The Complex Ginzburg Landau Model for an Oscillatory Convection in a Rotating Fluid Layer

Abstract

A weakly nonlinear thermal instability is investigated under rotation speed modulation. Using the perturbation analysis, a nonlinear physical model is simplified to determine the convective amplitude for oscillatory mode. A non-autonomous complex Ginzburg-Landau equation for the finite amplitude of convection is derived based on a small perturbed parameter. The effect of rotation is found either to stabilize or destabilize the system. The Nusselt number is obtained numerically to present the results of heat transfer. It is found that modulation has a significant effect on heat transport for lower values of ωf while no effect for higher values. It is also found that modulation can be used alternately to control the heat transfer in the system. Further, oscillatory mode enhances heat transfer rather than stationary mode.

The Effect of Modulation on Heat Transport by a Weakly Nonlinear Thermal Instability in the Presence of Applied Magnetic Field and Internal Heating

“…We use the following boundary conditions to solve the above system. The stress free and isothermal boundary conditions are given by Kiran et al [10,16,22,28], Bhadauria and Kiran [32], Manjula et al [47], Bhadauria et al [22,32] at ,…”

“…We now introduce the following asymptotic expansions (Malkus and Veronis [46], Manjula et al [47,58], Kiran et al [48,49,57] ...…”

“…The horizontally averaged Nusselt number Nu    for the stationary mode of convection is given by (Bhaduria and Kiran [39,40], Kiran [41,42,45], Keshri et al [44], Manjula et al [47])…”

“…Substituting 1  , 1 T and T 2 into Eqs (3.13)-(3.14), we can obtain expressions for R 31 , R 32 easily. Now by applying the solvability condition for the existence of third order solution, we get the Ginzburg-Landau equation (Bhaduria and Kiran [39,40,54], Kiran [41,42,45,61], Keshri et al [44], Manjula et al [47],) for stationary convection with time-periodic coefficients in the form…”

The Effect of Thermal Modulation on Double Diffusive Convection in the Presence of Applied Magnetic Field and Internal Heat Source

“…Through local nonlinear stability analysis, heat mass transfer was quantified. The effect of internal solutal Rayleigh number and rotation on weakly nonlinear [41][42][43][44][45] thermal instability was studied by Kiran [39] and Kiran and Manjula [40]. The rotation and negative internal solutal Rayleigh number reduce the mass transfer in the system (see: Malkus and Veronis [41]).…”