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|Title: ||Solitary waves with recirculation zones in axisymmetric rotating flows|
|Authors: ||Derzho, Oleg G.|
Grimshaw, Roger H.J.
|Issue Date: ||2002|
|Publisher: ||© Cambridge University Press|
|Citation: ||DERZHO, O.G. and GRIMSHAW, R.H.J., 2002. Solitary waves with recirculation zones in axisymmetric rotating flows. Journal of Fluid Mechanics, 464, pp. 217-250.|
|Abstract: ||In this paper, we describe a theoretical asymptotic model for large-amplitude travelling
solitary waves in an axially symmetric rotating flow of an inviscid incompressible fluid
confined in an infinitely long circular tube. By considering the special, but important,
case when the upstream flow is close to that of uniform axial flow and uniform
rotation, we are able to construct analytical solutions which describe solitary waves
with `bubbles', that is, recirculation zones with reversed flow, located on the axis of the
tube. Such waves have amplitudes which slightly exceed the critical amplitude, where
there is incipient flow reversal. The effect of the recirculation zone is to introduce into
the governing amplitude equation an extra nonlinear term, which is proportional to
the square of the difference between the wave amplitude and the critical amplitude.
We consider in detail a special, but representative, class of upstream inflow conditions.
We find that although the structure of the recirculation zone is universal, the presence
of such solitary waves is quite sensitive to the actual upstream axial and rotational
velocity shear configurations. Our results are compared with previous theories and
observations, and related to the well-known phenomenon of vortex breakdown.|
|Description: ||This article was published in the journal, Journal of Fluid Mechanics [© Cambridge University Press] and is available at: http://journals.cambridge.org/action/displayJournal?jid=FLM.|
|Appears in Collections:||Published Articles (Maths)|
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