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

Published online by Cambridge University Press:  27 February 2013

Ammar M. Abdilghanie  and
Peter J. Diamessis
Ammar M. Abdilghanie
Affiliation:
Leadership Computing Facility, Argonne National Laboratory, Argonne, IL 60439, USA
Peter J. Diamessis*
Affiliation:
School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853, USA
*
†Email address for correspondence: [email protected]
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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, $\mathit{Re}= UD/ \nu \in [5\times 1{0}^{3} , 1{0}^{5} ] $ and internal Froude numbers, $\mathit{Fr}= 2U/ (ND)\in [4, 16, 64] $ ($U$, $D$ are characteristic body velocity and length scales, and $N$ is the buoyancy frequency) is examined. At the higher $\mathit{Re}$ 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 $Nt\approx 100$. In contrast, IGW emission at the lower $\mathit{Re}$ investigated does not continue beyond $Nt\approx 50$ for the three $\mathit{Fr}$ values considered. The horizontal wavelengths of the most energetic IGWs, obtained by continuous wavelet transforms, increase with $\mathit{Fr}$ and appear to be smaller at the higher $\mathit{Re}$, 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 $\mathit{Re}$, 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 $\mathit{Re}$, 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.

JFM classification

Geophysical and Geological Flows: Stratified flows Wakes/Jets: Wakes/Jets Waves/Free-surface Flows: Waves/Free-surface Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 720 , 10 April 2013 , pp. 104 - 139
Copyright
©2013 Cambridge University Press

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