Effects of Lateral Domain Size on the Rayleigh-Taylor Instability

The Rayleigh-Taylor instability (RTI) occurs when a light fluid accelerates into a heavy fluid due to a constant acceleration at an unstable interface. RTI is characterized by a growth rate, a value that depends on initial conditions and is consistently measured with lower values in simulations than experiments. Previous studies suggest that the lateral extent of the computational domain may influence the growth rate observed in simulations. The computational domain must be able to resolve the peak of the perturbation, but as the simulation progresses, other wavelengths that initially had small amplitudes will grow and dominate. The longest wavelength allowable is restricted by the lateral size of the domain, a length typically chosen based on the expected late time height of the mixing layer. The impact of the domain dimensions on RTI evolution is not fully understood. A number of studies focus on grid refinement, but this only ensures sufficient resolution of the high wavenumbers and not of the low wavenumbers. In this study, pseudo-spectral direct numerical simulations of the Navier-Stokes equations under the Boussinesq approximation are used to study how the domain size affects the growth rate for a given initial perturbation spectrum. From these simulations, heuristic relations to determine the optimal lateral domain size for a given initial perturbation will also be provided.