Journal of Fluid Mechanics

Papers

The internal gravity wave field emitted by a stably stratified turbulent wake

Ammar M. Abdilghaniea1 and Peter J. Diamessisa2 c1

a1 Leadership Computing Facility, Argonne National Laboratory, Argonne, IL 60439, USA

a2 School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853, USA

Abstract

The internal gravity wave (IGW) field emitted by a stably stratified, initially turbulent, wake of a towed sphere in a linearly stratified fluid is studied using fully nonlinear numerical simulations. A wide range of Reynolds numbers, and internal Froude numbers, (, are characteristic body velocity and length scales, and is the buoyancy frequency) is examined. At the higher examined, secondary Kelvin–Helmholtz instabilities and the resulting turbulent events, directly linked to a prolonged non-equilibrium (NEQ) regime in wake evolution, are responsible for IGW emission that persists up to . In contrast, IGW emission at the lower investigated does not continue beyond for the three values considered. The horizontal wavelengths of the most energetic IGWs, obtained by continuous wavelet transforms, increase with and appear to be smaller at the higher , especially at late times. The initial value of these wavelengths is set by the wake height at the beginning of the NEQ regime. At the lower , consistent with a recently proposed model, the waves propagate over a narrow range of angles that minimize viscous decay along their path. At the higher , wave motion is much less affected by viscosity, at least initially, and early-time wave propagation angles extend over a broader range of values which are linked to increased efficiency in momentum extraction from the turbulent wake source.

(Received February 07 2012)

(Revised October 24 2012)

(Accepted December 19 2012)

(Online publication February 27 2013)

Key words

  • stratified flows;
  • wakes/jets;
  • waves/free-surface flows

Correspondence

c1 Email address for correspondence: pjd38@cornell.edu

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