Sergey K. Zhdanov, Denis G. Gaidashev
On the instability of solitons in shear hydrodynamic flows
(323K, pdf)
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.