15 research outputs found
On the stratorotational instability in the quasi-hydrostatic semi-geostrophic limit
The linear normal-mode stratorotational instability (SRI) is analytically
reexamined in the inviscid limit where the length scales of horizontal
disturbances are large compared their vertical and radial counterparts.
Boundary conditions different than channel walls are also considered. This
quasi-hydrostatic, semi-geostrophic (QHSG) approximation allows one to examine
the effect of a vertically varying Brunt-Vaisaila frequency, . It is found
that the normal-mode instability persists when increases quadratically
with respect to the disc vertical coordinate. However we also find that the SRI
seems to exist in this inviscid QHSG extreme only for channel wall conditions:
when one or both of the reflecting walls are removed there is no instability in
the asymptotic limit explored here. It is also found that only exponential-type
SRI modes (as defined by Dubrulle et al. 2005) exist under these conditions.
These equations also admit non-normal mode behaviour. Fixed Lagrangian pressure
conditions on both radial boundaries predicts there to be no normal mode
behaviour in the QHSG limit. The mathematical relationship between the results
obtained here and that of the classic Eady (1949) problem for baroclinic
instability is drawn. We conjecture as to the mathematical/physical nature of
the SRI.
The general linear problem, analyzed without approximation in the context of
the Boussinesq equations, admits a potential vorticity-like quantity that is
advectively conserved by the shear. Its existence means that a continuous
spectrum \emph{is a generic feature of this system}. It also implies that in
places where the Brunt-Vaisaila frequency becomes dominant the linearized flow
may two-dimensionalize by advectively conserving its vertical vorticity.Comment: 16 pages. Accepted in MNRAS (09/05). New sections added and abstract
change