The onset of convection in a viscoelastic fluid that obeys the Jeffreys model is investigated. Two boundary conditions have been considered separately: free-free and rigid-rigid. The role played by the retardation time, characteristic of the Jeffreys model, is emphasised. The threshold values of the parameters (critical Rayleigh number, critical wavenumber, onset frequency, etc.) for stationary and oscillatory convection are obtained. The frontier between oscillatory and stationary convection is calculated and the possibility to obtain a codimension-two point is discussed.

Pattern selection and stability in viscoelastic convection are studied in the framework of amplitude equations derived in the vicinity of stationary and oscillatory instabilities. The oscillatory instability corresponds to a Hopf bifurcation with broken translational symmetry. When this instability is the first to appear with increasing Rayleigh number, such systems may be described by coupled one-dimensional complex Ginzburg-Landau equations for counterpropagating waves. The coefficients of these equations, as computed from the underlying Navier-Stokes equations, are such that the selected pattern corresponds to standing waves. The phase dynamics of these waves is derived and leads to coupled Kuramoto-Sivashinsky equations. Their stability range is also determined for different typical fluid parameters. ͓S1063-651X͑96͒03108-X͔

In this work we report theoretical and numerical results on convection for a binary magnetic mixture under rotation. We obtain explicit expressions of convective thresholds in terms of the control parameters of the system for stationary convection. Finally, we analyze the stabilizing effect of rotation on instability thresholds for aqueous suspensions. r 2006 Published by Elsevier B.V.