Stability of viscoelastic fluids in a modulated gravitational field

Abstract

The instability of a viscoelastic fluid layer heated from below in a modulated gravitational field is studied numerically. Fluids satisfying the Maxwellian model and the Boussinesq approximation are considered. A system of linear equations with periodic coefficients describing the behavior of disturbances, is obtained by linear stability theory. The disturbances are expanded by double series of mixed Fourier and Chebyshev form. An algorithm combining Galerkin and collocation methods is employed to trace the stability boundary between stable and unstable stales. For the case of viscoelastic fluids acted on by a constant gravity, a transition Deborah number is found for each Prandtl number. Below and above this transition value stationary and oscillatory convections, respectively, will develop at the onset of instability. For the case of Newtonian fluids acted on by a modulated gravity, modulation has a destabilization effect at low frequencies and a slight stabilization effect at high frequencies, which increases with increasing the amplitude of modulation. The critical Rayleigh number approaches the quasi-steady limit, as the frequency tends to zero. For the case of a viscoelastic fluid acted On by a modulated gravity, modulation has the same effects at both very low and very high frequencies, as those of Newtonian fluids. While in the range of intermediate frequency, subharmonic disturbances are found to enhance the stabilization effect at small Deborah numbers and the destabilization effect at large Deborah numbers. Copyright (C) 1996 Elsevier Science Ltd.