9 Mar 2005; Mat-Nat Faculty (UITO), room U1. Wednesday 10:15-12:00

Per Jacobsen

"Probability densities for waveturbulence"

In the usual approach to waveturbulence one derive closed equations for second order cumulants of the random wavefield using multiple scale expansions. The equation for the second cumulant is called the Kinetic equation and is the analog of the Boltzmann equation from statistical mechanics.

In this lecture I will approach waveturbulence from the dynamical system point of view. A probability measure on the space of fields will be considered, an asymptotically valid equation for the measure (the Brout-Prigogine equation) will be derived and its relation to the kinetic equation will be discussed. The BP equation has an H-theorem with respect to the usual Gibbs entropy. Relation between this entropy and the entropy used in waveturbulence will be also discussed.

A toy model of the kinetic equation for four-wave interaction will be introduced (the Lied equation) and I will expand on Alan Newell's suggestion that this equation might be an example of a SOC system. The theory will not be developed in a rigorous manner (can't be done, this is field theory folks!), but I will at least try to state what is not rigorous.