scientimate.velocity2surfaceelevfft#

Eta, t = scientimate.velocity2surfaceelevfft(U, fs, duration, h, heightfrombed=0, fKuvmin=None, fcL=0, fcH=None, KuvafterfKuvmin='constant', kCalcMethod='beji', dispout='no')

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#

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
U=(np.pi/5)*(2*Eta)*(np.cosh(k*hfrombed)/np.sinh(k*h))
Eta1,t=sm.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.

scientimate.velocity2surfaceelevfft

Contents