for the semi-implicit Euler
equations, 357, 358
solution of, 340-342
pressure gradient computation over
topography, 378-379
primitive equations
in generalized vertical
coordinates, 375-377
in height coordinates,
374-375
in (1 coordinates, 377-378
energy conservation,
383-387
semi-implicit
time-differencing,
387-389
vertical differencing,
381-383
projection method, 337, 371-372
pseudo-incompressible
approximation, 21, 24
pseudo-incompressible system, 22
pseudospectral methods, 191-195
radiation boundary condition
definition and applicability of,
395-397
for the I-D shallow-water
equations, 400-401
for the 2-D shallow-water
equations,414-419
and time-dependent boundary
data, 401-402
for 2-D stratified flow
lateral boundaries, 419-423
upperboundary, 424-431
Rankine-Hugoniot condition, 245
rarefaction wave, 246-248,
273-274
residual, 174
Reynolds number, 138, 167
Riemann invariant, 399
Riemann problem, 244, 272-274
Robert-Asselin filter, see Asselin
filter
Index
463
Rossby waves, 11, 15-16, 20,
335-336,347,
390-391
Runge-Kutta method s
for trajectory calculations in
semi-Lagrangian
schemes, 311-313
higher-order, 65-71,360
second order, 53, 56
Schwarz inequality, 42
semi-implicit method, 371-372
comparison with the projection
method,357
for the Euler equations,
353-359
for the oscillation equation,
345-347
for the primitive equations in
(1 coordinates, 387-389
for the shallow-water
equations, 347-350
semi-implicit semi-Lagrangian
methods, 320-324
semi-Lagrangian methods
for the advection equation,
305-313
accuracy of, 306-313
stability of, 306
comparison with Eulerian
schemes, 330-331
comparison with the method of
characteristics, 318-320
computation of the backward
trajectory, 310-313
defined ,304
for the forced advection
equation, 313-318
using generalized trajectories,
324-329
noninterpolating, 325-327
and positive definite advection,
327-329
for the shallow-water
equations,320-324