scientimate.directionalpsdetauv#

Syy2d, f2d, theta = scientimate.directionalpsdetauv(Eta, Ux, Uy, fs, h, UVheightfrombed=0, dtheta=15, coordinatesys='xyz', fKuvmin=None, fcL=0, fcH=None, KuvafterfKuvmin='constant', kCalcMethod='beji', nfft=None, SegmentSize=256, OverlapSize=128, dispout='no')

Description#

Calculate wave directional spectrum 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)
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
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

‘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#

import scientimate as sm
import numpy as np
import scipy as sp
from scipy import signal

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=np.linspace(0,duration-dt,N) #Time
Eta=sp.signal.detrend(0.5*np.cos(2*np.pi*0.2*t)+(-0.1+(0.1-(-0.1)))*np.random.rand(N))
hfrombed=4
h=5
k=0.2
Ux=(np.pi/5)*(2*Eta)*(np.cosh(k*hfrombed)/np.sinh(k*h))
Uy=0.2*Ux
Syy2d,f2d,theta=sm.directionalpsdetauv(Eta,Ux,Uy,fs,h,4,15,'xyz',0.7,0,fs/2,'constant','beji',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.

scientimate.directionalpsdetauv

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