A turbulence model with stochastic soliton motion

Abstract

A dissipative Benjamin–Ono equation is used to study fluid and plasma turbulence. The system is studied by an exact nonlinear mode truncation method in which a finite number of poles are used to present the solution. The justification of the pole expansion approach is discussed with the proof of a completeness theorem. The stability and spectrum analysis show that asymptotic behavior of the system is completely represented by a finite number of nonlinear modes. The behavior of those nonlinear modes resembles solitons, and exhibits a wide range of bifurcation phenomena and routes to turbulence.