Hostname: page-component-745bb68f8f-cphqk Total loading time: 0 Render date: 2025-01-09T22:09:35.291Z Has data issue: false hasContentIssue false
  • English
  • Français

Parametric instability in oscillatory shear flows

Published online by Cambridge University Press:  28 April 2003

FRANCIS J. POULIN ,
G. R. FLIERL  and
J. PEDLOSKY
FRANCIS J. POULIN
Affiliation:
Mathematical Institute, University of St. Andrews, St. Andrews, Fife, KY16 9SS, UK Present address: Mathematical Institute, North Haugh, Room 221, University of St. Andrews, St. Andrews, Fife, KY16 9SS, UK.
G. R. FLIERL
Affiliation:
Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
J. PEDLOSKY
Affiliation:
Woods Hole Oceanographic Institution, MS 21, Woods Hole Road, Woods Hole, MA 02543, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

In this article we investigate time-periodic shear flows in the context of the two-dimensional vorticity equation, which may be applied to describe certain large-scale atmospheric and oceanic flows. The linear stability analyses of both discrete and continuous profiles demonstrate that parametric instability can arise even in this simple model: the oscillations can stabilize (destabilize) an otherwise unstable (stable) shear flow, as in Mathieu's equation (Stoker 1950). Nonlinear simulations of the continuous oscillatory basic state support the predictions from linear theory and, in addition, illustrate the evolution of the instability process and thereby show the structure of the vortices that emerge. The discovery of parametric instability in this model suggests that this mechanism can occur in geophysical shear flows and provides an additional means through which turbulent mixing can be generated in large-scale flows.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 481 , 25 April 2003 , pp. 329 - 353
Copyright
© 2003 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)