Chaos in a triple diffusive system involving a viscoelastic fluid layer

Abstract

This study investigates the linear and weakly nonlinear stability analysis in a Rayleigh-Bénard configuration with a viscoelastic fluid layer influenced by two additional solutal components. The governing equations for both stationary and oscillatory convective regimes, and the critical point at which convection sets in is derived. The comparative analysis is performed for three different viscoelastic fluid models: Oldroyd-B, Maxwell, Rivlin-Ericksen fluid, along with the Newtonian fluid model. In weakly nonlinear stability analysis, a generalized eight-mode Lorenz model is developed that satisfies the general properties of a classical Lorenz model. From this reduced model, the critical points and Hopf-Rayleigh number, representing the initiation of chaos through Hopf bifurcation are determined. The Lyapunov exponents are used to characterize the chaotic, periodic and quasi-periodic motions of the system. The results show that the viscoelastic and triple diffusion parameters affect the initiation of convection and transition to chaos. It is also observed that the Maxwell fluid exhibits the earliest initiation of chaos and the Newtonian fluid the latest, with Oldroyd-B and Rivlin-Ericksen exhibiting intermediate behaviour. The presence of additional solutal concentrations delays the onset of chaotic motion.