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Volume 2,     Number 2,     Spring 1994

 

RESONANT FLOW OF A ROTATING
FLUID PAST AN OBSTACLE:
THE RADIALLY UNBOUNDED CASE
R. GRIMSHAW AND Y. ZHU

Abstract. We consider the resonant interaction of a swirling flow past an axisymmetric obstacle on the axis of the flow. Here we consider the case when the swirling flow is radially unbounded, thus extending the work of Grimshaw [2] who considered the analogous problem for a radially confined flow. We show that in the weakly nonlinear long-wave regime the governing evolution equation for the amplitude of the dominant resonant mode is similar in structure to the forced Korteweg-de Vries equation derived by Grimshaw [2] in the radially confined case, and is a forced version of an equation derived by Leibovich [6] for freely propagating weakly nonlinear waves on a radially unbounded swirling flow.

 

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