Regular Ocean Waves (Linear Waves) HηczLxstill waterline (SWL)dacresttroughsea bottom η = displacement of the water surface, varies with time and location, (meters, feet, etc.) H = wave height, constant with time at a given location, (m, ft) a = wave amplitude (m, ft) ( aH=/2 for linear waves) L = wave length (m, ft) T = wave period, time required for one complete wave to pass a fixed point (seconds, minutes, hours) f = wave frequency = 1/T (cycles/sec = Hertz, Hz) ω = wave circular or radian frequency = 2π/T= 2πf (radians/sec) c = wave celerity or wave speed, c = L/T (m/sec, ft/sec, etc.) cg = wave group velocity (m/sec, ft/sec, etc.) d = water depth (m, ft, fathoms (fm) = 6 ft) k = wave number = 2π/L (m-1, ft-1, etc.) u = water particle velocity in the x (horizontal) direction (m/sec, ft/sec, etc.) w = water particle velocity in the z (vertical) direction (m/sec, ft/sec, etc.) ax = water particle acceleration in the x (horizontal) direction (m/sec2, ft/sec2, etc.) az = water particle acceleration in the z (vertical) direction (m/sec2, ft/sec2, etc.) Wave Displacement ()ηω=−akxcos t Wave Number kL=2π Radian Frequency ωπ=2 T Dispersion Relation ()ω2= gk kdtanhShallow Water Intermediate Deep Water d/L < 1/20, 0.05 0.05 < d/L <1/2 d/L > 1/2 d/(gT2) < 0.0025 d/(gT2) > 0.08 Wave Speed cLTgd== ()cLTkgkkd===ωtanh ccLTgLO===2π Wave Length LTgd= LgTdL=222ππtanh LgT=22π Wave Period TLgd= ()LLgd=22ππtanhL TLg=2π Group Velocity ccg= ()ccdLdLg=+2144ππsinhccg=2 Horizontal Water Particle Velocity ()()()()()()tkxkdkdkzatkxkdkdkzagkuω−+ω=ω−+ω=cossinhcoshcoscoshcosh Vertical Water Particle Velocity ()()()()()()tkxkdkdkzatkxkdkdkzagkwω−+ω=ω−+ω=sinsinhsinhsincoshsinh Horizontal Water Particle Acceleration ()()()axagkkz kdkdkx t=+−coshcoshsinω Vertical Water Particle Acceleration ()()()azagkkz kdkdkx t=−+−sinhcoshcosω Energy per unit surface area Ega gH==122182ρρ Energy per unit wave crest width EgaLgHT==122182ρρL Energy flux per unit wave crest width EEc gac gHcgg==