The instability of streamwise varying shear flow that is marginally stable to
long Rossby waves is examined. Both Hamiltonian and non-Hamiltonian flows
are considered within the framework of coupled wave instability (CWI). The
CWI is shown to be mediated by a ‘physical’ wave and a ‘virtual’ wave. The
physical/virtual wave model concisely describes the differences between the
instabilities that develop on locally supercritical flow and those that
develop on globally subcritical flow. Globally subcritical Hamiltonian flows
are proven to be stable. In contrast, non- Hamiltonian flows may be unstable
in both locally supercritical and globally subcritical regimes. In locally
supercritical flow, the CWI grows via wave-resonance between the
physical/virtual wave pair and is highly localized to the supercritical
region. In contrast, in globally subcritical flow, the CWI grows via
pseudomomentum extraction from the background flow and either radiates away
or remains attached to the streamwise variation in the flow.
Publié le : 2007-12-15
Classification:
linear instability,
coupled wave,
long Rossby waves,
streamwise varying,
76B65,
76E09,
76E15,
76E20
@article{1199377553,
author = {Hodyss, Daniel and Nathan, Terrence R.},
title = {Instability of marginally stable streamwise varying shear flow to long rossby
waves},
journal = {Commun. Math. Sci.},
volume = {5},
number = {1},
year = {2007},
pages = { 833-849},
language = {en},
url = {http://dml.mathdoc.fr/item/1199377553}
}
Hodyss, Daniel; Nathan, Terrence R. Instability of marginally stable streamwise varying shear flow to long rossby
waves. Commun. Math. Sci., Tome 5 (2007) no. 1, pp. 833-849. http://gdmltest.u-ga.fr/item/1199377553/