Linear and nonlinear electroconvection under AC electric field

Linear and non-linear stability analyses of electroconvection under an AC electric field are investigated using the normal mode method and truncated representation of Fourier series respectively. The principle of exchange of stabilities is shown to be valid and subcritical instability is ruled out. Several qualitative results on stability are discussed on the governing linear autonomous system, and also by using the concept of a self-adjoint operator. Spectral analysis of electroconvection is also made to provide information on the relative dominance of various modes on convection. The quantification of heat transfer is done on the Nusselt number-Rayleigh number plane for steady finite amplitude convection and through time series plots of the Nusselt number for unsteady finite amplitude convection. The effect of the electric number on stream line pattern and Nusselt number is delineated. Time series plots of the amplitudes of thermal conduction and convection are also presented. It is found that the effect of increasing the electric number is to enhance the amplitudes and thereby the heat transport. The sensitive dependence of the solution of the Lorenz system of electroconvection to the choice of initial conditions points to the possibility of chaos.