When Do JONSWAP Spectra Lead to Soliton Gases in Deep Water Conditions?

Abstract

When a large number of solitons dominates the dynamics of a system, scientists describe this collective behaviour of solitons as a soliton gas. Soliton gases are currently the subject of intense practical and theoretical investigations. The existence of soliton gases has been confirmed in experiments, but is not clear what kind of sea states might lead to soliton gases. Therefore, in order to determine the wave parameters for sea states that lead to soliton gases, large numbers of surface wave elevations are generated by the well-known JOSNWAP model in this paper. Here, we only discuss soliton gases in deep water governed by the nonlinear Schrödinger (NLS) equation. The nonlinear Fourier transform (NFT) with vanishing boundary conditions is applied to the simulated ocean surface waves. The resulting nonlinear Fourier spectrum is used to calculate the energy of radiation waves and solitons. We investigate which JONSWAP parameters result in sea states that can be characterized as soliton gases, and find that a large Phillip’s parameter α, a large peak enhancement parameter γ and a short peak period T_P are important factors for soliton gas conditions. The results allow researchers to estimate how likely soliton gases are in deep waters. Furthermore, we find that the appearance of rogue waves is slightly increased in highly nonlinear sea states with soliton gas-like conditions.