EVENT DETAILS AND ABSTRACT

Title: Self-organisation in soliton wave turbulence
Speaker: Professor C. Josserand
Speaker Info: U. Chicago
Brief Description:
Special Note:
Abstract:

A fascinating feature of many turbulent fluid and plasma systems is the emergence and persistence of large-scale organized states, or coherent structures, in the midst of small-scale turbulent fluctuations. A familiar example is the formation of macroscopic quasi-steady vortices in a turbulent large Reynolds number two dimensional fluid. Such phenomena also occur for many classical Hamiltonian systems, even though their dynamics is formally reversible. In the present work, we shall focus our attention on another class of nonlinear partial differential equations whose solutions exhibit the tendency to form persistent coherent structures immersed in a sea of microscopic turbulent fluctuations. This is the class of nonlinear wave systems described by the well-known nonlinear Schrodinger equation. We will particularly investigate a statistical approach which describe the behavior of such a dynamics for long time for a finite number of modes. An interesting comparison will be made between this statistical equilibrium theory and numerical simulations. Finally, an important analogy will be presented between this problem and the two dimensional turbulence.