Effect of Thermal Parametric Excitation on the Destabilization of a Linearly Stable System

In this paper, we focus on analyzing the linear stability of a Newtonian fluid layer whose upper surface is subjected to parametric thermal excitation that is periodic in time with zero mean. The fluid layer is considered of infinite extension in the horizontal directions. The Floquet theory and the Chebyshev spectral collocation method are used to solve the linear stability problem in the case of rigid-rigid boundary conditions. Although the unmodulated version of this configuration, where the fluid layer is heated from above, is known to be linearly stable, it turns out that destabilization is possible in the presence of modulation on the top surface. Parametric resonances appear at the onset of the instability, and the convection threshold is harmonic or sub-harmonic depending on the range of oscillation frequencies. The dynamics of this instability is characterized by the existence of a bifurcation point in codimension two, giving rise to a discontinuity in the evolution of the critical wavenumber at a specific frequency number.