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

TL;DR

This paper uses spectral element simulations to accurately reproduce and analyze the phases and finite size effects of single-mode Rayleigh-Taylor instability experiments, providing new insights into late-time dynamics and secondary flows.

Contribution

It demonstrates the effectiveness of spectral element methods in replicating experimental smRTI behavior and reveals detailed flow features and finite size effects not previously documented.

Findings

Simulations match experimental phases of smRTI.

Finite size effects like wall drag and lift are observed.

Late-time dynamics reach higher Froude numbers than before.

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.