We numerically study the effects of zero-mean, time-dependent gravity modulation on the mixing characteristics of two interdiffusing miscible fluids initially separated by a thin vertical diffusion layer. For harmonic vertical modulation in 2D with frequency ω, the evolution of the interface between the fluids is governed by the Grashof number, Gr = [special characters omitted], based on the viscous length scale, l_ν = [special characters omitted], the Schmidt number, Sc = [special characters omitted], the phase angle of the harmonic modulation, &phis;, and other geometric parameters. When &phis; = 0, π, we observe four different flow regimes with increasing Gr: neutral oscillations at the forcing frequency; successive folds which propagate diffusively; localized shear instabilities; and both shear and convective instabilities leading to rapid mixing. When &phis; ≠ 0 or π, the flow is similar to a modulated lock exchange flow.

We also study the effects of zero-mean stochastic vertical gravity modulation which is normally distributed and characterized by an exponentially damped cosine auto-correlation function, i.e. ⟨g( t) · g(t + τ)⟩/⟨ g²(t)⟩ = e ^−λτcos(ωτ). We observe the propagation of gravity currents, Kelvin-Helmholtz and Rayleigh-Taylor instabilities, even for extremely small Gr. Narrow-band modulations lead to the largest mixed volumes followed by harmonic modulations and then broad-band modulations. This non-monotonicity is explained on the basis of the competition between the effects of excitation of lower frequencies and the effects of the reduction in the energy content at the dominant frequency.

For harmonic horizontal modulation, we observe a critical Gr for the occurrence of Rayleigh-Taylor instability. As Gr is increased, we observe that the flow-field becomes chaotic through a sequence of period-doubling bifurcations with a Feigenbaum-type scenario. Stochastic modulation leads to Rayleigh-Taylor instabilities at smaller equivalent Gr than harmonic modulation.

We study the effects of three dimensionality, which is generated by introducing a small streamwise vorticity perturbation to the 2D flow. For perturbed flows, increased pairing of the spanwise rollers due to counter-rotating streamwise vortices results in larger rollers which in turn enhance mixing. We find that vortex stretching is the mechanism for the increase in streamwise vorticity.