Abstract
The linear stability problem for an incompressible viscous poorly conducting Ohmic liquid between two rigid horizontal boundaries with time-periodic temperature distribution and under steady transverse electric field is considered. The free charge in the liquid is due only to the nonuniform electroconduction. The electrohydrodynamic (EHD) approximation is used. Floquet theory is applied for finding various instability thresholds in linear approximation. The influence of time-dependent temperature field modulation on the liquid layer behavior is studied with and without an additional steady component. The boundaries of instability and the characteristics of critical disturbances are determined. Depending on the frequency and amplitude of modulation, the temperature gradient can destabilize the equilibrium of the liquid or stabilize otherwise unstable base state. In addition to synchronous and subharmonic responses to external modulation, the instability can be associated with quasiperiodic disturbances. The critical electric Rayleigh number is given as a function of frequency and heating level. The limit of low frequency modulation is studied by an asymptotic method.
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