Euler equation, 1–2

in wave groups, 177–181

relevant to given spectrum and DWR, 56f

relevant to JONSWAP spectrum, 52f

relevant to JONSWAP spectrum, 51–52

and spectrum, 45

analysis, spectrum used for, 49f

effect, 71–74

waves approaching, 25f

waves transformation near, 25–42

arbitrary contour lines, 27–31

straight contour lines, 25–27, 26f, 232, 296–297, 303, 266

maximum expected, 78

probability of, 69–70

homogeneous random wave field, 145–146

nonhomogeneous random wave fields, 151–153

in polar coordinates, 152f

of pressure fluctuation, 289f, 290

maximum expected wave height at, 117–119

advanced approach and, 111

equations of deterministic waves, 209–211, 213f

occurrence of exceptionally large waves, 212

wave loads on structures, 214–219

equations of deterministic waves, 219

occurrence of exceptionally large waves, 220

three-dimensional wave group, 173–176

from time series data, 186–187

calculation of, 245

in lee of upright breakwater, 149–151

before long upright breakwater, 148–149

of wind seas, 150f

classic approach, 120–122

directional distribution, first wave family of, 140f

definition and characteristic shape, 119–120

function WLENGTH, 137

obtaining, reference scheme, 123f

program TESTDS, 131–136

subroutine FOUR, 126–128

subroutine SDI, 128–129

subroutine SDIR, 129–131

worked example, 137–141, 139f

oscillating water discharge, 272

and pressure fluctuation, 278f, 289f

definition and characteristic form of, 90–91

quotient between summation and total time, 90f–91f

time duration of, 96f

design sea state for given lifetime and, 100–102, 101f

general inequality for, 100

definition and property of, 92–93

maximum expected wave height in, 91–92

regression base height of, 93–95

sea storm by NDBC buoy, 94f

experiment on wave periods, 75

random variable β, 75–77

for basic parameters on deep water, 79–83

for basic parameters on finite water depth, 83–84

for basic parameters on maximum expected wave, 84–85

PLAT, 246, 257

QD software for hydraulic verifications, 296–303

TUNN, 252, 257

definition, 44

duration of wave record, 55–57

Fourier series, 54–55

FORTRAN program, 35–41

wave force on solid body and, 200–204

graphic aid to understand, 68f

joint Gaussian pdf, 68–69

of time, 44

algorithm, 123–126

base of new approach, 126

autocorrelation relevant to, 52f

autocovariance relevant to, 51–52

function obtained from, 72f

relationship T_p(H_s) based on, 52–53

and TMA spectrum, 53–54

isolated bodies, 181, 198, 207

advanced approach, 103–109

design sea state pattern, 102–103

probability functions, 103

design sea state, 100–102

estimate of the largest wave height, 102–111

first worked example, 266–267

overall stability of upright section, 259–261

diffraction coefficients, 148–149

gauges of recent small scale field experiment, 224f

nonhomogeneous random wave field, 151

zero up-crossing wave, 225f

at a given array of points in the design sea state, 117–119

in a given sea state, 77–78

in a nonhomogeneous sea state, 154

program for, 84–85

in a storm of given H_s(t), 91–92

method of, 241–242

of the spectrum, 48

field tests of, 229–235

force calculated with, 231–234

random force process calculated with, 233f

force calculated with, 231–234

K_E of sea state as whole, 234–235

method for obtaining C_in and C_dg, 229–231

cross-correlation of surface elevation, 153

in lee of upright breakwater, 152–153

before long upright breakwater, 151

cross section of, 270f

horizontal, 210–211, 218–219

in wave groups, 177–181

deterministic, 196–197

in discharge plant, cross-covariance of, 289f

effect of the amplitude of, 202, 206

time shift between water discharge and, 278f

resorting to time series data of, 187

of a peak of a sectional wave force on a cylinder, 231–234

of a wave height in a sea state, 69–74

of exceedance, 74f, 77, 90, 92, 111–112, 232, 234

of the H_s of the sea state wherein the maximum wave height in the lifetime will occur, 103–111

of the maximum wave height in a sea state of given duration, 86f

of the maximum wave height in the lifetime, 103–111

deterministic wave function from time series data, 186–187

experiment for verification, 187–188

resorting to time series data of pressure head waves, 187

arbitrary configurations of solid boundary, 195–196, 196f

core of, 176–177

cross-covariances, use of, 145–146

experimental verification of, 186–188, 220–224

mechanics of diffracted wave groups, 209–226

mechanics of reflected wave groups, 209–226

mechanics of wave forces on large isolated bodies, 181, 198, 207

mechanics of wave groups, 173–194

in Montecarlo simulations, 242

overall synthesis, 207–208

sea states nonhomogeneous in space, 146–151

onto wave statistics, 71–74

subroutine, 182–186

homogeneous, 145–146

nonhomogeneous, 151–153

with arbitrary contour lines, 27–31

with straight contour lines, 25–27, 26f

formal solution for, 95–98

corollaries of, 69–70

mean wave period, 70

between water level and roof of the chamber and pressure in air pocket, 291–293

concept, See Concept of sea state

definition, 44

nonhomogeneous in space, near breakwaters, 146–147

numerical simulation of, 55–56, 131–132, 138, 242

space-time theory of, 115–144

wave statistics, 63–88

in the Atlantic Ocean, 94f

average persistence, 95–99

encounter probability of, 99–100

Poisson process, 99–100, 99f

return period, 95–99

interaction between waves and, 18f

wavefronts behind, 19f

definition, 44

distribution at a location, 90, 93

actual and deterministic waves, of 1990, 189f

deterministic force on floating tunnel, of 1993, 205f

equipment of on effectiveness of Morison equation, 232f

model of piece of floating tunnel, of 1993, 199f

plan of wave gauges in, 188f

polar diagram, of 1993, 202f

results of, 188–190

supporting structure of gravity offshore platform, of 1992, 198f

on U-oscillating water column, of 2005, 281f

to verify QD theory, 190f, 224f

vertical breakwater used for, 264f

wave pressure at various points, of 1992 and 1993, 200f, 201f

zero down-crossing wave, of 2010, 191f

zero up-crossing wave, 225f

comparing wave force to Froude–Krylov force, 200–203, 203–204

comparing wave pressures, 198–199

deterministic pressure fluctuations on, 196–197

arbitrary solid boundary, 196f

for QD theory, See Quasi-determinism (QD) theory

and autovariance, 45

evidences from SSFEs, 264–265

modes of failure, 260–261

to first order, 5–7, 10–11, 17–18

to second order, 7–10, 9f

reference scheme, See Froude–Krylov force

wave height, 33

wave–current interaction in, 31–35

See also Froude–Krylov force; Straits of Messina

wave forces calculation on, 245–258

joint probability of, 66–67

probability of, 64

proof relevant to ensemble at fixed time instant, 65–66

proof relevant to realization, 64–65

variance of, 46, 148f

for finite water depth, 83–84

See also Froude–Krylov force; Straits of Messina

work forces on, 250–254

cross section of, 271f

interaction between wave and, 276–282

for the Mediterranean Sea, 306f

for ocean, 307f

water and air flow inside, 285–288, 286f, 288f

first worked example, 266–267

overall stability of upright section, 259–261

pressure exerted by wave crest, 17f

wave field before, 15f

height, 159–160, 166, 169, 209, 219, 263

period T_h of, 71

concept of, 46–48

wave crest, 263

wave trough, 263

advanced solution, 279–282

basic solution, 277–279

logic followed, 276–277

diffraction coefficient, 19–20, 20f

interaction with semi-infinite breakwater, 17–19, 18f

wave forces calculation, 257

extreme loads, 293–294

hydraulic verifications, 291–296

overall design, 304–308

overall stability, 295–296

production of electrical energy, 288–290

concept of homogeneous wave field, 115–116

random surface elevation, 116–117

velocity potential, 116–117

calculation of, 237–240

calculation on gravity platforms, 245–258

calculation on submerged tunnels, 245–258

calculation, three-dimensional space frames, 227–244

on gravity offshore platform, 245–250

hypothesis of submerged tunnel, 251f

model for calculating diffraction coefficient of, 205–207

on solid body and Froude–Krylov force, 202–204

on submerged tunnel, 250–254

worked example, 246f

first deterministic wave function, 166–168

second deterministic wave function, 169

velocity potential associated with, 168–169

G1, 178–179

G2, 179–181

of maximum expected zero down-crossing wave height, 241f

mechanics of diffracted wave groups, 209–226

mechanics of reflected wave groups, 209–226

particle velocity and acceleration in, 177–181

in time domain, 176f

dimensionless versus dimensionless wave period, 75f

distribution, 75–77

effects of, 29–31

under general bandwidth assumptions, 71–74

maximum expected, 77–78

probability of, 69–70

refraction, 29f

of sea state (H_s), 90–91

on wave depth, 27, 28f

peaks on tunnel, 255f

on tunnel, 252–254

angular frequency, 4

on space domain, 3f

on time domain, 3f

wave amplitude, 4

wave motion, 4, 4f

wave number, 4

wave steepness, 3–4

necessary condition for, 163–166

sufficient condition for, 159–163

analysis of function f(T, ξ), 165

general necessary condition, 163

necessary condition, 165–166

probability P(H, T, ξ), 164–165

control volume from, 31f

two sets of, 30f

Goda’s model, 261–263, 262f

of isolated solid body with equivalent water body, 198–199

risk of impulsive breaking, 265–266

at various points, 200f

virtual-height model, 263

on wall and on base of upright breakwater, 260f

general solution for η and ɸ, 13–14

orthogonal attack, 14–16

pressure distribution on breakwater, 16–17

reference scheme, 13f

vertical breakwater, See Vertical breakwater

QD theory consequences onto, 71–74

in sea states, 63–88

near coasts, 25–42

current only, 31–32

on various depths, 32f

wave height, 33–35

wavelength, 32–33

on water depth, 34f

re-analysis of problem, 272–274

wave train striking a converter, 275f

wave train striking wall, 275f

JONSWAP spectrum, 50–51