Instabilities of a Time-Dependent Shear Flow
MetadataShow full item record
This study offers a systematic stability analysis of unsteady shear flows representing large-scale, lowfrequency internal waves in the ocean. The analysis is based on the unbounded time-dependent Couette model. This setup makes it possible to isolate the instabilities caused by uniform shear from those that can be attributed to resonant triad interactions or to the presence of inflection points in vertical velocity profiles. Linear analysis suggests that time-dependent spatially uniform shears are unstable regardless of the Richardson number (Ri). However, the growth rate of instability monotonically decreases with increasing Ri and increases with increasing frequency of oscillations. Therefore, models assuming a steady basic state—which are commonly used to conceptualize shear-induced instability and mixing—can be viewed as singular limits of the corresponding timedependent systems. The present investigation is focused on the supercritical range of Richardson numbers (Ri . 1/4) where steady parallel flows are stable. An explicit relation is proposed for the growth rate of shear instability as a function of background parameters. For moderately supercritical Richardson numbers (Ri ; 1), we find that the growth rates obtained are less than, but comparable to, those expected for Kelvin–Helmholtz instabilities of steady shears at Ri , 1/4. Hence, we conclude that the instability of timedependent flows could represent a viable mixing mechanism in the ocean, particular in regions characterized by relatively weak wave activity and predominantly supercritical large-scale shears.
The article of record as published may be found at http://dx.doi.org/10.1175/JPO-D-19-0067.1
Showing items related by title, author, creator and subject.
Gannon, A.J.; Hobson, G.V. (2009-05);An investigation of the behavior of a transonic compressor rotor when operating close to stall is presented. The specific areas of interest are the behavior and location of lowfrequency instabilities close to stall. In ...
Gulliver, Larry T. (Monterey, California. Naval Postgraduate School, 2017-09);Baroclinic instability in the ocean is a primary cause of mesoscale eddies, which are pockets of water in the scale of 100km that have different density, thermal, and rotational characteristics than their surroundings. ...
Nguyen, Lien K. (Monterey, California. Naval Postgraduate School, 2004-03);Inter-domain routing connects individual pieces of Internet topology, creating an integral, global data delivery infrastructure. Currently, this critical function is performed by the Border Gateway Protocol (BGP) version ...