directionalpsdpuv#

[Syy2d, f2d, theta] = directionalpsdpuv(P, Ux, Uy, fs, h, Pheightfrombed, UVheightfrombed, dtheta, coordinatesys, fmaxpcorr, fminpcorr, fKuvmin, fcL, fcH, fmaxpcorrCalcMethod, Kpafterfmaxpcorr, KuvafterfKuvmin, kCalcMethod, Rho, nfft, SegmentSize, OverlapSize, dispout)

Description#

Calculate wave directional spectrum using pressure and horizontal orbital velocity

Inputs#

P: Water pressure time series data in (N/m^2)
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)
Pheightfrombed=0;: Pressure sensor height from bed that data collected at in (m)
UVheightfrombed=0;: Velocity sensor height from bed that data collected at in (m)
dtheta=15;: Direction interval at which directional spectrum calculated between 0 and 360 (Degree)
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
fmaxpcorr=fs/2;: Maximum frequency that a pressure attenuation factor applies up on that (Hz)

If fmaxpcorrCalcMethod=’user’, then the smaller of calculated and user defined fmaxpcorr will be chosen
fminpcorr=0;: Minimum frequency that is used for defining fmaxpcorr if fmaxpcorrCalcMethod=’auto’ (Hz)

fminpcorr should be smaller than fp

If swell energy exists, fminpcorr should be smaller than fp of wind sea (fpsea) and larger than fp of swell (fpswell) if there swell
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)
fmaxpcorrCalcMethod=’auto’;: Define if to calculate fmaxpcorr and ftail or to use user defined

‘user’: use user defined value for fmaxpcorr

‘auto’: automatically define value for fmaxpcorr
Kpafterfmaxpcorr=’constant’;: Define a apressure response factor, Kp, value for frequency larger than fmaxpcorr

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

‘one’: Kp=1 for frequency larger than fmaxpcorr

‘constant’: Kp for f larger than fmaxpcorr stays equal to Kp at fmaxpcorr (constant)
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
Rho=1000;: Water density (kg/m^3)
nfft=length(P);: 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

‘2d’: 2 dimensional plot, ‘surface’: Surface plot, ‘polar’: Polar plot, ‘no’: not display

Outputs#

Syy2d: Directional wave power spectral density (m^2/Hz/Degree)
f2d: Directional frequency (Hz)
theta: Direction (Degree)

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;
P=Eta.*9.81.*1000.*(cosh(k*hfrombed)/cosh(k*h));
Ux=(pi/5).*(2.*Eta).*(cosh(k*hfrombed)/sinh(k*h));
Uy=0.2.*Ux;
[Syy2d,f2d,theta]=directionalpsdpuv(P,Ux,Uy,fs,h,4,4,15,'xyz',0.7,0,0.7,0,fs/2,'auto','constant','constant','beji',1025,N,256,128,'polar');

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.

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.

directionalpsdpuv

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