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   -> Volume 4, Issue 3

Preprint: Meteorological PDEs in the wavelet representation
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PostPosted: Mon Dec 02, 2002 5:45 pm    
Subject: Preprint: Meteorological PDEs in the wavelet representation
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Preprint: Meteorological PDEs in the wavelet representation

Title: Wavelet representation of lower-atmospheric long nonlinear wave
dynamics, governed by the Benjamin-Davis-Ono-Burgers equation
Author: Aime' Fournier

This is a modest note illustrating some advantages of the wavelet
representation for describing the local dynamic interactions between scales in
the theoretical evolution of certain dispersive, nonlinear atmospheric waves.
The wave displacement A(x,t) is governed by the PDE:

A = vA - H[A ] - AA ,
t xx xx x

where v is viscosity, and H is the Hilbert transform operator (without which
this would just be the Burgers equation). The use of a wavelet transform over
x to reduce this PDE to a set of ODEs for a 32-dimensional coefficient array
WA(t) is explained. Interactions between all 4 scales and 16 locations
(implied by 32=16+8+4+2+2) are retained, and numerical optimization is not a
concern. Solutions demonstrate such features as localized energy
cascades (normal and inverse) and also separate features at different scales,
such as dispersive wave trains.

I will be giving an oral presentation of this work at the Wavelet Applications
for Dual Use part of SPIE's 1995 Symposium on OE/Aerospace Sensing and Dual Use
Photonics (WD 3.14 #5).

This preprint is available by nonanonymous request to me at the address below.
I would be happy to e-mail a PostScript file, or mail a hard copy, and would
welcome comments.

Aime' Fournier
Yale University
Dept of Geology and Geophysics
PO Box 208109
New Haven CT 06520-8109 USA
tel: 203 432 3146 fax: 203 432 3134
All times are GMT + 1 Hour
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