diagnostictail

[fOut, SyyOut, Hm0, fp, Tp, Tm01, Tm02] = diagnostictail(fIn, SyyIn, ftail, tailtype, tailpower, h, transfCalcMethod, kCalcMethod, dispout)

Description

Replace a spectrum tail with JONSWAP (Hasselmann et al., 1973) or TMA Spectrum (Bouws et al., 1985)

Inputs

fIn

Frequency (Hz), Input

SyyIn

Power spectral density (m^2/Hz), Input

ftail

Frequency that diagnostic tail apply after that (typically: ftail=2.5fm where fm=1/Tm01)

tailtype=’jonswap’;

Define type of the diagnostic tail to be applied

‘jonswap’: JONSWAP Spectrum tail, ‘tma’: TMA Spectrum tail

tailpower=-5;

Tail power that diagnostic tail apply based on that

tailpower=-3 for shallow water, tailpower=-5 for deep water

h=0;

Mean water depth in (m)

transfCalcMethod=’approx’;

Transformation function from JONSWAP into TMA calculation method

‘approx’: approximated method, ‘tucker’: Tucker (1994), ‘kitaigordskii’: Kitaigordskii et al. (1975)

kCalcMethod=’beji’;

Wave number calculation method

‘hunt’: Hunt (1979), ‘beji’: Beji (2013), ‘vatankhah’: Vatankhah and Aghashariatmadari (2013)

‘goda’: Goda (2010), ‘exact’: calculate exact value

dispout=’no’;

Define to display outputs or not (‘yes’: display, ‘no’: not display)

Outputs

fOut

Frequency (Hz), Output

SyyOut

Power spectral density (m^2/Hz) with diagnostic tail, Output

Hm0

Zero-Moment Wave Height (m)

fp

Peak wave frequency (Hz)

Tp

Peak wave period (second)

Tm01

Wave Period from m01 (second), Mean Wave Period

Tm02

Wave Period from m02 (second), Mean Zero Crossing Period

Examples

N=2^11; %Total number of points
fs=8; %Sampling frequency
df=fs/N; %Frequency difference
f(:,1)=[0:df:fs/2]; %Frequency vector
f(1,1)=f(2,1)/2; %Assign temporarily non-zero value to fisrt element of f to prevent division by zero
Syy=0.016.*9.81.^2./((2.*pi).^4.*(f.^5)).*exp(-1.25.*(0.33./f).^4); %Calculating Spectrum
f(1,1)=0;
Syy(1,1)=0;

[fOut,SyyOut,Hm0,fp,Tp,Tm01,Tm02]=diagnostictail(f,Syy,0.5,'jonswap',-5,5,'approx','beji','yes');

[fOut,SyyOut,Hm0,fp,Tp,Tm01,Tm02]=diagnostictail(f,Syy,0.5,'tma',-3,5,'approx','beji','yes');

References

Beji, S. (2013). Improved explicit approximation of linear dispersion relationship for gravity waves. Coastal Engineering, 73, 11-12.

Bouws, E.; Günther, H.; Rosenthal, W., and Vincent, C.L., (1985). Similarity of the wind wave spectrum in finite depth water: 1. Spectral form. Journal of Geophysical Research: Oceans, 90(C1), 975-986.

Goda, Y. (2010). Random seas and design of maritime structures. World scientific.

Hasselmann, K.; Barnett, T. P.; Bouws, E.; Carlson, H.; Cartwright, D. E.; Enke, K.; Ewing, J. A.; Gienapp, H.; Hasselmann, D. E.; Kruseman, P.; Meerbrug, A.; Muller, P.; Olbers, D. J.; Richter, K.; Sell, W., and Walden, H., (1973). Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP). Deutsche Hydrographische Zeitschrift A80(12), 95p.

Hunt, J. N. (1979). Direct solution of wave dispersion equation. Journal of the Waterway Port Coastal and Ocean Division, 105(4), 457-459.

Vatankhah, A. R., & Aghashariatmadari, Z. (2013). Improved explicit approximation of linear dispersion relationship for gravity waves: A discussion. Coastal engineering, 78, 21-22.