Baroclinic instability over topography : unstable at any wave number
MetadataShow full item record
KeywordTopography; Coastal; Coastal waves; Non linear; Slope; Wave propagation; Most unstable; Asymptotic theory; Potential vorticity
The instability of an inviscid, baroclinic vertically sheared current of uniform potential vorticity, flowing along a uniform topographic slope, becomes linearly unstable at all wave numbers if the flow is in the direction of propagation of topographic waves. The parameter region of instability in the plane of scaled topographic slope versus wave number then extends to arbitrarily large wave numbers at large slopes. The weakly nonlinear treatment of the problem reveals the existence of a nonlinear enhancement of the instability close to one of the two boundaries of this parametrically narrow unstable region. Because the domain of instability becomes exponentially narrow for large wave numbers, it is unclear how applicable the results of the asymptotic, weakly nonlinear theory are given that it must be limited to a region of small supercriticality. This question is pursued in that parameter domain through the use of a truncated model in which the approximations of weakly nonlinear theory are avoided. This more complex model demonstrates that the linearly most unstable wave in the narrow wedge in parameter space is nonlinearly stable and that the region of nonlinear destabilization is limited to a tiny region near one of the critical curves rendering both the linear and nonlinear growth essentially negligible.
Author Posting. © Sears Foundation for Marine Research, 2016. This article is posted here by permission of Sears Foundation for Marine Research for personal use, not for redistribution. The definitive version was published in Journal of Marine Research 74 (2016): 1-19, doi:10.1357/002224016818377595.
Showing items related by title, author, creator and subject.
Barth, John A. (Massachusetts Institute of Technology and Woods Hole Oceanographic Institution, 1987-10)A two-layer shallow water equation model is used to investigate the linear stability of a coastal upwelling front. The model features a surface front near a coastal boundary and bottom topography which is an arbitrary ...
Wilkin, John L. (Massachusetts Institute of Technology and Woods Hole Oceanographic Institution, 1988-09)A study is conducted of the scattering of freely-propagating subinertial frequency coastal-trapped waves (CTWS) by large variations in coastline and topography using analytical and numerical techniques. Particular attention ...
Cherian, Deepak A. (Massachusetts Institute of Technology and Woods Hole Oceanographic Institution, 2016-09)Eddies in the ocean move westwards. Those shed by western boundary currents must then interact with continental shelf-slope topography at the western boundary. The presence of other eddies and mean lows complicates this ...