The role of temperature-dependent solubility in the stability of thermohaline convection within a Voigt-fluid layer

Abstract

The study focuses on both linear and weakly nonlinear stability analyzes of thermohaline convection within a Voigt-fluid layer, considering the effects of temperature-dependent solubility. Analytical methods are employed to derive conditions for the onset of both stationary and oscillatory convection. The linear stability analysis is performed using normal mode analysis to explore how various physical parameters influence the initiation of convection. Notably, unlike Newtonian fluids, the Navier-Stokes-Voigt fluid suppresses the typical quasiperiodic bifurcation from a steady state. To gain deeper insight into the onset of convection, a weakly nonlinear stability analysis is conducted using a modified perturbation method, leading to the Ginzburg-Landau equation. This reveals the potential for subcritical instability, a phenomenon not fully captured by linear analysis alone. Additionally, the study examines how different physical parameters affect convective heat and mass transfer, with findings that align with previous studies in specific limiting cases.