Double-diffusive convective motions for a saturated porous layer subject to modulated surface heating

We examine convective motions in a horizontal porous layer saturated with a binary mixture. The effect of variable solar radiation heating is introduced by allowing the upper surface temperature of the region to vary sinusoidally with time. By modelling flow in the porous layer via Darcy's law and carrying out a linear stability analysis using Floquet theory, we discuss the response of the velocity, temperature and solute fields at the onset of convection. It is shown that each type of instability (synchronous, subharmonic or at a frequency unrelated to the heating frequency) can be characterized by the behaviour of the vertical components of the perturbation fields. We demonstrate this by considering the time-dependent stationary points of the vertical components over several periods of heating. Phase shifts in the Galerkin coefficients for the temperature and solutal perturbations are also compared with theoretical predictions.