Nonlinear dynamics of two-dimensional convection in a vertically stratified slot with and without gravity modulation (Q2710460)

The authors consider the convective flow in a vertical slot with differentially heated walls and vertical temperature gradient for very large Rayleigh numbers, where gravity is vertical and consists of a mean and a harmonic modulation (jitter). The time-dependent Boussinesq equations are solved numerically by means of an operator-splitting scheme with internal iterations. Central-difference approximations are used for differential operators which secures second-order approximation in space. The flow is investigated for a range of Prandtl numbers from \(Pr=1000\) when fluid inertia is insignificant and only thermal inertia plays a role to \(Pr=0.73\) when both are significant and of the same order. The response of the system to jitter, which adds two extra parameters to the flow, is investigated near the neutral curves of the various instability modes. The dominant physical feature of the considered flows is that gravity modulations couple strongly to the vertical stratification, suppressing or eliminating two-dimensional motions for stable stratification and exciting buoyancy-driven Rayleigh-Bénard modes for unstable stratification. The difference between the results of \textit{A. Farooq} and \textit{G. M. Homsy} [J. Fluid Mech. 313, 1-38 (1996; Zbl 0871.76027)], which are based on truncated Galerkin expansions, is dicussed. It is concluded that the stabilization is strongly nonlinear and cannot be captured by a Galerkin expansion that does not involve the stabilizing structure as one of the trial functions.