2010
DOI: 10.1051/0004-6361/201015210
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Potential vorticity dynamics in the framework of disk shallow-water theory

Abstract: Context. The Rossby wave instability in astrophysical disks is a potentially important mechanism for driving angular momentum transport in disks. Aims. We attempt to more clearly understand this instability in an approximate three-dimensional disk model environment which we assume to be a single homentropic annular layer we analyze using disk shallow-water theory. Methods. We consider the normal mode stability analysis of two kinds of radial profiles of the mean potential vorticity: the first type is a single … Show more

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Cited by 37 publications
(50 citation statements)
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“…The barotropic incarnation of the Rossby wave instability was interpreted in Umurhan (2010) to arise as a result of the interaction of the two Rossby waves that propagate along the azimuthal directions at the two locations, consistent with the more generic picture of interacting edgewave disturbances (Baines & Mitsudera 1994). An analogous form of this dynamic is present in this model and is especially pronounced for ξ 1.…”
Section: Barotropic Configurationsmentioning
confidence: 59%
See 1 more Smart Citation
“…The barotropic incarnation of the Rossby wave instability was interpreted in Umurhan (2010) to arise as a result of the interaction of the two Rossby waves that propagate along the azimuthal directions at the two locations, consistent with the more generic picture of interacting edgewave disturbances (Baines & Mitsudera 1994). An analogous form of this dynamic is present in this model and is especially pronounced for ξ 1.…”
Section: Barotropic Configurationsmentioning
confidence: 59%
“…This, in turn, permits a dynamical analysis purely in terms of the potential vorticity, which is typical of meteorological studies. This construction was used to re-examine the Rossby wave instability (Li et al 2000;Meheut et al 2010) by illustrating it in a setting stripped down to its essential components (Umurhan 2010).…”
Section: Introductionmentioning
confidence: 99%
“…From an analytical point of view, the first work that deals with the RWI in 3D is the one by Umurhan (2010). The vertical structure of the modes has recently be studied in more detail (Meheut et al 2012;Lin 2012) with dedicated tools as those presented in Zhang & Lai (2006).…”
Section: Outlooksmentioning
confidence: 99%
“…The analogy remains to be fully investigated. An interpretation of the Rossby instability as arising from the interaction of two "edge waves" on either side of the bump in L(r) is given by Umurhan (2010) who points out the analogy of the RWI with the diochotron instability (Buneman 1957;Knauer 1966) of rotating, non-neutral plasmas in a uniform magnetic field for cases where the plasma is annular with both inner and outer radii so that there are two edge waves.…”
Section: Schrödinger-like Equation For Perturbationmentioning
confidence: 99%