Direct numerical simulation of single mode three-dimensional Rayleigh-Taylor experiments

Abstract

The single-mode Rayleigh-Taylor instability (smRTI) is well defined, poorly understood, and applicable to many fluid flows directly and through its relationship to multi-mode Rayleigh-Taylor models. This study reproduces three low-Atwood smRTI experimental runs (Wilkinson and Jacobs, 2007) in a specialized version of the Nek5000 spectral element code. The simulations use the initial amplitude, wavelength, acceleration, Atwood number, and viscosity from the three specific experiments and impose no-slip and no-flux boundaries on the velocity and scalar, respectively. The simulations are shown to reproduce the linear, saturation, stagnation, and re-acceleration phases of the smRTI seen in the experiments. Additionally, access to the full velocity and scalar fields demonstrates three different finite size effects: wall drag, wall lift, and a long wavelength mode along the diagonal. One of the simulations is extended by a factor of two in the vertical direction and the resulting late-time dynamics reach Froude numbers around 1.8, higher than previously reported. Finally, inspection of the span-wise flow reveals secondary flows of the first kind that transport the scalar from the bubble-spike interfaces into the bubble and spike centers. The agreement between simulations and experiments inspires confidence in the spectral element method for studying the Rayleigh-Taylor instability.