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Numerical simulations of the shear instability and subsequent degeneration of basin scale internal standing waves

Andrew Grace, Marek Stastna, and Francis J. Poulin*

  • Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

  • *Corresponding author: a2grace@uwaterloo.ca
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Phys. Rev. Fluids 4, 014802 – Published 14 January, 2019

DOI: https://doi.org/10.1103/PhysRevFluids.4.014802

Abstract

We present high-resolution simulations of the instability and subsequent breakdown of standing waves, or seiches, in a fluid continuously stratified in the vertical direction. It is well known that such waves can evolve to form nonlinear, dispersive wave trains. When the initial dimensionless amplitude is large, it is possible that a stratified shear instability develops, possibly at the same time as dispersive wave trains. While both dispersion and shear instability serve to move energy from large to small scales, they are fundamentally different. The development into wave trains is nondissipative in nature, and in the asymptotic limit of small but finite amplitude seiches may be described by variants of the Korteweg–de Vries (KdV) equation. Shear instability, on the other hand, yields Kelvin-Helmholtz billows, which in turn provide one of the basic archetypes of transition to turbulence, with greatly increased rates of mixing and viscous dissipation. We discuss how the two phenomena vary as the aspect ratio of the tank and the height of the interface between lighter and denser fluids are changed, highlighting cases where the two phenomena coexist. A quantitative accounting for the evolution of the horizontal modewise decomposition of the kinetic energy of the system in addition to the creation of a semianalytical model of the evolution of the fundamental mode is presented. Finally, the mixing is characterized during the evolution of the seiche, illustrating a fundamental transition that occurs as the aspect ratio is decreased.

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Phys. Rev. Fluids 4, 014802– Published 14 January, 2019
  • Received 8 May 2018
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