Floquet and Nonlinear Energy Stability of Periodically Heated Thermosolutal Convection in a Shear-Thinning Micropolar Porous Layer

Abstract

The stability of a horizontal porous layer saturated by a binary, shear-thinning micropolar fluid is examined when the imposed temperature difference is sinusoidally modulated. A Darcy-Brinkman-micropolar formulation is coupled to thermal and solutal transport, while the apparent viscosity follows a regularized Carreau law. The conductive state is reduced by a normalmode Galerkin projection to a periodic linear system. Its monodromy matrix supplies the Floquet multipliers and the neutral thermal Rayleigh number. A weighted energy functional is then used without linearizing the advective terms; the resulting endpoint matrix inequalities provide a sufficient nonlinear decay threshold. For the reference parameter set, the unmodulated oscillatory threshold is 71.97. At modulation frequency 8, amplitudes 0.2 and 0.4 reduce the threshold to 65.39 and 59.36, respectively, through a subharmonic Floquet tongue. Micropolar coupling raises both the Floquet and energy thresholds, whereas stronger shear thinning contracts the finite-strain energy-stable region. Because the regularized viscosity equals its zero-shear value at the conductive state, the power-law index does not enter infinitesimal onset; it enters the nonlinear margin through amplitude-dependent dissipation. The separation between the Floquet and energy boundaries identifies a parameter interval in which linear decay is not yet accompanied by a global finite-amplitude guarantee.