Three-dimensional localized coherent structures of surface turbulence. II. Λ solitons

Abstract

We numerically construct Λ solitons as a function of the generalized Reynolds number δ. The numerical scheme is based on an impulse response analysis in which the nonlinear hump region is replaced with a Dirac delta function. We also examine the linear stability of Λ solitons with respect to three-dimensional disturbances. It is shown that the operator of the linearized system has both a discrete and a continuous spectrum. The discrete spectrum is always stable, while the continuous spectrum can be destabilized leading to a convective instability of Λ solitons. We demonstrate that the region of existence and stability of Λ solitons is 0.054<δ<0.51.