Journal of Fluid Mechanics

Weakly non-linear waves in rotating fluids

S.  Leibovich a1
a1 Department of Thermal Engineering, Cornell University, Ithaca, New York

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The Korteweg–de Vries equation is shown to govern formation of solitary and cnoidal waves in rotating fluids confined in tubes. It is proved that the method must fail when the tube wall is moved to infinity, and the failure is corrected by singular perturbation procedures. The Korteweg–de Vries equation must then give way to an integro-differential equation. Also, critical stationary flows in tubes are considered with regard to Benjamin's vortex breakdown theories.

(Published Online March 29 2006)
(Received June 14 1969)
(Revised January 5 1970)