02-393 Sergey K. Zhdanov, Denis G. Gaidashev

On the instability of solitons in shear hydrodynamic flows (323K, pdf) Sep 19, 02

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Abstract. The paper presents a stability analysis of plane solitons in hydrodynamic shear flows obeying a (2+1) analogue of the Benjamin-Ono equation. The analysis is carried out for the Fourier transformed linearized (2+1) Benjamin-Ono equation. The instability region and the short-wave instability threshold for plane solitons are found numerically. The numerical value of the perturbation wave number at this threshold turns out to be constant for various angles of propagation of the solitons with respect to the main shear flow. The maximum of the growth rate decreases with the increasing angle and becomes equal to zero for the perpendicular propagation. Finally, the dependency of the growth rate on the propagation angle in the long-wave limit is determined and the existence of a critical angle which separates two types of behavior of the growth rate is demonstrated.

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