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

The convective flow in a vertical slot with differentially heated walls and vertical temperature gradient is considered for very large Rayleigh number s. Gravity is taken to be vertical and to consist of both a mean and a harm onic modulation ('jitter') at a given frequency and amplitude. The time-dep endent Boussinesq equations governing the two-dimensional convection are so lved numerically. To this end an economic operator-splitting scheme is devi sed combined with internal iterations within a given time step. The approxi mation of the nonlinear terms is conservative and no scheme viscosity is pr esent in the approximation. The flow is investigated for a range of Prandtl numbers from Pr = 1000 when fluid inertia is insignificant and only therma l inertia plays a role to Pr = 0.73 when both are significant and of the sa me order. The dow is governed by several parameters. In the absence of jitt er, these are the Prandtl number, Pr, the Rayleigh number, Ra, and the dime nsionless critical stratification, tau (B) Simulations are reported for Pr = 10(3) and a range of tau (B) and Ra, with emphasis on mode selection and finite-amplitude states. The presence of jitter adds two more parameters, i .e. the dimensionless jitter amplitude epsilon and frequency omega, renderi ng the flow susceptible to new modes of parametric instability at a critica l amplitude epsilon (c). Stability maps of epsilon (c) vs. omega are given for a range of omega. Finally we investigate the response of the system to jitter near the neutral curves of the various instability modes.