372
Index
diffusion
numerical 61
operator approximation of non-linear
transfer 84
directional distribution 255
discrete interaction approximation 7,
83
dispersion 130, 142, 267, 272
dispersion ratio 17, 19, 156, 233, 262,
269,291
dissipation 2, 8, 28, 176, 289, 291
due to bottom friction 258
due to percolation 289
due to whitecapping 128, 133
of shallow-water waves 286
Doppler
frequency 19,155
shift due to currents 155
Earth's
radius 9, 11,35,43,52,295
rotation 29, 35
sphericity 9
eigen
frequency 31
functions/modes 20
energy, wave energy 58, 66, 86, 129,
153,163,179,187,224
angular distribution 93, 99
balance equation 2, 3, 7, 35, 36, 38,
39,49-51,54,56,59,65,74,75,78,
128,137,142,152,183,294,296,
317,335
diffusion 61
dissipation 81, 127, 132, 174, 229,
287,289,294,317
flux 4,28,126,183,248,255
input 81,138,247
non-linear transfer (between waves)
81,90,92,96,101,108
propagation of 79
spectrum: see spectrum 200, 254,
294
transfer (from wind to waves) 152,
176,198,263
equilibrium (range) 3, 69, 129, 130,
135,163,164,166,173,176,179,
185,189,267,284,308
Ermith function 216
Euler's method 70
exceptional waves (see also abnormal
waves, freak waves, and rogue
waves) 217
Feynman diagrams 28
finite difference method: see numerical
scheme 51
floes 284,335
four-wave interaction (see also
non-linear energy transfer) 3, 267
Fourier
integral 194,292,328
transformation 24, 326
freak waves (see also abnormal waves,
exceptional waves and rogue
waves) 217
frequency 14,51,132,292
intrinsic 31
friction
force 12
velocity 12, 123, 139, 239
garden-sprinkler effect 50, 51, 54, 56,
62
Gaussian
distribution 24, 139
process 24
general problem formulation 11, 35,
253
geodesic line 36
geometric(al) optics approximation 5,
14,18,166,193,223,260,317
global distance 35
gravity
acceleration 11, 336
waves 335, 342
Green formula 258, 281
Green function 335
grid point 49, 51, 53, 59, 78,263,297,
300
group velocity 17, 18, 33, 52, 153, 158,
178,188,193,214,229,241,257,
258,271,296,316,320
gustiness effect 138
Hamilton-Jacobi equation 16, 17
Hamiltonian equations (of motion)
17,25,153,154,223,317,319
Index
diffusion
numerical 61
operator approximation of non-linear
transfer 84
directional distribution 255
discrete interaction approximation 7,
83
dispersion 130, 142, 267, 272
dispersion ratio 17, 19, 156, 233, 262,
269,291
dissipation 2, 8, 28, 176, 289, 291
due to bottom friction 258
due to percolation 289
due to whitecapping 128, 133
of shallow-water waves 286
Doppler
frequency 19,155
shift due to currents 155
Earth's
radius 9, 11,35,43,52,295
rotation 29, 35
sphericity 9
eigen
frequency 31
functions/modes 20
energy, wave energy 58, 66, 86, 129,
153,163,179,187,224
angular distribution 93, 99
balance equation 2, 3, 7, 35, 36, 38,
39,49-51,54,56,59,65,74,75,78,
128,137,142,152,183,294,296,
317,335
diffusion 61
dissipation 81, 127, 132, 174, 229,
287,289,294,317
flux 4,28,126,183,248,255
input 81,138,247
non-linear transfer (between waves)
81,90,92,96,101,108
propagation of 79
spectrum: see spectrum 200, 254,
294
transfer (from wind to waves) 152,
176,198,263
equilibrium (range) 3, 69, 129, 130,
135,163,164,166,173,176,179,
185,189,267,284,308
Ermith function 216
Euler's method 70
exceptional waves (see also abnormal
waves, freak waves, and rogue
waves) 217
Feynman diagrams 28
finite difference method: see numerical
scheme 51
floes 284,335
four-wave interaction (see also
non-linear energy transfer) 3, 267
Fourier
integral 194,292,328
transformation 24, 326
freak waves (see also abnormal waves,
exceptional waves and rogue
waves) 217
frequency 14,51,132,292
intrinsic 31
friction
force 12
velocity 12, 123, 139, 239
garden-sprinkler effect 50, 51, 54, 56,
62
Gaussian
distribution 24, 139
process 24
general problem formulation 11, 35,
253
geodesic line 36
geometric(al) optics approximation 5,
14,18,166,193,223,260,317
global distance 35
gravity
acceleration 11, 336
waves 335, 342
Green formula 258, 281
Green function 335
grid point 49, 51, 53, 59, 78,263,297,
300
group velocity 17, 18, 33, 52, 153, 158,
178,188,193,214,229,241,257,
258,271,296,316,320
gustiness effect 138
Hamilton-Jacobi equation 16, 17
Hamiltonian equations (of motion)
17,25,153,154,223,317,319