Vorticity effects in the non-linear long wavelength convective instability of a viscoelastic fluid layer

Abstract

The effects of vorticity and poor conductivity boundaries on the non-linear long wavelength instability of an Oldroyd fluid layer heated from below is investigated. It is found a set of two coupled non-linear evolution equations with viscoelastic coefficients. A multiple scales approximation leads to a non-linear Ginzburg–Landau equation which has viscoelastic effects only when the Oldroyd model is corotational and not codeformational. The equation shows an important limitation in the magnitude of the nondimensional relaxation and retardation times. That is, for certain magnitudes of these times, the flow shows no saturation at all. For other magnitudes, the pattern selection is discussed by means of the viscoelastic Ginzburg–Landau equation.