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

• We studied the non-linear convection of viscoelastic fluids between poorly conducting walls.
• A set of evolution equations with viscoelastic effects was found.
• Three different viscoelastic fluid models were considered in this study.
• Viscoelasticity is more important in pattern formation for corrotational fluids.
• We examine the formation of roll, square and hexagonal patterns.

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.