1. Standard wave spectra#
In this example application, it is shown how wave spectra can be generated by means of standardized expressions. The following modules and packages are imported:
import numpy as np
import matplotlib.pyplot as plt
from netsse.base import WaveSpectrum
1.1. 1. Introduction#
In many engineering applications, such as the response analysis of marine structures exposed to waves, use of the wave spectrum is required in order to carry on the computations. In those cases, the sea state parameters can be exploited to reconstruct the wave spectrum by applying an adequately chosen parameterised spectrum.
There exist several standard forms of wave spectra. The choice of one form is application-specific and made based on the geographical area of study. Among other effects, the water depth, the predominance of wind sea over swell, or the opposite, and the fetch – defined as the length of the body of water that the wind blows over – should be considered (Mounet, 2023).
1.2. 2. Sea state parameters#
Assume a sea state characterised by the following two parameters:
Significant wave height: \(H_s =\) 2 m.
Peak wave period: \(T_p =\) 10 s.
Hs = 2
Tp = 10
fmax = 0.5
Nf = 100
f = np.linspace(0,fmax,Nf)
spec1d = WaveSpectrum(Hs,Tp,f,unit_freq='Hz')
spec1d.set_from_standard('JONSWAP',gamma=3.3)
spec1d.__dict__
JONSWAP spectrum with gamma = 3.3
{'Hs': 2,
'Tp': 10,
'timestamp': datetime.datetime(2024, 9, 4, 9, 53, 25, 621303),
'lat': 0,
'lon': 0,
'depth': 0,
'duration': 1800,
'f': array([0. , 0.00505051, 0.01010101, 0.01515152, 0.02020202,
0.02525253, 0.03030303, 0.03535354, 0.04040404, 0.04545455,
0.05050505, 0.05555556, 0.06060606, 0.06565657, 0.07070707,
0.07575758, 0.08080808, 0.08585859, 0.09090909, 0.0959596 ,
0.1010101 , 0.10606061, 0.11111111, 0.11616162, 0.12121212,
0.12626263, 0.13131313, 0.13636364, 0.14141414, 0.14646465,
0.15151515, 0.15656566, 0.16161616, 0.16666667, 0.17171717,
0.17676768, 0.18181818, 0.18686869, 0.19191919, 0.1969697 ,
0.2020202 , 0.20707071, 0.21212121, 0.21717172, 0.22222222,
0.22727273, 0.23232323, 0.23737374, 0.24242424, 0.24747475,
0.25252525, 0.25757576, 0.26262626, 0.26767677, 0.27272727,
0.27777778, 0.28282828, 0.28787879, 0.29292929, 0.2979798 ,
0.3030303 , 0.30808081, 0.31313131, 0.31818182, 0.32323232,
0.32828283, 0.33333333, 0.33838384, 0.34343434, 0.34848485,
0.35353535, 0.35858586, 0.36363636, 0.36868687, 0.37373737,
0.37878788, 0.38383838, 0.38888889, 0.39393939, 0.3989899 ,
0.4040404 , 0.40909091, 0.41414141, 0.41919192, 0.42424242,
0.42929293, 0.43434343, 0.43939394, 0.44444444, 0.44949495,
0.45454545, 0.45959596, 0.46464646, 0.46969697, 0.47474747,
0.47979798, 0.48484848, 0.48989899, 0.49494949, 0.5 ]),
'Sf': array([0.00000000e+000, 0.00000000e+000, 0.00000000e+000, 0.00000000e+000,
0.00000000e+000, 2.54146386e-130, 1.34092441e-061, 2.64173468e-032,
3.25376512e-018, 8.12466134e-011, 1.13343835e-006, 3.10637024e-004,
9.51438902e-003, 8.07194202e-002, 3.13007504e-001, 7.42569629e-001,
1.30732433e+000, 2.06147914e+000, 3.54781338e+000, 6.35293573e+000,
7.70300951e+000, 5.90522384e+000, 3.73016141e+000, 2.48105612e+000,
1.89555896e+000, 1.59247382e+000, 1.38611097e+000, 1.21438876e+000,
1.06293581e+000, 9.29120397e-001, 8.11736007e-001, 7.09372739e-001,
6.20451554e-001, 5.43379723e-001, 4.76647834e-001, 4.18878021e-001,
3.68842117e-001, 3.25462479e-001, 2.87803483e-001, 2.55058563e-001,
2.26535656e-001, 2.01642711e-001, 1.79874090e-001, 1.60798287e-001,
1.44047082e-001, 1.29306110e-001, 1.16306749e-001, 1.04819195e-001,
9.46465756e-002, 8.56199612e-002, 7.75941540e-002, 7.04441272e-002,
6.40620220e-002, 5.83546121e-002, 5.32411621e-002, 4.86516178e-002,
4.45250744e-002, 4.08084779e-002, 3.74555247e-002, 3.44257248e-002,
3.16836053e-002, 2.91980311e-002, 2.69416239e-002, 2.48902660e-002,
2.30226744e-002, 2.13200349e-002, 1.97656875e-002, 1.83448553e-002,
1.70444103e-002, 1.58526708e-002, 1.47592255e-002, 1.37547818e-002,
1.28310327e-002, 1.19805416e-002, 1.11966417e-002, 1.04733476e-002,
9.80527881e-003, 9.18759181e-003, 8.61592088e-003, 8.08632594e-003,
7.59524661e-003, 7.13946167e-003, 6.71605328e-003, 6.32237534e-003,
5.95602542e-003, 5.61481986e-003, 5.29677172e-003, 5.00007109e-003,
4.72306760e-003, 4.46425479e-003, 4.22225623e-003, 3.99581300e-003,
3.78377257e-003, 3.58507883e-003, 3.39876311e-003, 3.22393612e-003,
3.05978076e-003, 2.90554557e-003, 2.76053887e-003, 2.62412351e-003]),
'om': array([0. , 0.03173326, 0.06346652, 0.09519978, 0.12693304,
0.1586663 , 0.19039955, 0.22213281, 0.25386607, 0.28559933,
0.31733259, 0.34906585, 0.38079911, 0.41253237, 0.44426563,
0.47599889, 0.50773215, 0.53946541, 0.57119866, 0.60293192,
0.63466518, 0.66639844, 0.6981317 , 0.72986496, 0.76159822,
0.79333148, 0.82506474, 0.856798 , 0.88853126, 0.92026451,
0.95199777, 0.98373103, 1.01546429, 1.04719755, 1.07893081,
1.11066407, 1.14239733, 1.17413059, 1.20586385, 1.23759711,
1.26933037, 1.30106362, 1.33279688, 1.36453014, 1.3962634 ,
1.42799666, 1.45972992, 1.49146318, 1.52319644, 1.5549297 ,
1.58666296, 1.61839622, 1.65012947, 1.68186273, 1.71359599,
1.74532925, 1.77706251, 1.80879577, 1.84052903, 1.87226229,
1.90399555, 1.93572881, 1.96746207, 1.99919533, 2.03092858,
2.06266184, 2.0943951 , 2.12612836, 2.15786162, 2.18959488,
2.22132814, 2.2530614 , 2.28479466, 2.31652792, 2.34826118,
2.37999443, 2.41172769, 2.44346095, 2.47519421, 2.50692747,
2.53866073, 2.57039399, 2.60212725, 2.63386051, 2.66559377,
2.69732703, 2.72906028, 2.76079354, 2.7925268 , 2.82426006,
2.85599332, 2.88772658, 2.91945984, 2.9511931 , 2.98292636,
3.01465962, 3.04639288, 3.07812614, 3.10985939, 3.14159265]),
'Som': array([0.00000000e+000, 0.00000000e+000, 0.00000000e+000, 0.00000000e+000,
0.00000000e+000, 4.04486536e-131, 2.13414749e-062, 4.20445133e-033,
5.17852803e-019, 1.29308001e-011, 1.80392317e-007, 4.94394179e-005,
1.51426204e-003, 1.28468947e-002, 4.98166914e-002, 1.18183627e-001,
2.08067129e-001, 3.28094595e-001, 5.64652037e-001, 1.01110112e+000,
1.22597204e+000, 9.39845564e-001, 5.93673627e-001, 3.94872345e-001,
3.01687579e-001, 2.53450080e-001, 2.20606413e-001, 1.93275975e-001,
1.69171488e-001, 1.47874104e-001, 1.29191798e-001, 1.12900178e-001,
9.87479318e-002, 8.64815689e-002, 7.58608589e-002, 6.66665076e-002,
5.87030461e-002, 5.17989623e-002, 4.58053470e-002, 4.05938311e-002,
3.60542695e-002, 3.20924342e-002, 2.86278505e-002, 2.55918422e-002,
2.29258052e-002, 2.05797066e-002, 1.85107940e-002, 1.66824931e-002,
1.50634704e-002, 1.36268401e-002, 1.23494932e-002, 1.12115311e-002,
1.01957875e-002, 9.28742496e-003, 8.47359412e-003, 7.74314547e-003,
7.08638568e-003, 6.49487098e-003, 5.96123190e-003, 5.47902427e-003,
5.04260240e-003, 4.64701098e-003, 4.28789262e-003, 3.96140888e-003,
3.66417244e-003, 3.39318894e-003, 3.14580687e-003, 2.91967440e-003,
2.71270216e-003, 2.52303091e-003, 2.34900370e-003, 2.18914152e-003,
2.04212228e-003, 1.90676242e-003, 1.78200087e-003, 1.66688504e-003,
1.56055859e-003, 1.46225065e-003, 1.37126640e-003, 1.28697875e-003,
1.20882104e-003, 1.13628062e-003, 1.06889308e-003, 1.00623729e-003,
9.47930887e-004, 8.93626336e-004, 8.43007402e-004, 7.95786030e-004,
7.51699555e-004, 7.10508218e-004, 6.71992950e-004, 6.35953390e-004,
6.02206108e-004, 5.70583018e-004, 5.40929949e-004, 5.13105370e-004,
4.86979233e-004, 4.62431940e-004, 4.39353407e-004, 4.17642227e-004]),
'nature': 'standard',
'method': 'JONSWAP',
'gamma': 3.3}
1.3. References#
Mounet, R.E.G. (2023). Sea State Estimation Based on Measurements from Multiple Observation Platforms. PhD Thesis. Technical University of Denmark. https://orbit.dtu.dk/en/publications/sea-state-estimation-based-on-measurements-from-multiple-observat