174
Index
F
Finite differences
explicit, implicit, 8, 9
forward, backward, centred, 66
Flooding algorithm, 73, 77–82, 84, 93, 94, 120,
157, 163
Flow
anticyclonic, 124, 156, 160
baroclinic, 43
barotropic, 43, 124
cyclonic, 124, 149, 152, 156, 160, 161
frontal, 153, 154, 156, 158, 159, 160
geostrophic, 122–128, 129, 130, 132, 137,
140, 141, 142, 143, 144, 146, 148, 150,
154, 155, 157, 158
quasi-geostrophic, 127, 129, 157, 158
shear, 58, 132–134, 135, 136
Force
apparent, 28, 43–44, 45
buoyancy, 34–36, 37, 38, 39
centrifugal, 43–45, 46–47, 50, 51
centripetal, 44–45, 46, 47, 51, 52
coriolis, 28, 43–57, 62, 63, 68, 91, 99,
119–120, 121, 122, 123, 137, 139, 152,
164, 165, 166
gravity, 35, 41, 50, 51, 165, 166
pressure-gradient, 41–43, 46, 47, 50, 51,
79, 119, 123, 130, 137, 148
reduced-gravity, 165, 166
Froude number, 62
G
Geostrophic
adjustment, 151–157
equations, 123–124
method, 124
H
Hydrostatic balance, 41, 42, 47, 123
I
Inertial
oscillations, 48, 50, 51, 55, 56–57, 156
period, 50, 63, 68, 91, 121, 123, 152, 154
radius, 50
Instability
baroclinic, 157–158
barotropic, 132, 133, 134–137, 157, 158,
162
Internal wave, 86, 87, 151, 154, 156
K
Kelvin wave, 120–122
L
Lagrangian trajectory, 28
Lateral
friction, 99, 112, 113–114, 117, 119, 149,
154, 159
momentum diffusion, 112, 113, 117, 118,
130, 135, 144, 145, 147, 148, 149, 159
Level of no motion, 149
Local vertical, 50–51, 52
M
Merian’s formula, 87
N
Navier–Stokes equations, 60–61, 63, 68
Nonlinear terms, 29, 30, 60, 62, 68, 70, 91, 99,
111–112, 113, 119, 122, 123, 138, 145,
147, 148, 149, 156, 159
Numerical diffusion, 77, 104, 106, 107, 112,
117, 122
Numerical stability criterion
for advection, 106
for diffusion, 115
Numerical waves, 73
P
Permanent thermocline, 148, 150
Phase speed, 21, 24, 25, 62, 68, 70, 85, 86, 87,
88, 91, 96, 97, 98, 106, 121, 128, 131,
151, 154, 155
Prandtl’s mixing length, 59
R
Reduced-gravity
concept, 149–151, 153
plume, 162, 163–167
Reynolds
approach, 57–58
number, 113, 117
Richardson number, 58, 59
Rossby
number, 63, 122, 123, 127, 129, 132, 135,
138
(internal) radius of deformation, 121, 122,
128, 153, 154, 155
wave, 127–128, 130, 131, 132
S
Scaling, 61–63, 68, 122–123, 133, 139
Semi-implicit approach
for bottom friction, 99–100, 120
for Coriolis force, 53–54, 120
Index
F
Finite differences
explicit, implicit, 8, 9
forward, backward, centred, 66
Flooding algorithm, 73, 77–82, 84, 93, 94, 120,
157, 163
Flow
anticyclonic, 124, 156, 160
baroclinic, 43
barotropic, 43, 124
cyclonic, 124, 149, 152, 156, 160, 161
frontal, 153, 154, 156, 158, 159, 160
geostrophic, 122–128, 129, 130, 132, 137,
140, 141, 142, 143, 144, 146, 148, 150,
154, 155, 157, 158
quasi-geostrophic, 127, 129, 157, 158
shear, 58, 132–134, 135, 136
Force
apparent, 28, 43–44, 45
buoyancy, 34–36, 37, 38, 39
centrifugal, 43–45, 46–47, 50, 51
centripetal, 44–45, 46, 47, 51, 52
coriolis, 28, 43–57, 62, 63, 68, 91, 99,
119–120, 121, 122, 123, 137, 139, 152,
164, 165, 166
gravity, 35, 41, 50, 51, 165, 166
pressure-gradient, 41–43, 46, 47, 50, 51,
79, 119, 123, 130, 137, 148
reduced-gravity, 165, 166
Froude number, 62
G
Geostrophic
adjustment, 151–157
equations, 123–124
method, 124
H
Hydrostatic balance, 41, 42, 47, 123
I
Inertial
oscillations, 48, 50, 51, 55, 56–57, 156
period, 50, 63, 68, 91, 121, 123, 152, 154
radius, 50
Instability
baroclinic, 157–158
barotropic, 132, 133, 134–137, 157, 158,
162
Internal wave, 86, 87, 151, 154, 156
K
Kelvin wave, 120–122
L
Lagrangian trajectory, 28
Lateral
friction, 99, 112, 113–114, 117, 119, 149,
154, 159
momentum diffusion, 112, 113, 117, 118,
130, 135, 144, 145, 147, 148, 149, 159
Level of no motion, 149
Local vertical, 50–51, 52
M
Merian’s formula, 87
N
Navier–Stokes equations, 60–61, 63, 68
Nonlinear terms, 29, 30, 60, 62, 68, 70, 91, 99,
111–112, 113, 119, 122, 123, 138, 145,
147, 148, 149, 156, 159
Numerical diffusion, 77, 104, 106, 107, 112,
117, 122
Numerical stability criterion
for advection, 106
for diffusion, 115
Numerical waves, 73
P
Permanent thermocline, 148, 150
Phase speed, 21, 24, 25, 62, 68, 70, 85, 86, 87,
88, 91, 96, 97, 98, 106, 121, 128, 131,
151, 154, 155
Prandtl’s mixing length, 59
R
Reduced-gravity
concept, 149–151, 153
plume, 162, 163–167
Reynolds
approach, 57–58
number, 113, 117
Richardson number, 58, 59
Rossby
number, 63, 122, 123, 127, 129, 132, 135,
138
(internal) radius of deformation, 121, 122,
128, 153, 154, 155
wave, 127–128, 130, 131, 132
S
Scaling, 61–63, 68, 122–123, 133, 139
Semi-implicit approach
for bottom friction, 99–100, 120
for Coriolis force, 53–54, 120