The convective flow in a vertical slot with differentially heated walls and vertical
temperature gradient is considered for very large Rayleigh numbers. Gravity is taken
to be vertical and to consist of both a mean and a harmonic modulation (‘jitter’) at a
given frequency and amplitude. The time-dependent Boussinesq equations governing
the two-dimensional convection are solved numerically. To this end an economic
operator-splitting scheme is devised combined with internal iterations within a given
time step. The approximation of the nonlinear terms is conservative and no scheme
viscosity is present in the approximation. 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
flow is governed by several parameters. In the absence of jitter, these are the Prandtl
number, Pr, the Rayleigh number, Ra, and the dimensionless critical stratification,
τB. Simulations are reported for Pr = 103 and a range of τB 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 ε and frequency ω, rendering
the flow susceptible to new modes of parametric instability at a critical amplitude
εc. Stability maps of εc vs. ω
are given for a range of ω. Finally we investigate the
response of the system to jitter near the neutral curves of the various instability modes.