Date post: | 31-Dec-2015 |
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(W is scalar for displacement, T is scalar for traction)
Note that matrix does not depend on m
Algorithm for toroidal modes
• Choose harmonic degree and frequency
• Compute starting solution for (W,T)
• Integrate equations to top of solid region
• Is T(surface)=0? No: go change frequency and start again. Yes: we have a mode solution
T(surface) for harmonic degree 1
Radial and Spheroidal modes
Spheroidal modes
Minors
• To simplify matters, we will consider the spheroidal mode equations in the Cowling approximation where we include all buoyancy terms but ignore perturbations to the gravitational potential
Spheroidal modes w/ self grav
(three times slower than for Cowling approx)
Red > 1%; green .1--1%; blue .01--.1%
Red>5; green 1--5; blue .1--1 microHz
Mode energy densities
Dash=shear, solid=compressional energy density
Norm
alized radius
(black dots are observed modes)
All modes for l=1
(normal normal modes)
ScS --not observed
hard to compute
(not-so-normal normal modes)