90 



THEORY OF SEAKEEPING 



Nomenclature for Chapter 1 



= harmonic wave amplitude, half-height of 

 trochoidal and Stokes' waves 

 c'n, b„, (•„ = coefficients of the nth term of the Fourier 

 series expansion of a function 

 .1,,, B„. C„ = coefficients of the air-pressure-function ex- 

 pansion 

 coefficients 



w'ave celerity (also known as phase velocity) 

 a coefficient 



dynamic (i.e., pressure) drag coefficient 

 pressure coefficient 

 frictional-drag coefficient 

 total tlrag coefficient 

 gust diameter (Eckart, Section 4.1 ) 

 energy 



wave-energy content per unit of sea surface 

 per second. Energy indicated Ijy the spec- 

 trum area (true energy divided by pg) 

 spectral energy (divided by pg) density in 

 terms of wave period, frequency and circular 

 frequencv, respectively 

 directional sjjectrum energj- density in terms 

 of wave number ]5rojections on x and y- 

 axes 

 directional spectrum energy density in terms 

 of circular frequency and wave-pro])agation 

 direction 

 Ep = wave energy per unit sea area j^er second trans- 

 mitted from wind to waves by normal air 

 pressures 

 Ej, = wave energy jier unit area per second dissipated 

 liy waves 

 El. -2 = wave energies carried through reference planes 

 at fetches F, and F-2 

 f = frequency \/T = iai/'2t 



f = number of degrees of freedom in spectral anal- 

 ysis (equation 126) 

 fc = cut-off (Nyquist) frequency 

 F = fetch 



g = acceleration of gravity 

 h = water depth 

 h = number of integrations of an autocovariance 



function in computing spectral density 

 // = wave height 

 H = ajijiarent wave height 

 H = mean apjjarent wave height 

 fiilz, Hiiid, etc. = mean height of 'A, Vio. etc., of highest waves 

 H = etiuivalent wave height (Darbyshire, Section 

 0.1) 

 i = V-l 



k = wave number = 2?r/X = a^/g 

 Lk = "raw" value of spectral density 

 (?) = maximum numlier of time lags in autocovari- 

 ance analysis 

 »!,. = moments of scalar si)ectrum defined by equa- 

 tion (128a) 

 ??!,,, = moments of the directional spectrum defined 

 by equation (142) 

 n = order of harmonic comijonents in a Fourier 

 Series 



n = number of intervals \t in a sample of duration 



r 



II = generallj- an index or a subscript of a meaning 

 to be specified 



n = ratioof turbulentand molecularviscositie8,M*/^ 

 A'o = number of zero up crosses of a wave record 

 .Vi = number of maxima of a wave record 

 p = pressure 

 p = inunber of lags, r/At 

 p = index of the wave mmiber i/ in directional- 



sijectrum analysis 

 q = index of the wave niunber !■ in directional- 

 spectrum analysis 

 q = successive numbering of ordinates of record of 



a random function 

 r = proportion of negative maxima in a wave 

 record 

 Rir) = autocovariance function 

 /?(r)//?(0) = autocorrelation function 

 R, $ = polar co-ordinates 

 rms = root-mean-scjuare 



s = Jeffreys' sheltering coefficient 

 s = Miles' (Section 4.5) mass parameter 

 iS = setup of water surface caused by wind drag 

 Si = setu]3 of water surface smoothed by a detergent 

 S; = setup of water s\irface caused by wave resist- 

 ance 

 / = time 



T = ijeriod of harmonic waves 

 T = duration of a wave record, sec 

 7' = duration or life of a gust (Eckart, Section 4,1) 

 T — surface tension 



T = mean apparent jieriod of irregular waves de- 

 fined by nvmilier of zero up-crosses per sec- 

 — ontl 



T* = mean apparent jieriod of irregular waves de- 

 fined as time intervals between dominant 

 wave crests 

 u = horizontal component of orbital velocity 

 (/ = ])rojection of the wave number k on j-axis 

 ii{z) = wind velocity at the height ; 



[/ = air velocity affected by the ]5roximity of a 

 body. Air velocity at anemometer height 

 U — energy contained in a liand of frequencies 



Af'r = spectral wave energy (in energy imits) con- 

 tained in the band a7' of wave periods 

 (Neumann, Section 6.2) 

 Uc = gust travel velocity (Phillips. Section 4.2) 

 r = vertical comjjonent of the orbital velocity 

 r = [irojection of the wave number k on y axis 

 V = velocity of undisturbed air. Oadient wind 



velocity 

 Vc = formula velocity (Section 2. .5) 

 X, y = Cartesian co-ordinates 

 ;/(/) = an ordinate of a stochastic function record 

 z = height of wind-velocity measurement 

 Zy = roughness parameter (Section 2.7 1 

 a = coefficient of Voznessensky and Firsoff's 

 (Section 6.6) spectrum, characteristic of sea 

 irregularity (sjiectrimi broadness) 

 P = coefficient of \'oznessensk\- anil Firsoff's 

 (Section 6.6) spectrum, characteristic of 

 wave fref|ueiicv 



