Onset of double-diffusive convection in a saturated porous layer with time-periodic surface heating

The stability of a fluid saturated, horizontal porous layer in the presence of a solute concentration gradient and time-periodic thermal gradient is examined. The modulated gradient is the result of a sinusoidal upper surface temperature which models the effect of variable solar radiation heating of the layer. Darcy's law and the Boussinesq approximation are employed, and we assume an equation of state linear in temperature and concentration. A linear stability analysis is carried out to obtain predictions for the onset of convection and critical wavenumbers for the system. The critical conditions are obtained via the Galerkin method and Floquet theory. The effects of variable concentration gradient, temperature modulation amplitude and frequency are examined, and compared with the results obtained analytically from the corresponding unmodulated problem. It is shown that instabilities can occur as convective motions which are synchronous or subharmonic with the surface heating, or can be identified via complex conjugate Floquet exponents. The neutral stability curves at the transitions between instabilities are found to be bimodal when the temperature is time-periodic, and are characterized by jumps in the critical wavenumbers.