  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.
