Rheology-dependent nonlinear stability in Jeffreys fluids subject to vertical throughflow

The present research originates from [1], where the authors proposed a model for non-isothermal Jeffreys viscoelastic fluids occupying a horizontal layer uniformly heated from below and invested by a vertical constant mass flow. In [1], the authors show that the standard kinetic energy fails to capture explicitly the contribution of viscoelastic parameters on the nonlinear stability threshold. For this reason, we revisit the nonlinear stability analysis by introducing a generalized energy functional that accounts for the memory coefficient and the relaxation rate γ , which characterize the rheological properties of the Jeffreys fluids. The Lyapunov function that we propose allows us to derive a nonlinear stability condition depending explicitly on the viscoelastic parameters. We show numerically that this approach improves the estimate of the nonlinear stability threshold.