wavefromvelocitypsd#

[Hm0, fp, Tp, Tm01, Tm02, f, Syy, m0] = wavefromvelocitypsd(Ux, Uy, fs, h, heightfrombed, fKuvmin, fcL, fcH, KuvafterfKuvmin, kCalcMethod, nfft, SegmentSize, OverlapSize, dispout)

Description#

Calculate wave properties from wave orbital velocity by converting it to water surface elevation power spectral density

Inputs#

Ux: Wave horizontal orbital velocity data in x direction in (m/s)
Uy: Wave horizontal orbital velocity data in y direction in (m/s)
fs: Sampling frequency that data collected at in (Hz)
h: Water depth in (m)
heightfrombed=0;: Height from bed that data collected at in (m)
fKuvmin=fs/2;: Frequency that a velocity conversion factor (Kuv) at that frequency is considered as a minimum limit for Kuv
fcL=0;: Low cut-off frequency, between 0*fs to 0.5*fs (Hz)
fcH=fs/2;: High cut-off frequency, between 0*fs to 0.5*fs (Hz)
KuvafterfKuvmin=’constant’;: Define conversion factor, Kuv, value for frequency larger than fKuvmin

‘nochange’: Kuv is not changed for frequency larger than fKuvmin

‘one’: Kuv=1 for frequency larger than fKuvmin

‘constant’: Kuv for f larger than fKuvmin stays equal to Kuv at fKuvmin (constant)
kCalcMethod=’beji’;: Wave number calculation method

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

‘goda’: Goda (2010), ‘exact’: calculate exact value
nfft=length(Eta);: Total number of points between 0 and fs that spectrum reports at is (nfft+1)
SegmentSize=256;: Segment size, data are divided into the segments each has a total element equal to SegmentSize
OverlapSize=128;: Number of data points that are overlapped with data in previous segments
dispout=’no’;: Define to display outputs or not (‘yes’: display, ‘no’: not display)

Outputs#

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
f: Frequency (Hz)
Syy: Power spectral density (m^2/Hz)
m0: Zero-Moment of the power spectral density (m^2)

Examples#

fs=2; %Sampling frequency
duration=1024; %Duration of the data
N=fs*duration; %Total number of points
df=fs/N; %Frequency difference
dt=1/fs; %Time difference, dt=1/fs
t(:,1)=linspace(0,duration-dt,N); %Time
Eta(:,1)=detrend(0.5.*cos(2*pi*0.2*t)+(-0.1+(0.1-(-0.1))).*rand(N,1));
hfrombed=4;
h=5;
k=0.2;
Ux=(pi/5).*(2.*Eta).*(cosh(k*hfrombed)/sinh(k*h));
Uy=0.2.*Ux;
[Hm0,fp,Tp,Tm01,Tm02,f,Syy,m0]=wavefromvelocitypsd(Ux,Uy,fs,5,4,0.6,0,fs/2,'constant','beji',N,256,128,'yes');

References#

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

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

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.

Wiberg, P. L., & Sherwood, C. R. (2008). Calculating wave-generated bottom orbital velocities from surface-wave parameters. Computers & Geosciences, 34(10), 1243-1262.

Welch, P. (1967). The use of fast Fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms. IEEE Transactions on audio and electroacoustics, 15(2), 70-73.

wavefromvelocitypsd

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