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Internal waves generated by a stratified wake: experiment and theory

Published online by Cambridge University Press:  09 May 2018

P. Meunier Open the ORCID record for P. Meunier [Opens in a new window] ,
S. Le Dizès Open the ORCID record for S. Le Dizès [Opens in a new window] ,
L. Redekopp  and
G. R. Spedding
P. Meunier*
Affiliation:
AME Department, University of Southern California, Los Angeles, CA 90089-1191, USA Aix Marseille Univ., CNRS, Centrale Marseille, IRPHE, 13384 Marseille, France
S. Le Dizès
Affiliation:
Aix Marseille Univ., CNRS, Centrale Marseille, IRPHE, 13384 Marseille, France
L. Redekopp
Affiliation:
AME Department, University of Southern California, Los Angeles, CA 90089-1191, USA
G. R. Spedding
Affiliation:
AME Department, University of Southern California, Los Angeles, CA 90089-1191, USA
*
†Email address for correspondence: meunier@irphe.univ-mrs.fr
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Abstract

This paper presents experimental and theoretical results on the internal waves emitted by a bluff body moving horizontally in a linearly stratified fluid. Three different bluff bodies (a sphere, a spheroid and a cylinder) have been used in order to study the effect of the shape of the bluff body, although most of the results are obtained for the sphere. Two types of internal waves have been observed experimentally: large wavelength lee waves generated by the bluff body itself and small wavelength coherent wake waves generated by the turbulent wake. First, the lee waves are separated from the wake waves by averaging the experimental measurements in the frame moving with the bluff body. The velocity amplitude of the lee waves scales as the inverse of the Froude number $F=2U_{B}/(ND)$ for $F>2$ (where $U_{B}$ is the towing velocity, $D$ the diameter and $N$ the buoyancy frequency). This scaling proves that the internal waves are related to the drag of the bluff body which is due to the separation of the flow behind the bluff body. This separation is usually not taken into account in the classical models which assume that the flow is dipolar. The drag can be modelled as a point force in the Navier–Stokes equations, which gives a correct prediction of the structure and the amplitude of the lee waves. Second, the wake waves have been separated from the lee waves by averaging the velocity fields in the frame moving at the phase velocity of the waves. The phase velocity and the wavelength scale as $F^{-2/3}$ and $F^{1/3}$ respectively which correspond to the velocity and distance between same sign vortices of the von Kármán vortex street. A simplified model is derived for the internal waves emitted by the double row of moving point vortices of the von Kármán street. The amplitude of the wake waves is measured experimentally and seems to depend on the Reynolds number.

JFM classification

Geophysical and Geological Flows: Internal waves Geophysical and Geological Flows: Stratified flows Wakes/Jets: Wakes
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 846 , 10 July 2018 , pp. 752 - 788
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Copyright
© 2018 Cambridge University Press 

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