Stability and Weakly Nonlinear Dynamics of Rotating Convection of a Casson Fluid with Helical Force

Linear and weakly nonlinear instabilities in thermosolutal rotating convection of a Casson fluid, incorporating the effects of helical forcing, are investigated. The governing equations, expressed in non-dimensional form, are solved by employing the normal mode method. We have shown the effect of various key parameters on convective regions and presented them graphically. The parameter regimes corresponding to the onset of stationary and oscillatory instabilities are systematically delineated. The effect of different key parameters on linear theory is obtained. The Taylor number, helical force parameter, and solute Rayleigh number have a stabilizing effect, whereas the Lewis number and Casson parameter have a destabilizing effect on the system. Within the framework of weakly nonlinear analysis, an amplitude equation is derived using the method of multiple scales. The amplitude equation is solved numerically to calculate the convective amplitude. Using the Nusselt and Sherwood numbers, the heat and mass transfer are analyzed.