Double‐diffusive convection in a rotating viscoelastic fluid layer

Abstract

AbstractThe linear instability and a weakly nonlinear stability of a rotating double‐diffusive convection in a viscoelastic fluid layer are investigated. An Oldroyd‐B constitutive equation is used to describe the rheological behavior of the viscoelastic fluid. Several remarkable departures from those of single‐diffusive and double‐diffusive viscoelastic fluid systems are explored by performing the linear instability analysis. Under certain conditions, it is observed that (i) a non‐rotating double diffusive viscoelastic fluid layer becomes destabilized by rotation, (ii) a rotating viscoelastic fluid layer gets destabilized by the addition of heavy solute to the bottom of the layer, (iii) disconnected closed convex oscillatory neutral curve from the stationary neutral curve exists, and (iv) three critical thermal Rayleigh numbers are required to specify the linear instability criteria, as opposed to a single critical value. The nature of linear instability characteristics for Oldroyd‐B, Maxwell and Newtonian fluids is found to be contradictory for the identical values of governing parameters. By performing a weakly nonlinear stability analysis, a cubic Landau equation for the amplitude corresponding to stationary convection is derived and the stability of bifurcating equilibrium solution is discussed. The viscoelastic parameters influence the stability of stationary bifurcation despite their effect is not felt on the stationary onset. The influence of various parameters on heat and mass transfer is also elucidated.