dependent D.D.C. in both the diffusive and the finger regimes. The compositional heterogeneities at the CMB are far more complex than the local thermal structure because of the large Le and may have important implications for the scattering of seismic waves off the CMB. The effects of increasing the buoyancy ratio R_ρ are to suppress time-dependent D.D.C. even at high Ra. In narrow slots shear-heating instabilities can be triggered in the finger regime by the abrupt overturn of the compositional interface. This phenomenon may occur in tall magma chambers with low dissipation numbers of of order 0 (0.01).