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|Title: ||Steady multipolar planar vortices with nonlinear critical layers|
|Authors: ||Caillol, P.|
Grimshaw, Roger H.J.
|Issue Date: ||2003|
|Abstract: ||This article considers a family of steady multipolar planar vortices which are the superposition of
an axisymmetric mean flow, and an azimuthal disturbance in the context of inviscid, incompressible
flow. This configuration leads to strongly nonlinear critical layers when the angular velocities of the
mean flow and the disturbance are comparable. The poles located on the same critical radius possess
the same uniform vorticity, whose weak amplitude is of the same order as the azimuthal disturbance.
This problem is examined through a perturbation expansion in which relevant nonlinear terms are
retained in the critical layer equations, while viscosity is neglected. In particular, the associated
singularity at the meeting point of the separatrices is treated by employing appropriate re-scaled
variables. Matched asymptotic expansions are then used to obtain a complete analytical description
of these vortices.|
|Description: ||This pre-print has been submitted, and accepted, to the journal, Geophysical and Astrophysical Fluid Dynamics [© Taylor & Francis]. The definitive version: CALLIOL, P. and GRIMSHAW, R.H.J., 2004. Steady multipolar planar vortices with nonlinear critical layers. Geophysical and Astrophysical Fluid Dynamics, 98(6), pp. 473-506 is available at: http://www.tandf.co.uk/journals/online/0309-1929.asp.|
|Appears in Collections:||Pre-prints (Maths)|
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