# Graduate School in Nonlinear Science

**
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.