Graduate School in Nonlinear Science

Sponsored by The Danish Research Agency


MIDIT                              OFD                          CATS
Modelling, Nonlinear Dynamics      Optics and Fluid Dynamics    Chaos and Turbulence Studies
and Irreversible Thermodynamics    Risø National Laboratory     Niels Bohr Institute and 
Technical University of Denmark    Building 128                 Department of Chemistry
Building 321                       P.O. Box 49                  University of Copenhagen 
DK-2800 Lyngby                     DK-4000 Roskilde             DK-2100 Copenhagen Ø
Denmark                            Denmark                      Denmark

THE CHARNEY-HASEGAWA-MIMA EQUATION RE-VISITED

Chris Lashmore-Davies
UKAEA Fusion,
Culham Science centre

Friday, August 16, 2002, 10:00 h
at Meeting Room, Building 108
Risų National Laboratory, 4000 Roskilde

Abstract: The Charney-Hasegawa-Mima (CHM) equation was developed as a simple model to explore some of the properties of drift/Rossby wave turbulence. A spectrum cascade occurring through three non-linearly interacting drift waves was obtained by Hasegawa, Maclennan and Kodama leading to zonal flows in the direction perpendicular to the gradient. The generalized CHM equation was later introduced in which the zonal flow is explicitly included. In this case, the fundamental non-linear coupling is through a four wave interaction. Employing the concept of the equivalent quantum or action for each of the four modes, conservation laws for the quanta are obtained, including the zero frequency zonal flow. A self-consistent scheme to calculate the spectrum of modes to replace the heuristic method used by Hasegawa, Maclennan and Kodama is discussed.