Newsgroups: sci.physics.plasma
From: news@seagoon.newcastle.edu.au
Organization: Uni of Newcastle, Australia
Subject: MHD fundamental frequency question

When solving the ideal MHD equations for a cylindrical sunspot with a
constant axial magnetic field inside the cylinder, and no magnetic field
outside the cylinder, you obtain a dispersion relation F(w/k,ka) = 0,
where w/k is the phase speed, k the wavenumber and a the radius of the
sunspot.

If you determine the values of w/k that satisfy the relation for ka values
ranging from say 1 to 40 and plot them, you end up with three sets of
curves, which in ascending order of phase speed are 1) the slow surface
modes, 2) the slow body modes and 3) the fast body modes. (cf The
Astrophysical Journal, 348:346-356, Jan 1 1990. The Oscillations of a
Magnetic Flux Tube and its Applications to Sunspots, D. Evans and B. Roberts)

The fast body modes show up as a fundamental with phase speed that of the
external sound speed and drop rapidly to be asymptotic with the internal
sound speed. The harmonics follow the same pattern but each harmonic has
slightly higher phase speed.

The slow body modes, on the other hand, have a fundamental that is of
*higher* phase speed than the harmonics, each higher harmonic being at
a slightly *lower* phase speed.

Can anyone explain, or direct me to some information, why/how the fundamental
has *higher* phase speed for the resonant oscillations called slow body modes.

I believe the situation also arises in rotational fluid flow.

Any help would be greatly appreciated.

Alan Gore
Dept of Mathematics
The University of Newcastle
Australia

email: mmag@maths.newcastle.edu.au