velocity2surfaceelevfft

[Eta, t] = velocity2surfaceelevfft(U, fs, duration, h, heightfrombed, fKuvmin, fcL, fcH, KuvafterfKuvmin, kCalcMethod, dispout)

Description

Calculate water surface elevation time series from wave orbital velocity time series by using Fast Fourier Transform

Inputs

U

Wave horizontal orbital velocity data in (m/s)

fs

Sampling frequency that data collected at in (Hz)

duration

Duration time that data are collected (second)

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

dispout=’no’;

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

Outputs

Eta

Water surface elevation time series in (m)

t

Time (s)

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;
U=(pi/5).*(2.*Eta).*(cosh(k*hfrombed)/sinh(k*h));
[Eta,t]=velocity2surfaceelevfft(U,fs,duration,5,4,0.6,0,fs/2,'constant','beji','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.