wavediretauv#

[Wavedir, theta1, theta2, f] = wavediretauv(Eta, Ux, Uy, fs, h, UVheightfrombed, dirCalcMethod, coordinatesys, fKuvmin, fcL, fcH, KuvafterfKuvmin, kCalcMethod, nfft, SegmentSize, OverlapSize, dispout)

Description#

Calculate wave direction using water surface elevation and horizontal orbital velocity

Inputs#

Eta: Water surface elevation time series data in (m)
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)
UVheightfrombed=0;: Velocity sensor height from bed that data collected at in (m)
dirCalcMethod=’puv1’;: Wave number calculation method

‘puv1’: PUV Method 1, ‘puv2’: PUV Method 2, ‘puv3’: PUV Method 3
coordinatesys=’xyz’;: Define the coordinate system

‘xyz’: XYZ coordinate system, ‘enu’: ENU (East North Up) coordinate system

If coordinatesys=’enu’, then x is East and y is North

If coordinatesys=’enu’, results are reported with respect to true north

In true north coordinate system, wave comes from as:

0 degree: from north, 90 degree: from east, 180 degree: from south, 270 degree: from west
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 overlaped with data in previous segments
dispout=’no’;: Define to display outputs or not (‘yes’: display, ‘no’: not display)

Outputs#

Wavedir: Mean wave direction (Degree)
theta1: Mean wave direction as a function of frequency (Degree)
theta2: Principal wave direction as a function of frequency (Degree)
f: Frequency (Hz)

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;
[Wavedir,theta1,theta2,f]=wavediretauv(Eta,Ux,Uy,fs,h,4,'puv1','xyz',0.7,0,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.

Deo, M. C., Gondane, D. S., & Sanil Kumar, V. (2002). Analysis of wave directional spreading using neural networks. Journal of waterway, port, coastal, and ocean engineering, 128(1), 30-37.

Earle, M. D., McGehee, D., & Tubman, M. (1995). Field Wave Gaging Program, Wave Data Analysis Standard (No. WES/IR/CERC-95-2). ARMY ENGINEER WATERWAYS EXPERIMENT STATION VICKSBURG MS.

Ewans, K. C. (1998). Observations of the directional spectrum of fetch-limited waves. Journal of Physical Oceanography, 28(3), 495-512.

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

Grosskopf, W., Aubrey, D., Mattie, M., & Mathiesen, M. (1983). Field intercomparison of nearshore directional wave sensors. IEEE Journal of Oceanic Engineering, 8(4), 254-271.

Herbers, T. H. C., Elgar, S., & Guza, R. T. (1999). Directional spreading of waves in the nearshore. Journal of Geophysical Research: Oceans, 104(C4), 7683-7693.

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.

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.

wavediretauv

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