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Three-dimensional instabilities of a stratified cylinder wake

Published online by Cambridge University Press:  20 October 2014

M. Bosco  and
P. Meunier
M. Bosco*
Affiliation:
Aix-Marseille Université CNRS, Centrale Marseille, IRPHE UMR 7342, 13384, Marseille, France
P. Meunier
Affiliation:
Aix-Marseille Université CNRS, Centrale Marseille, IRPHE UMR 7342, 13384, Marseille, France
*
†Email address for correspondence: bosco@irphe.univ-mrs.fr
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Abstract

This paper describes experimentally, numerically and theoretically how the three-dimensional instabilities of a cylinder wake are modified by the presence of a linear density stratification. The first part is focused on the case of a cylinder with a small tilt angle between the cylinder’s axis and the vertical. The classical mode A well-known for a homogeneous fluid is still present. It is more unstable for moderate stratifications but it is stabilized by a strong stratification. The second part treats the case of a moderate tilt angle. For moderate stratifications, a new unstable mode appears, mode S, characterized by undulated layers of strong density gradients and axial flow. These structures correspond to Kelvin–Helmholtz billows created by the strong shear present in the critical layer of each tilted von Kármán vortex. The last two parts deal with the case of a strongly tilted cylinder. For a weak stratification, an instability (mode RT) appears far from the cylinder, due to the overturning of the isopycnals by the von Kármán vortices. For a strong stratification, a short wavelength unstable mode (mode L) appears, even in the absence of von Kármán vortices. It is probably due to the strong shear created by the lee waves upstream of a secondary recirculation bubble. A map of the four different unstable modes is established in terms of the three parameters of the study: the Reynolds number, the Froude number (characterizing the stratification) and the tilt angle.

JFM classification

Instability: Instability Geophysical and Geological Flows: Stratified flows Wakes/Jets: Wakes
Type
Papers
Information
Journal of Fluid Mechanics , Volume 759 , 25 November 2014 , pp. 149 - 180
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Copyright
© 2014 Cambridge University Press 

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