The structure and evolution of elliptical barotropic modons

Explicit stationary solutions to the equations of vorticity conservation on the $f$- and $\beta $-planes are considered, describing barotropic dipoles (modons) with elliptical frontiers. The far field – outside the elliptical separatrix demarcating the regions of closed and open streamlines – is giv...

Full description

Saved in:
Bibliographic Details
Published in:Journal of fluid mechanics Vol. 530; pp. 1 - 30
Main Authors: KHVOLES, R., BERSON, D., KIZNER, Z.
Format: Journal Article
Language:English
Published: Cambridge, UK Cambridge University Press 10.05.2005
Subjects:
Earth, ocean, space
Exact sciences and technology
External geophysics
Fluid mechanics
Meteorology
Other topics
Other topics in atmospheric geophysics
Physics of the oceans
algorithms
Beta plane approximation
Vorticity
digital simulation
Vortex pair
Vortex
Barotropic mode
Modeling
Elliptical flow
ISSN:0022-1120, 1469-7645
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Explicit stationary solutions to the equations of vorticity conservation on the $f$- and $\beta $-planes are considered, describing barotropic dipoles (modons) with elliptical frontiers. The far field – outside the elliptical separatrix demarcating the regions of closed and open streamlines – is given analytically, whereas the interior is solved numerically using a successive linearization algorithm. Both ellipses extended along the translation axis and those extended in the transverse direction are considered. In the latter case, it is shown that, among the possible solutions, there exist the so-called supersmooth modons marked by continuity of the vorticity derivatives at the separatrix. On the $\beta$-plane, the separatrix aspect ratio that allows a supersmooth solution varies depending on the modon translation speed and size, while on the $ f$-plane, there is only one such separatrix aspect ratio. In this context, the limiting transition from the $\beta $-plane to the $f$-plane is discussed. The dependence between the absolute (or relative) vorticity $q$ and the ‘co-moving’ streamfunction $\Psi $, which is nonlinear in the interior of non-circular modons, is analysed in detail for both $\beta $- and $f$-planes, the main concern being the relation between the separatrix form, on the one hand, and the shape of the $q$ against $\Psi $ scattergraph on the other. The stability of elliptical dipoles versus the separatrix aspect ratio is examined based on numerical simulations of the temporal evolution of the modons found. The supersmooth modons appear to be the most stable among all the elliptical dipoles.
Bibliography:ark:/67375/6GQ-LJDQQHR2-3
istex:2FE98D001A2C385A2B6B5E62DE710DFF169FF3C3
PII:S0022112004003234
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ObjectType-Article-2
content type line 23
ISSN:0022-1120
1469-7645
DOI:10.1017/S0022112004003234