464
Index
shallow-water equations
hyperbolie nature of, 13-16
for the middle-latitude ß
plane , 389-390
1-D linearized, 107-108
on the sphere
linear, 200-202
nonlinear, 207-212
radiation boundary eonditions
for the 2-D system,
413-419
semi-implicit approximations
tO,347-350
semi-implicit serni-Lagrangian
approximations to, 321,
324
shoek, speed of, 245
a eoordinate, 377
slant derivative method, 104
slope limiters, 275-276
sound waves, 11,335-337,
352-356
dispersion relation, 19
filtering of, 20-26
speed of, 18
spatial smoothing, 82-86
speetral method, 29
aeeuraey of, 182-184
eomparison with
finite-difference methods ,
177-184
eonservation properties of,
189-190
and the Galerkin
approximation, 176-177
improving effieieney of,
184-189
remote influenee in, 181-182
for spherical domains,
195-212,379-381
speetral radius, 109
spherieal harmonie funetions
eomparison of triangular and
rhomboidal truneations,
197-200
defined , 195-196
in global primitive equation
models, 379-381
in global shallow-water
models, 207-209
reeurrenee relations for, 196
transforming between physical
and wave-number spaee,
202-203
spongelayers, 431-435
stability
and eonvergenee, 40-41
energy-method analysis of,
41-42, 154-158
problems at the poles, 200-202
of systems of finite-difference
equations, 108-113
Von Neumann analysis of, 43,
45,91, 108-111
staggered meshes, 113-117
C grid, 127
Strang perturbation theorem,
146-147
Strang splitting, 131-132
stream funetion, 163,208
superbee limiter, 267-271 ,
285-290
Taylor-Galerkin method, 217-219
total variation, 252
in two dimensions, 256-257
total variation diminishing method,
252-254,256-257,
274-276,292
sufficient eonditions for,
264-268
transform method
for the Fourier speetral
method, 184-189
for the spherieal harmonie
speetral method,
202-207,209-212
transonic rarefaetion wave, 274
trapezoidal time-differencing, 50,
53,55,56,202