Stud. Geophys. Geod., 48 (2004), 519−537 519 © 2004 StudiaGeo s.r.o., Prague LINEAR STABILITY OF A DOUBLE DIFFUSIVE LAYER OF AN INFINITE PRANDTL NUMBER FLUID WITH TEMPERATURE- DEPENDENT VISCOSITY A. MAMBOLE 1,2 , G. LABROSSE 1 , E. TRIC 3* , L. FLEITOUT 2 1 Université Paris-Sud, L.I.M.S.I.-C.N.R.S., Bâtiment 508, 91405 Orsay Cedex, France, (axel.mambole@paris.iufm.fr, labrosse@limsi.fr) 2 Laboratoire de Géologie de l’E.N.S., 24, rue Lhomond 75231 Paris Cedex 5, France (fleitout@geologie.ens.fr) 3 Laboratoire Géosciences Azur, Université de Nice-Sophia Antipolis, 250 rue A. Einstein, 06560 Valbonne, France (tric@unice.fr) * Corresponding author Received: May 24, 2002; Revised: January 23, 2004; Accepted: February 5, 2004 ABSTRACT An infinite horizontal layer, with vertically stratified temperature and solute concentration, is considered in the case where the viscosity is exponentially dependent on temperature, and the Prandtl number is infinite. Its linear stability is investigated when the destabilizing thermal gradient acts against a stabilizing solute gradient. The analysis is performed using horizontal Fourier and vertical Chebyshev polynomial expansions. For the constant viscosity case, the laws well established in the free boundary configuration are seen to be directly suitable for the rigid one. In the variable viscosity case, characterised by a given viscosity contrast c, the scaling laws with c are settled extrapolating to the double diffusive situation the approach initiated by Stengel et al. (1982). In contrast with the constant viscosity case, the critical wave number is found to be strongly dependent on the solutal Rayleigh number in the marginal oscillatory obtained at large contrast values. Keywords: double diffusive convection, linear stability, high viscosity, Mantle convection, Rayleigh number 1. INTRODUCTION Since the very first works of Bénard (1900, 1901) and Rayleigh (1916), the stability of an horizontal layer is still a subject of analysis, but in non conventional configuration. The case under consideration here refers to a general situation where a mixture is submitted to opposite thermal and a compositional gradients, in presence of gravity. Depending on whether the solute is denser or lighter than the solvant, competitive or cooperative buoyancies act in the layer leading to specific bifurcation maps (Platten and Legros, 1984). Real fluids in nature (oceans, Earth’s mantle, magma chambers) or in industrial processes (elaboration of materials), are more likely of this type (if not more complex)