-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathwave_physics_functions.py
712 lines (614 loc) · 25.8 KB
/
wave_physics_functions.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
# #!/usr/bin/env python3
# -*- coding: utf-8 -*-
# ==================================================================================
# === 0. Import Packages ===========================================================
# ==================================================================================
import numpy as np
import sys
from scipy.interpolate import griddata
######################
######################
# [Ekxky,kx,ky,kx2,ky2] = wavespec_Efth_to_Ekxky(eft1s,fren,dfreq,dirn,dth,dkx=0.0001,dky=0.0001,nkx=250,nky=250,doublesided=0)
def wavespec_Efth_to_Ekxky(eft1s,fren,dfreq,dirn,dth,depth=3000.,dkx=0.0001,dky=0.0001,nkx=250,nky=250,doublesided=1,verbose=0,doplot=0,trackangle=0) :
'''
Converts E(f,theta) spectrum from buoy or model to E(kx,ky) spectrum similar to image spectrum
2023/11/14: preliminary version, assumes dfreq is symmetric (not eaxctly true with WW3 output and waverider data)
inputs :
- etfs1 : spectrum
output :
- Ekxky: spectrum
- kx: wavenumber in cycles / m
'''
[nf,nt]=np.shape(eft1s)
tpi=2*np.pi
grav=9.81
# makes a double sided spectrum
if doublesided == 1:
eftn=0.5*(eft1s+np.roll(eft1s,nt//2,axis=1))
else:
eftn=eft1s
Hs1 = 4*np.sqrt(np.sum(np.sum(eftn,axis=1)* dfreq)*dth)
# wraps around directions
dlast=dirn[0]+360.
dirm=np.concatenate([dirn,[dlast]])
elast=eftn[:,0]
eftm1=np.concatenate([eftn.T,[elast]]).T
# adds zero energy in a low frequency to avoid interpolation across k=0
ffirst=fren[0]-0.9*(fren[1]-fren[0])
frem=np.concatenate([[ffirst],fren])
efirst=eftm1[0,:]*0
eftm=np.concatenate([[efirst],eftm1])
#plt.pcolormesh(fren, dirm, np.log10(eftm).T)
km=(2*np.pi*frem)**2/(grav*2*np.pi) # cycles / meter
for ii in range(nf):
km[ii]=k_from_f(frem[ii],D=depth)/(2*np.pi) # finite water depth
km2=np.tile(km.reshape(nf+1,1),(1,nt+1))
# eftn*df*dth = Ek*k*dk*dth -> Ek = efth *df /(k * dk) = efth *Cg /k
Cg2=np.sqrt(grav/(km2*tpi))*0.5
Jac=Cg2/km2
dirm2=np.tile(dirm.T,(nf+1,1))*np.pi/180.
kxn=km2*np.cos(dirm2+trackangle)
kyn=km2*np.sin(dirm2+trackangle)
#plt.scatter(kxn,kyn, marker='.', s = 20)
kx=np.linspace(-nkx*dkx,(nkx-1)*dkx,nkx*2)
ky=np.linspace(-nky*dky,(nky-1)*dky,nky*2)
kx2, ky2 = np.meshgrid(kx,ky,indexing='ij') #should we transpose kx2 and ky2 ???
Ekxky = griddata((kxn.flatten(), kyn.flatten()), (eftm*Jac).flatten(), (kx2, ky2), method='nearest')
Hs2=4*np.sqrt(np.sum(np.sum(Ekxky))*dkx*dky)
# make sure energy is exactly conserved (assuming kmax is consistent with fmax
if verbose==1:
print('Hs1,Hs2:',Hs1,Hs2)
Ekxky = Ekxky * (Hs1/Hs2)**2
return Ekxky,kx,ky,kx2,ky2
#############################################################################
def wavespec_Efth_to_first3(efth,fren,dfreq,dirn,dth,cut=1E4) :
'''
Computes first 3 moments from E(f,theta) spectrum
inputs :
- etfs1 : spectrum
output :
- Ef, th1m ...
'''
d2r=np.pi/180
grav=9.81
wn=(2*np.pi*fren)**2/grav
wavelength=2*np.pi/wn
Cg=grav/(4*np.pi*fren)
dk=2*np.pi*dfreq/Cg
[nf,nt]=np.shape(efth)
dir2=np.tile((dirn*d2r).reshape(1,nt),(nf,1))
Ef=np.sum(efth, axis=1)*dth
inds=np.where(wavelength < cut)[0]
Etot=np.sum(Ef[inds]*dfreq[inds])
eftn=0.5*(efth+np.roll(efth,nt//2,axis=1))
#a1E=np.sum(efth*np.cos(dir2),axis=1)*dth
#b1E=np.sum(efth*np.sin(dir2),axis=1)*dth
a1=np.zeros(nf)
b1=np.zeros(nf)
m1=np.zeros(nf)
Q1=np.zeros(nf)
Q2=0
# print('TEST:',np.shape(dirn),np.shape(efth),dirn,dth)
for ind in range(nf):
#Ef[ind]=np.sum(efth[ind,:] )*dth
a1[ind]=np.sum(efth[ind,:]*np.cos(dirn[:]*d2r))*dth/Ef[ind]
b1[ind]=np.sum(efth[ind,:]*np.sin(dirn[:]*d2r))*dth/Ef[ind]
m1[ind]=np.sqrt(a1[ind]**2+b1[ind]**2)
Q1[ind]=np.sum(eftn[ind,:]**2)*dth
Q2=Q2+Q1[ind]*dfreq[ind]*grav**2/(2*((np.pi*2)**4*fren[ind]**3 ))
# print('ft:',ind,fren[ind],wn[ind],'Cg:',Cg[ind],dfreq[ind]/(wn[ind]*dk[ind]),grav**2/(2*((np.pi*2)**4*fren[ind]**3 )) )
Qkk=np.sqrt(Q2)/Etot
Qf=np.sqrt(np.sum(Ef**2*dfreq))/Etot
Tm0m1=np.sum(Ef[inds]*dfreq[inds]/fren[inds])/Etot
Em2=np.sum(Ef[inds]*dfreq[inds]*fren[inds]**2)+Ef[-1]*dfreq[-1]*0.5*fren[-1]**3 # integral including f^-5 tail
Tm02=np.sqrt(Etot/Em2)
Hs=4*np.sqrt(Etot)
# print('WHAT:',ind,fren[ind],Ef[ind],a1[ind],b1[ind],m1[ind],efth[ind,:])
th1m=np.arctan2(b1,a1)/d2r
# print('TEST:',nf,nt,m1,'##',np.sum(efth[5,:]*np.cos(dirn))*dth/Ef[5],a1[5],b1[5],m1[5])
sth1m=np.sqrt(np.abs(2.0*(1-m1)))/d2r
return Ef,th1m,sth1m,Hs,Tm0m1,Tm02,Qf,Qkk
#############################################################################
def wavespec_Ekxky_to_first3(Ekxky,kx2,ky2,f_max=0.15,trackangle=0,depth=1000) :
'''
Computes first 3 moments from E(kx,ky) spectrum
inputs :
- Ekxky : spectrum
output :
- Ef, th1m, sth1m ...
'''
ky=ky2[:,0] # warning: these are in cycles / m, not rad/m
kx=kx2[0,:]
tpi=np.pi*2
d2r=np.pi/180
grav=9.81
k2=np.sqrt(kx2**2+ky2**2)
f2=np.sqrt((grav*tpi)*k2*np.tanh(k2*(tpi*depth)))/tpi
Cg2=f2/(2*k2) # need depth correction
jacobian=k2/Cg2
cartesian_interpolator = interp.RegularGridInterpolator((ky, kx), Ekxky*jacobian, method='linear', fill_value=None)
# Define the polar grid (r, theta)
df=0.005
f_min = 0.025
num_f=int((f_max-f_min)/df)+1
fren = np.linspace(f_min, f_max, num_f)
dfreq=np.zeros(num_f)+df
km=(2*np.pi*fren)**2/(grav*2*np.pi) # cycles / meter
print('Interp:',fren)
for ii in range(num_f):
km[ii]=k_from_f(fren[ii],D=depth)/(2*np.pi) # finite water depth
nth=72
theta = np.linspace(0, 360,nth+1)
dth=(theta[1]-theta[0])*d2r
K, Theta = np.meshgrid(km, theta*d2r)
# Convert polar grid to Cartesian coordinates (x, y)
X_polar = K * np.cos(Theta-trackangle*d2r)
Y_polar = K * np.sin(Theta-trackangle*d2r)
cartesian_points = np.vstack([X_polar.ravel(), Y_polar.ravel()]).T
polar_values = cartesian_interpolator(cartesian_points)
# Step 6: Reshape the interpolated values back into the polar grid shape
efth = polar_values.reshape(K.shape).T[:,0:nth]
[nf,nt]=np.shape(efth)
Ef=np.sum(efth, axis=1)*dth
Etot=np.sum(Ef[:]*df)
eftn=0.5*(efth+np.roll(efth,nt//2,axis=1))
a1=np.zeros(nf)
b1=np.zeros(nf)
m1=np.zeros(nf)
Q1=np.zeros(nf)
Q2=0
# print('TEST:',np.shape(dirn),np.shape(efth),dirn,dth)
for ind in range(nf):
#Ef[ind]=np.sum(efth[ind,:] )*dth
a1[ind]=np.sum(efth[ind,:]*np.cos(theta[0:nth]*d2r))*dth/Ef[ind]
b1[ind]=np.sum(efth[ind,:]*np.sin(theta[0:nth]*d2r))*dth/Ef[ind]
m1[ind]=np.sqrt(a1[ind]**2+b1[ind]**2)
Q1[ind]=np.sum(eftn[ind,0:nth]**2)*dth
Q2=Q2+Q1[ind]*dfreq[ind]*grav**2/(2*((np.pi*2)**4*fren[ind]**3 ))
# print('ft:',ind,fren[ind],wn[ind],'Cg:',Cg[ind],dfreq[ind]/(wn[ind]*dk[ind]),grav**2/(2*((np.pi*2)**4*fren[ind]**3 )) )
Qkk=np.sqrt(Q2)/Etot
Qf=np.sqrt(np.sum(Ef**2*dfreq))/Etot
Tm0m1=np.sum(Ef*dfreq/fren)/Etot
Em2=np.sum(Ef*dfreq*fren**2)+Ef[-1]*dfreq[-1]*0.5*fren[-1]**3 # integral including f^-5 tail
Tm02=np.sqrt(Etot/Em2)
Hs=4*np.sqrt(Etot)
# print('WHAT:',ind,fren[ind],Ef[ind],a1[ind],b1[ind],m1[ind],efth[ind,:])
th1m=np.arctan2(b1,a1)/d2r
# print('TEST:',nf,nt,m1,'##',np.sum(efth[5,:]*np.cos(dirn))*dth/Ef[5],a1[5],b1[5],m1[5])
sth1m=np.sqrt(np.abs(2.0*(1-m1)))/d2r
# Checking total energy:
Etot=np.sum(efth)*df*dth
E_mask=np.where( k2 < km[-1], Ekxky, 0)
dkx=kx[1]-kx[0]
dky=ky[1]-ky[0]
Etotxy=np.sum(Ekxky*dkx*dky)
Etotm=np.sum(E_mask*dkx*dky)
print('H:',4*np.sqrt(Etot),4*np.sqrt(Etotxy),4*np.sqrt(Etotm))
return efth,fren,theta[0:nth],Ef,th1m,sth1m
#############################################################################
def wavespec_Efth_to_Uss(efth,fren,dfreq,dirn,dth) :
'''
Computes first 3 moments from E(f,theta) spectrum
inputs :
- etfs1 : spectrum
output :
- Ef, th1m ...
'''
d2r=np.pi/180
grav=9.81
sig=(2*np.pi*fren)
wn=(sig)**2/grav # warning this is only valid for deep water
wavelength=2*np.pi/wn
Cg=grav/(4*np.pi*fren)
dk=2*np.pi*dfreq/Cg
[nf,nt]=np.shape(efth)
dir2=np.tile((dirn*d2r).reshape(1,nt),(nf,1))
a1=np.zeros(nf)
b1=np.zeros(nf)
Ef=np.sum(efth, axis=1)*dth
Etot=np.sum(Ef*dfreq)
Hs=4*np.sqrt(Etot)
for ind in range(nf):
a1[ind]=np.sum(efth[ind,:]*np.cos(dirn[:]*d2r))*dth
b1[ind]=np.sum(efth[ind,:]*np.sin(dirn[:]*d2r))*dth
Ussx=2*np.sum(a1*wn*sig*dfreq) # warning this is only valid for deep water
Ussy=2*np.sum(b1*wn*sig*dfreq)
return Hs,Ussx,Ussy
#############################################################################
def wavespec_Efth_to_first5(efth,fren,dfreq,dirn,dth) :
'''
Computes first 5 moments from E(f,theta) spectrum
inputs :
- etfs1 : spectrum
output :
- Ef, th1m ...
'''
d2r=np.pi/180
grav=9.81
wn=(2.*np.pi*fren)**2/grav
Cg=grav/(4*np.pi*fren)
dk=2.*np.pi*dfreq/Cg
[nf,nt]=np.shape(efth)
dir2=np.tile((dirn*d2r).reshape(1,nt),(nf,1))
Ef=np.sum(efth, axis=1)*dth
Etot=np.sum(Ef*dfreq)
eftn=0.5*(efth+np.roll(efth,nt//2,axis=1))
#a1E=np.sum(efth*np.cos(dir2),axis=1)*dth
#b1E=np.sum(efth*np.sin(dir2),axis=1)*dth
a1=np.zeros(nf)
b1=np.zeros(nf)
m1=np.zeros(nf)
a2=np.zeros(nf)
b2=np.zeros(nf)
m2=np.zeros(nf)
Q1=np.zeros(nf)
Q2=0
# print('TEST:',np.shape(dirn),np.shape(efth),dirn,dth)
for ind in range(nf):
#Ef[ind]=np.sum(efth[ind,:] )*dth
a1[ind]=np.sum(efth[ind,:]*np.cos(dirn[:]*d2r))*dth/Ef[ind]
b1[ind]=np.sum(efth[ind,:]*np.sin(dirn[:]*d2r))*dth/Ef[ind]
m1[ind]=np.sqrt(a1[ind]**2+b1[ind]**2)
a2[ind]=np.sum(efth[ind,:]*np.cos(2*dirn[:]*d2r))*dth/Ef[ind]
b2[ind]=np.sum(efth[ind,:]*np.sin(2*dirn[:]*d2r))*dth/Ef[ind]
m2[ind]=np.sqrt(a2[ind]**2+b2[ind]**2)
Q1[ind]=np.sum(eftn[ind,:]**2)*dth
Q2=Q2+Q1[ind]*dfreq[ind]*grav**2/(2*((np.pi*2)**4*fren[ind]**3 ))
# print('ft:',ind,fren[ind],wn[ind],'Cg:',Cg[ind],dfreq[ind]/(wn[ind]*dk[ind]),grav**2/(2*((np.pi*2)**4*fren[ind]**3 )) )
Qkk=np.sqrt(Q2)/Etot
Qf=np.sqrt(np.sum(Ef**2*dfreq))/Etot
Tm0m1=np.sum(Ef*dfreq/fren)/Etot
Hs=4*np.sqrt(Etot)
# print('WHAT:',ind,fren[ind],Ef[ind],a1[ind],b1[ind],m1[ind],efth[ind,:])
th1m=np.arctan2(b1,a1)/d2r
th2m=np.arctan2(b2,a2)/d2r
# print('TEST:',nf,nt,m1,'##',np.sum(efth[5,:]*np.cos(dirn))*dth/Ef[5],a1[5],b1[5],m1[5])
sth1m=np.sqrt(np.abs(2.0*(1-m1)))/d2r
sth2m=np.sqrt(np.abs(0.5*(1-m2)))/d2r
return Ef,th1m,sth1m,th2m,sth2m, Hs,Tm0m1,Qf,Qkk
#############################################################################
def wavespec_MEM(a0,a1,a2,b1,b2, ndirs):
"""(a1,a2,b1,b2,en,ndirs):
% This function calculates the Maximum Entropy Method estimate of
% the Directional Distribution of a wave field.
%
% NOTE: The normalized directional distribution array (NS) and the Energy
% array (NE) have been converted to a geographic coordinate frame in which
% direction is direction from.... but that assumes a1,b1 ... use same convention
%
% First Version: 1.0 - 8/00
%
% Latest Version: 1.0 - 8/00
%
% calculate directional energy spectrum based on Maximum Entropy Method (MEM)
% of Lygre & Krogstad, JPO V16 1986.
%
% switch to Krogstad notation
% # Maximum entropy method to estimate the Directional Distribution
# Maximum Entropy Method - Lygre & Krogstad (1986 - JPO)
# Eqn. 13:
# phi1 = (c1 - c2c1*)/(1 - abs(c1)^2)
# phi2 = c2 - c1phi1
# 2piD = (1 - phi1c1* - phi2c2*)/abs(1 - phi1exp(-itheta) -phi2exp(2itheta))^2
# c1 and c2 are the complex fourier coefficients
"""
nfreq = np.size(a0)
dr=np.pi/180
dtheta=360/ndirs
dirs=np.arange(0.,ndirs,1.)*dtheta
#print(nfreq,ndirs,np.size(dirs),dirs)
c1 = a1+1j*b1
c2 = a2+1j*b2
p1 = (c1-c2*np.conj(c1))/(1.-abs(c1)**2)
p2 = c2-c1*p1
# numerator(2D) : x
x = 1.-p1*np.conj(c1)-p2*np.conj(c2)
x = np.tile(np.real(x),(ndirs,1)).T
# denominator(2D): y
a = dirs*dr
e1 = np.tile(np.cos(a)-1j*np.sin(a),(nfreq,1))
e2 = np.tile(np.cos(2*a)-1j*np.sin(2*a),(nfreq,1))
p1e1 = np.tile(p1,(ndirs,1)).T*e1
p2e2 = np.tile(p2,(ndirs,1)).T*e2
y = abs(1-p1e1-p2e2)**2
D = x/(y)
# normalizes the spreading function,
# so that int D(theta,f) dtheta = 1 for each f
tot = np.tile(np.sum(D, axis=1),(ndirs,1)).T
D = D/tot
sp2d = np.tile(a0,(ndirs,1)).T*D/(dr*dtheta)
return sp2d,D,dirs
#############################################################################
### 1. Dispersion relation and associated ##################################
def phase_speed_from_k(k,depth=None,g=9.81):
if depth == 'None':
# print("Deep water approximation")
C=np.sqrt(g/k)
else:
# print("General case")
C=np.sqrt(g*np.tanh(k*depth)/k)
return C
def phase_speed_from_sig_k(sig,k):
return sig/k
def group_speed_from_k(k,depth=None,g=9.81):
C=phase_speed_from_k(k,depth=depth,g=g)
if depth == 'None':
# print("Deep water approximation")
Cg=C/2
else:
# print("General case")
Cg=C*(0.5+ ((k*depth)/(np.sinh(2*k*depth)) ))
return Cg
def sig_from_k(k,D=None,g=9.81):
if D=='None':
# print("Deep water approximation")
sig = np.sqrt(g*k)
else:
# print("General case")
sig = np.sqrt(g*k*np.tanh(k*D))
return sig
def f_from_sig(sig):
return sig/(2*np.pi)
def f_from_k(k,D=None,g=9.81):
sig = sig_from_k(k,D=D,g=g)
return sig/(2*np.pi)
def sig_from_f(f):
return 2*np.pi*f
def period_from_sig(sig):
return (2*np.pi)/sig
def period_from_wvl(wvl,D=None):
k=(2*np.pi)/wvl
sig=sig_from_k(k,D=D)
T = period_from_sig(sig)
return T
def k_from_f(f,D=10000.,g=9.81):
# inverts the linear dispersion relation (2*pi*f)^2=g*k*tanh(k*dep) to get
#k from f and dep. 2 Arguments: f and dep.
eps=0.000001
sig=np.array(2*np.pi*f)
if D > 1000.:
# print("Deep water approximation")
k=sig**2/g
else:
Y=D*sig**2/g
X=np.sqrt(Y)
I=1
F=1.
while (abs(np.max(F)) > eps):
H=np.tanh(X)
F=Y-(X*H)
FD=-H-(X/(np.cosh(X)**2))
X=X-(F/FD)
k=X/D
return k # wavenumber
#############################################################################
### 2. Get quick translation info (T0/k/f/L) ###############################
def infos_from_wvl(wvl,D=None):
wvnb = 2*np.pi/wvl
f = f_from_k(wvnb,D=D)
P = 1/f
print('From a wavelength of ',wvl, ' m : -----------------------')
print(' - wavenumber k = '+f'{wvnb:.4f}'.rjust(6)+' rad/m')
if D is None:
print(' With the infinite depth approximation :')
else:
print(' With a depth of ',D,' m')
print(' - frequency f = '+f'{f:.3f}'.rjust(6)+' Hz')
print(' - period T = '+f'{P:.2f}'.rjust(6)+' s')
print('--------------------------------------------------------')
def infos_from_wvnb(wvnb,D=None):
wvl = 2*np.pi/wvnb
f = f_from_k(wvnb,D=D)
P = 1/f
print('From a wavenumber of ',wvnb, ' rad/m : -----------------------')
print(' - wavelength L = '+f'{wvl:.1f}'.rjust(6)+' m')
if D is None:
print(' With the infinite depth approximation :')
else:
print(' With a depth of ',D,' m')
print(' - frequency f = '+f'{f:.3f}'.rjust(6)+' Hz')
print(' - period T = '+f'{P:.2f}'.rjust(6)+' s')
print('--------------------------------------------------------')
def infos_from_T0(P,D=None):
f = 1/P
wvnb = k_from_f(f,D=D)
wvl = 2*np.pi/wvnb
print('From a period of ',P, ' s : -----------------------')
print(' - frequency f = '+f'{f:.3f}'.rjust(6)+' Hz')
if D is None:
print(' With the infinite depth approximation :')
else:
print(' With a depth of ',D,' m')
print(' - wavelength L = '+f'{wvl:.1f}'.rjust(6)+' m')
print(' - wavenumber k = '+f'{wvnb:.4f}'.rjust(6)+' rad/m')
print('--------------------------------------------------------')
def infos_from_f(f,D=None):
P = 1/f
wvnb = k_from_f(f,D=D)
wvl = 2*np.pi/wvnb
print('From a frequency of ',f, ' Hz : -----------------------')
print(' - period T = '+f'{P:.2f}'.rjust(6)+' s')
if D is None:
print(' With the infinite depth approximation :')
else:
print(' With a depth of ',D,' m')
print(' - wavelength L = '+f'{wvl:.1f}'.rjust(6)+' m')
print(' - wavenumber k = '+f'{wvnb:.4f}'.rjust(6)+' rad/m')
print('--------------------------------------------------------')
#############################################################################
### 2. Classical Wave spectra ##############################################
## ---- 2.1. 1D Wave spectra along f or k -----------------------------------
def PM_spectrum_f(f,fm,g=9.81):
# There are 2 ways of writing the PM spectrum:
# - eq 12 of Pierson and Moskowitz (1964) with exp(-0.74 * (f/fw)**-4) where fw=g*U10/(2*pi)
# - eq of Hasselmann et al. 1973 with exp(-5/4 * (f/ fm)**-4) where fm is the max frequency ...
# See Hasselmann et al. 1973 for the explanation
alpha=8.1*10**-3
E = alpha*g**2*(2*np.pi)**-4*f**-5*np.exp((-5/4)*((fm/f)**4))
return E
def PM_spectrum_k(k,fm,D=None,g=9.81):
# There are 2 ways of writing the PM spectrum:
# - eq 12 of Pierson and Moskowitz (1964) with exp(-0.74 * (f/fw)**-4) where fw=g*U10/(2*pi)
# - eq of Hasselmann et al. 1973 with exp(-5/4 * (f/ fm)**-4) where fm is the max frequency ...
# See Hasselmann et al. 1973 for the explanation
f=sig_from_k(k,D=D)/(2*np.pi)
Ef = PM_spectrum_f(f,fm,g=g)
dfdk = dfdk_from_k(k,D=D)
return Ef*dfdk
## ---- 2.2. 2D Wave spectra ------------------------------------------------
def define_spectrum_PM_cos2n(k,th,T0,thetam,n=4,D=None):
Ek=PM_spectrum_k(k,1/T0,D=D)
dth=th[1]-th[0]
Eth=np.cos(th-thetam)**(2*n)
II=np.where(np.cos(th-thetam) < 0)[0]
Eth[II]=0
sth=sum(Eth*dth)
Ekth=np.broadcast_to(Ek,(len(th),len(k)))*np.broadcast_to(Eth,(len(k),len(th))).T /sth
return Ekth,k,th
def define_Gaussian_spectrum_kxky(kX,kY,T0,theta_m,sk_theta,sk_k,D=None):
if (len(kX.shape)==1) & (len(kY.shape)==1):
kX,kY = np.meshgrid(kX,kY)
elif (len(kX.shape)==1) | (len(kY.shape)==1):
print('Error : kX and kY should either be: \n - both vectors of shapes (nx,) and (ny,) \n OR - both matrices of shape (ny,nx)')
print('/!\ Proceed with caution /!\ kX and kY have been flattened to continue running')
kX = kX.flatten()
kY = kY.flatten()
kp = k_from_f(1/T0,D=D)
# rotation of the grid => places kX1 along theta = theta_m
kX1 = kX*np.cos(theta_m)+kY*np.sin(theta_m)
kY1 = -kX*np.sin(theta_m)+kY*np.cos(theta_m)
Z1_Gaussian =1/(2*np.pi*sk_theta*sk_k)* np.exp( - 0.5*((((kX1-kp)**2)/((sk_k)**2))+kY1**2/sk_theta**2))
return Z1_Gaussian,kX,kY
#############################################################################
### 3. Jacobians and variable changes ######################################
## ---- 3.1 Jacobians -------------------------------------------------------
def dfdk_from_k(k,D=None):
Cg = group_speed_from_k(k,depth=D,g=9.81)
return Cg/(2*np.pi)
## ----- 3.2 Change variables from spectrum ---------------------------------
def spectrum_from_fth_to_kth(Efth,f,th,D=10000.):
shEfth = np.shape(Efth)
# print(shEfth)
if len(shEfth)<2:
print('Error: spectra should be 2D')
else:
if shEfth[0]==shEfth[1]:
print('Warning: same dimension for freq and theta.\n Proceed with caution: The computation is done considering Efth = f(f,th)')
elif (shEfth[1]==len(f)) &(shEfth[0]==len(th)):
Efth = np.swapaxes(Efth,0,1)
elif (shEfth[1]==len(th)) &(shEfth[0]==len(f)):
print('All good: Efth have the shape : (f,th)')
else:
print('shEfth[1] : ',shEfth[1], ' vs ',len(f),'// shEfth[0] :',shEfth[0],' vs ',len(th))
print('Error: Efth should have the shape : (f,th)')
shEfth = np.shape(np.moveaxis(Efth,0,-1))
k=k_from_f(f,D=D)
dfdk=dfdk_from_k(k,D=D)
Ekth = Efth*np.moveaxis(np.broadcast_to(dfdk,shEfth),-1,0)
return Ekth, k, th
def spectrum_from_kth_to_kxky(Ekth,k,th):
try:
shEkth = np.shape(Ekth)
# print(shEkth,np.shape(k),np.shape(th))
if len(shEkth)<2:
print('Error: spectra should be 2D')
else:
if shEkth[0]==shEkth[1]:
print('Warning: same dimension for k and theta.\n Proceed with caution: The computation is done considering Ekth = f(k,th)')
elif ((shEkth[1]==len(k)) &(shEkth[0]==len(th))) | ((shEkth[1]==len(th)) &(shEkth[0]==len(k))):
if (shEkth[1]==len(k)) &(shEkth[0]==len(th)):
Ekth = np.swapaxes(Ekth,0,1)
else:
print('shEkth[1] : ',shEkth[1], ' vs ',len(k),'// shEkth[0] :',shEkth[0],' vs ',len(th))
print('Error: Ekth should have the shape : (k,th)')
shEkth2 = np.shape(np.moveaxis(Ekth,0,-1)) # send k-axis to last -> in order to broadcast k along every dim
shEkth2Dkth = Ekth.shape[0:2] # get only shape k,th for the broadcast of the dimensions kx,ky
# print('shEkth2Dkth : ',shEkth2Dkth)
if np.max(th)>100:
th=th*np.pi/180
kx = np.moveaxis(np.broadcast_to(k,shEkth2Dkth[::-1]),-1,0) * np.cos(np.broadcast_to(th,shEkth2Dkth))
ky = np.moveaxis(np.broadcast_to(k,shEkth2Dkth[::-1]),-1,0) * np.sin(np.broadcast_to(th,shEkth2Dkth))
Ekxky = Ekth/np.moveaxis(np.broadcast_to(k,shEkth2),-1,0)
#print(np.shape(Ekxky))
return Ekxky, kx, ky
except Exception as inst:
print('in spec to kxky : ',inst,', line number : ',sys.exc_info()[2].tb_lineno)
def spectrum_from_fth_to_kxky(Efth,f,th,D=10000.):
shEfth = np.shape(Efth)
#print(shEfth)
if len(shEfth)<2:
print('Error: spectra should be 2D')
else:
if shEfth[0]==shEfth[1]:
print('Warning: same dimension for freq and theta.\n Proceed with caution: The computation is done considering Efth = f(f,th)')
elif ((shEfth[1]==len(f)) &(shEfth[0]==len(th))) | ((shEfth[1]==len(th)) &(shEfth[0]==len(f))):
if (shEfth[1]==len(f)) &(shEfth[0]==len(th)):
Efth = np.swapaxes(Efth,0,1)
else:
print('Error: Efth should have the shape : (f,th)')
shEfth2 = np.shape(np.moveaxis(Efth,0,-1)) # send f-axis to last -> in order to broadcast f along every dim
shEfth2Dfth = Efth.shape[0:2] # get only shape f,th for the broadcast of the dimensions kx,ky
k=k_from_f(f,D=D)
dfdk=dfdk_from_k(k,D=D)
if np.max(th)>100:
th=th*np.pi/180
kx = np.moveaxis(np.broadcast_to(k,shEfth2Dfth[::-1]),-1,0) * np.cos(np.broadcast_to(th,shEfth2Dfth))
ky = np.moveaxis(np.broadcast_to(k,shEfth2Dfth[::-1]),-1,0) * np.sin(np.broadcast_to(th,shEfth2Dfth))
Ekxky = Efth * np.moveaxis(np.broadcast_to(dfdk /k,shEfth2),-1,0)
return Ekxky, kx, ky
def spectrum_to_kxky(typeSpec,Spec,ax1,ax2,D=None):
if typeSpec==0: # from f,th
Ekxky, kx, ky = spectrum_from_fth_to_kxky(Spec,ax1,ax2,D=D)
elif typeSpec==1: # from k,th
Ekxky, kx, ky = spectrum_from_kth_to_kxky(Spec,ax1,ax2)
else:
print('Error ! typeSpec should be 0 = (f,th) or 1 = (k,th)')
Ekxky = Spec
kx = ax1
ky = ax2
return Ekxky, kx, ky
def spectrum_f_to_k(Ef,f,D=None):
shEf = np.array(np.shape(Ef))
ind = np.where(shEf == len(f))[0]
if len(ind)==0:
print('Error: spectra should have an axis with same dimension as f')
elif len(ind)>1:
print('Warning: same dimension for different axes.\n Proceed with caution: The computation is done considering Ef = f(...,f)')
if ind[-1]<(len(shEf)-1):
Ef=np.swapaxes(Ef,ind[-1],-1)
elif len(ind)==1:
Ef=np.swapaxes(Ef,ind,-1) # pass the f axis as last dim : to broadcast
k=k_from_f(f,D=D)
dfdk=dfdk_from_k(k,D=D)
shEf2 = np.shape(Ef)
Ek = np.swapaxes(Ef*np.broadcast_to(dfdk,shEf2),-1,ind)
return Ek, k
def spectrum_k_to_f(Ek,k,D=None):
shEk = np.array(np.shape(Ek))
ind = np.where(shEk == len(k))[0]
if len(ind)==0:
print('Error: spectra should have an axis with same dimension as k')
elif len(ind)>1:
print('Warning: same dimension for different axes.\n Proceed with caution: The computation is done considering Ek = f(...,k)')
if ind[-1]<(len(shEk)-1):
ind0 = int(ind[-1])
Ek=np.swapaxes(Ek,ind0,-1)
elif len(ind)==1:
ind0 = int(ind)
Ek=np.swapaxes(Ek,ind0,-1) # pass the f axis as last dim : to broadcast
f=f_from_k(k,D=D)
dfdk=dfdk_from_k(k,D=D)
shEk2 = np.shape(Ek)
Ef = np.swapaxes(Ek/np.broadcast_to(dfdk,shEk2),-1,ind0)
return Ef, f
#############################################################################
def PM_spectrum_k(k,fm,g=9.81):
#pmofk(k,T0,H)
alpha=8.1*10**-3
w0=2*np.pi/T0
w=np.sqrt(g*k*tanh(k*H))
#Cg=(0.5+k.*H/sinh(2.*k.*H)).*w./k;
#pmofk=0.008.*g.^2.*exp(-0.74.*(w./w0).^(-4))./(w.^5).*Cg+5.9;
E = alpha*g**2*(2*np.pi)**-4*f**-5*np.exp((-5/4)*((fm/f)**4))
return E
#############################################################################