CENS Seminar: Exact solutions to kinetic equations for weakly nonlinear waves

Venue:

Institute of Cybernetics, Akadeemia Rd 21, Tallinn, Room B101

Date:

16:00, November 17, 2003

Speaker:

Tarmo Soomere, Marine Systems Institute at Tallinn Technical University

Abstract:

The kinetic equation describes slow evolution of weakly nonlinear waves owing to enegy exchange between wave components. It is well known that the structure of the set of thermodynamically equilibrated solutions to kinetic equations is different for different wave classes. We show that this structure basically depends only on the parity of the number of resonantly interacting waves. Formally, solutions that correspond to negative energies in certain area of wave vectors may arise. We show the existence of such solutions and analyse their stability, physical meaning and realizability conditions.

Rossby waves (large-scale oscillations in the oceans and the atmosphere) serve as a rich model system where many attractive results can be derived analytically in the kinetic framework. In particular, Rossby wave fields can be described as a superposition of a number of vertical modes in which energy exhange rate depends on both interaction and coupling coefficients and is described by a multi-modal kinetic equation. Explicit analytical expressions for the coupling coefficients are obtained for the three-layer model. Several types of interactions vanish in the case of simple vertical structures of the water masses that normally do not occur in the open ocean but frequently appear in the Baltic Sea conditions.

Advanced Study School: Nonlinear Processes in Marine Sciences

Venue:

Hageri, Estonia

Date:

October 12--19, 2003

Objective and topics:

The main objective of the school is to give a systematic survey on contemporary ideas and methods dealing with the most important nonlinear phenomena in marine sciences that will be presented by leading scientists in these fields.

From a wide variety of issues of both theoretical and practical interest, the school concentrates on the wave mechanics and transport processes. An introduction to the state-of-the-art of geophysical turbulent boundary layers and Lagrangian transport in geophysical flows will be presented.

The courses are mostly designed for PhD students. Also, well-prepared MSc students may participate. The school might be also of interest for young researchers and marine engineers who want to get an overview of several key nonlinear processes in marine sciences and/or are specialised in different areas of marine and environmental sciences including, yet not limited with meteorology, oceanography, geophysical hydrodynamics, ocean and coastal engineering, pollution control.

Announcement and a time table