Parametric instability in oscillatory shear flows
MetadataShow full item record
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.
Author Posting. © Cambridge University Press, 2003. This article is posted here by permission of Cambridge University Press for personal use, not for redistribution. The definitive version was published in Journal of Fluid Mechanics 481 (2003): 329-353, doi:10.1017/S0022112003004051.
Suggested CitationJournal of Fluid Mechanics 481 (2003): 329-353
Showing items related by title, author, creator and subject.
On nonhydrostatic coastal model simulations of shear instabilities in a stratified shear flow at high Reynolds number Zhou, Zheyu; Yu, Xiao; Hsu, Tian-Jian; Shi, Fengyan; Geyer, W. Rockwell; Kirby, James T. (John Wiley & Sons, 2017-04-11)The nonhydrostatic surface and terrain-following coastal model NHWAVE is utilized to simulate a continually forced stratified shear flow in a straight channel, which is a generic problem to test the existing nonhydrostatic ...
Double diffusion, shear instabilities, and heat impacts of a pacific summer water intrusion in the Beaufort Sea Fine, Elizabeth C.; MacKinnon, Jennifer A.; Alford, Matthew H.; Middleton, Leo; Taylor, John R.; Mickett, John B.; Cole, Sylvia T.; Couto, Nicole; Le Boyer, Arnaud; Peacock, Thomas (American Meteorological Society, 2022-02-01)Pacific Summer Water eddies and intrusions transport heat and salt from boundary regions into the western Arctic basin. Here we examine concurrent effects of lateral stirring and vertical mixing using microstructure data ...
Wang, Jinbo; Spall, Michael A.; Flierl, Glenn R.; Malanotte-Rizzoli, Paola (American Geophysical Union, 2012-05-16)A simple barotropic quasi-geostrophic model is used to demonstrate that instabilities radiated from an unstable eastern boundary current can generate zonal striations in the ocean interior with realistic wavelengths and ...