The nonpropagating hydrodynamic soliton in annular geometries

Abstract

The nonpropagating hydrodynamic soliton discovered by Wu et al. [Phys. Rev. Lett. 52, 16 (1984)] exists as a localized finite amplitude disturbance in a parametrically excited rectangular channel. The behavior of the nonpropagating soliton in annular resonators of various radii of curvature is investigated. The distortion of the soliton profile, which increases with decreasing radius of curvature, suggests that as energy is moved from lower to higher wavenumbers, the dispersion must increase to balance the increasing nonlinearity. At a critical radius of curvature, the soliton changes form. As the inner annular radius decreases further, the soliton merges with a nonlinear mode of the circular tank. This mode resembles the (1,2) normal mode in that it consists of a localized maximum‐minimum pair, but occurs at a frequency slightly below that of the (0,2) normal mode. The behavior and properties of this nonlinear “sub‐(0,2)" mode are compared to that of the one‐dimensional nonpropagating soliton. [Work supported by ONR.]