def amplitude(M,i,field='omega',display=False):
xmin,xmax,ymin,ymax = positions(M,i,field='omega',display=False)
Zfilt = smoothing(M,i,field='omega',sigma=3.)
x = M.x[0,:]
y = -M.y[:,0]
dx = M.x[0,1]-M.x[0,0]
Omegai = interpolate.RectBivariateSpline(y, x, Zfilt,kx=3,ky=3)
U,d = vgradient.make_Nvec(M,i) # Z : d+1 dimension np array
b0 = 10.
imin,imax,jmin,jmax,Zfilt,X,Y = position_index(M,i,field=field,display=display)
tau1 = strain.strain_tensor_loc(U,imin,jmin,d,b=b0)
tau2 = strain.strain_tensor_loc(U,imax,jmax,d,b=b0)
G = []
for tau in [tau1,tau2]:
omega,enstrophy = strain.vorticity(tau,d=2,norm=False)
div = strain.divergence_2d(tau,d=2)
G.append((omega[0,0]) * np.pi*b0**2*dx**2) #-div[0,0]
# divergence.append(div[0,0]/np.abs(omega[0,0]))
val_min = Omegai(-ymin,xmin)
val_max = Omegai(-ymax,xmax)
return val_min[0,0],val_max[0,0],G
def compute_vorticity(M, i):
"""
"""
U = M.Ux[..., i]
V = M.Uy[..., i]
X = M.x
Y = M.y
x = M.x[0, :]
y = M.y[:, 0]
n = 3
Xp, Yp = np.meshgrid(x[n:-n], y[n:-n])
dx = np.mean(np.diff(x))
dimensions = np.shape(U) + (2, )
Z = np.reshape(np.transpose([V, U], (1, 2, 0)), dimensions)
dZ = strain_tensor.strain_tensor(Z, d=2)
omega, enstrophy = strain_tensor.vorticity(dZ, d=2, norm=False)
omega = omega / dx
return Xp, Yp, omega
def circulation_2(M, i, fignum=1, display=False):
Omega = access.get(M, 'omega', i)
x, y = space_axis_vorticity(M)
X, Y, data, center, factor = normalize(x, y, Omega[..., 0])
dx = M.x[0, 1] - M.x[0, 0]
#print(dx)
U, d = vgradient.make_Nvec(M, i) # Z : d+1 dimension np array
nx, ny = X.shape
R_list = np.arange(1., 15., 0.5)
Gamma = []
divergence = []
for b in R_list:
# print(b)
tau = strain_tensor.strain_tensor_loc(U,
center[0],
center[1],
d=2,
b=b)
omega, enstrophy = strain_tensor.vorticity(tau, d=2, norm=False)
div = strain_tensor.divergence_2d(tau, d=2)
G = (omega[0, 0] - div[0, 0]) * np.pi * b**2 * dx**2
Gamma.append(G)
divergence.append(div[0, 0] / np.abs(omega[0, 0]))
R_list = np.asarray(R_list) * dx
if display:
graphes.graph(R_list, Gamma, fignum=fignum, label='bo')
graphes.legende('r (mm)', 'Circulation (mm^2/s)', '')
graphes.graph(R_list, divergence, fignum=fignum + 1, label='ko')
graphes.graph(R_list,
np.zeros(len(R_list)),
fignum=fignum + 1,
label='r--')
graphes.legende('r (mm)', 'Relative 2d divergence', '')
graphes.set_axis(0, 30 * dx, -0.3, 0.3)
return R_list, Gamma, center, factor
def vorticity_field(M, i, step=1, type=2, rescale=False):
"""
Compute the vorticity field using the stephane.jhtd.strain_tensor module
INPUT
-----
M : Mdata set object
Contain the data, either 2d or 3d in space
i : int
index in time. Could be removed to compute the strain tensor both in space and time
OUTPUT
-----
omega : np array of dimension (nx-6,ny-6)
vorticity field
name : str
name of the field to add to the dataset
"""
d = len(M.shape()) - 1
dZ, field = dU_field(M, i, step=step, type=type, rescale=rescale)
omega, enstrophy = strain_tensor.vorticity(dZ, d=d, norm=False)
return omega, 'omega'
def vortex_maps(x, y, Z, dx=1, display_map=False):
dZ1 = strain_tensor.strain_tensor(Z, d=2) / dx
blist = np.arange(0.5, 6., 0.5)
b0 = 2.5
dZ2 = {}
for b in blist:
print('Compute vorticity with r=' + str(b))
dZ2[b] = strain_tensor.strain_tensor_C(Z, d=2, b=b) / dx
omega1, enstrophy2 = strain_tensor.vorticity(dZ1, d=2, norm=False)
omega2, enstrophy2 = strain_tensor.vorticity(dZ2[b0], d=2, norm=False)
eigen1 = strain_tensor.Lambda(dZ1, d=2)
eigen2 = strain_tensor.Lambda(dZ2[b0], d=2)
strain1 = np.sqrt(
np.power(eigen1['Lambda_0'], 2) + np.power(eigen1['Lambda_1'], 2))
strain2 = np.sqrt(
np.power(eigen2['Lambda_0'], 2) + np.power(eigen2['Lambda_1'], 2))
figs = {}
# dimensions = np.shape(omega1)
#graphes.hist(np.reshape(omega,np.prod(dimensions)),fignum=1)
#figs.update(graphes.legende('vorticity (s^-1)','PDF',''))
# graphes.set_axis(-2.5,2.5,0,40000)
n = 3
Xp1, Yp1 = np.meshgrid(x[n:-n], y[n:-n])
Xp2, Yp2 = np.meshgrid(x, y)
if display_map:
for i in range(2):
for j in range(2):
graphes.color_plot(Xp1,
Yp1,
dZ1[..., i, j],
fignum=i + j * 2 + 2)
graphes.colorbar()
title = 'dU_' + str(i) + '/x_' + str(j)
figs.update(graphes.legende('X', 'Y', title, cplot=True))
graphes.cla(6)
graphes.color_plot(Xp1, Yp1, -omega1, fignum=6)
graphes.colorbar()
figs.update(graphes.legende('X', 'Y', 'Vorticity', cplot=True))
graphes.color_plot(Xp1, Yp1, strain1, fignum=7)
graphes.colorbar()
figs.update(graphes.legende('X', 'Y', 'Strain', cplot=True))
#dissipation
dissipation1 = np.sum(np.power(dZ1, 2), axis=(2, 3))
graphes.color_plot(Xp1, Yp1, dissipation1, fignum=8)
graphes.colorbar()
figs.update(graphes.legende('X', 'Y', 'Dissipation', cplot=True))
i1 = Xp1.shape[0] // 2
i2 = Xp2.shape[0] // 2
Xp = Xp2[i2, :]
omega_th = profile_omega(Xp, sigma=2.)
graphes.graph(Xp1[i1, :], omega1[i1, :], label='b-', fignum=9)
graphes.graph(Xp2[i2, :], omega2[i2, :], label='k-', fignum=9)
graphes.graph(Xp, omega_th, label='r--', fignum=9)
graphes.legende('r', 'vorticity', 'Radial vorticity profile')
graphes.graph(Xp1[i1, :], strain1[i1, :], label='b.-', fignum=10)
graphes.graph(Xp2[i2, :], strain2[i2, :], label='k^-', fignum=10)
graphes.legende('r--', 'strain', 'Radial strain profile')
j2 = Xp2.shape[1] // 2
for b in blist:
omega2, enstrophy2 = strain_tensor.vorticity(dZ2[b], d=2, norm=False)
graphes.graph(Xp2[i2, :], omega2[i2, :], label='k-', fignum=11)
graphes.legende('r', 'vorticity',
'Radial vorticity profile, various b')
graphes.graph([b], [omega2[i2, j2]], label='k^', fignum=12)
graphes.legende('Circle radius r (in box unit)', 'max. vorticity',
'Influence of contour size')
print(Xp.shape)
print(Xp2.shape)
# graphes.color_plot(X,Y,R,fignum=3,vmin=0,vmax=10)
print(figs)
return figs
def profile_avg(Mlist,i,display=False,fignum=1):
field = 'omega'
R_list=np.arange(0.25,15.,0.25)
R = np.arange(0.,15.,0.25)
n = len(Mlist)
figs = {}
Gamma = np.zeros((n,len(R),2))
Flux = np.zeros((n,len(R),2))
for k,M in enumerate(Mlist):
x = M.x[0,5:]
y = -M.y[:,0]
dx = M.x[0,1]-M.x[0,0]
U,d = vgradient.make_Nvec(M,i) # Z : d+1 dimension np array
imin,imax,jmin,jmax,Zfilt,X,Y = position_index(M,i,field=field,display=display)
G = [[] for j in range(len(R_list)+1)]
G[0].append(0)
G[0].append(0)
D = [[] for j in range(len(R_list)+1)]
D[0].append(0)
D[0].append(0)
for j,b in enumerate(R_list):
tau1 = strain.strain_tensor_loc(U,imin,jmin,d,b=b)
tau2 = strain.strain_tensor_loc(U,imax,jmax,d,b=b)
for tau in [tau1,tau2]:
omega,enstrophy = strain.vorticity(tau,d=2,norm=False)
div = strain.divergence_2d(tau,d=2)
G[j+1].append((omega[0,0]) * np.pi*b**2*dx**2) #-div[0,0]
D[j+1].append((div[0,0]) * np.pi*b**2*dx**2) #-div[0,0]
Gamma[k,...] = np.asarray(G)
Flux[k,...] = np.asarray(D)
graphes.graph(R,-Gamma[k,:,0],label = 'kv',fignum=fignum*2)
graphes.graph(R,Gamma[k,:,1],label = 'k^',fignum=fignum*2)
graphes.graph(R,Flux[k,:,0],label = 'kv',fignum=fignum*2+1)
graphes.graph(R,Flux[k,:,1],label = 'k^',fignum=fignum*2+1)
Gamma_moy = np.nanmean(Gamma,axis=0)
Flux_moy = np.nanmean(Flux,axis=0)
graphes.graph(R,-Gamma_moy[:,0],label = 'r--',fignum=fignum*2)
graphes.graph(R,Gamma_moy[:,1],label = 'r--',fignum=fignum*2)
graphes.graph(R,np.nanmean(np.asarray([Gamma_moy[:,1],-Gamma_moy[:,0]]),axis=0),label = 'rs',fignum=fignum*2)
figs.update(graphes.legende('Distance to center (mm)','Circulation (mm^2/s)',''))
graphes.graph(R,Flux_moy[:,0],label = 'r--',fignum=fignum*2+1)
graphes.graph(R,Flux_moy[:,1],label = 'r--',fignum=fignum*2+1)
graphes.graph(R,np.nanmean(np.asarray([Flux_moy[:,1],Flux_moy[:,0]]),axis=0),label = 'rs',fignum=fignum*2+1)
figs.update(graphes.legende('Distance to center (mm)','Divergence (mm^2/s)',''))
savedir = title(Mlist[0])
graphes.save_figs(figs,savedir=savedir,suffix='',prefix='frame_'+str(i),frmt='pdf',dpi=300,display=True)
M_profile = np.nanmean(np.asarray([Gamma_moy[:,1],-Gamma_moy[:,0]]),axis=0)
return np.mean(M_profile[-10:]),np.std(Gamma[:,-10:,1])
def example(filename):
figs = {}
savedir = '/Users/stephane/Documents/Postdoc_Chicago/Process_data/Scripts/Example/Smoothing/'
M = M_manip.load_Mdata_file(filename, data=True)
M.get('E')
M.get('omega')
nx, ny, nt = M.shape()
x, y = M.x, M.y
i = nt / 2
# display raw energy
graphes.Mplot(M, 'E', i, vmin=0, vmax=50000, fignum=1, colorbar=True)
figs.update(
graphes.legende('$x$ (mm)',
'$y$ (mm)',
'Energy without pre-processing',
cplot=True))
#Display raw vorticity
graphes.Mplot(M, 'omega', i, vmin=0, vmax=80, fignum=2, colorbar=True)
figs.update(
graphes.legende('$x$ (mm)',
'$y$ (mm)',
'Vorticity without pre-processing',
cplot=True))
# Look for bada data point in amplitude
E = M.E[..., i]
tup, errors = cdata.rm_baddata(E, borne=2.)
xc = []
yc = []
for t in tup:
xc.append([x[t[0], t[1]]])
yc.append([y[t[0], t[1]]])
graphes.graph(xc, yc, label='ro', fignum=2)
print(figs)
graphes.save_figs(figs, savedir=savedir)
Ux, Uy = M.Ux[..., i], M.Uy[..., i]
#replace component of the velocity
Ux = cdata.replace_data(Ux, tup)[..., 0]
Uy = cdata.replace_data(Uy, tup)[..., 0]
U = np.transpose(np.asarray([Uy, Ux]), (1, 2, 0))
dU = strain.strain_tensor_C(U, b=2.)
omega, enstrophy = strain.vorticity(dU, d=2, norm=False)
E = Ux**2 + Uy**2
graphes.color_plot(x, y, omega, vmin=0, vmax=80, fignum=4)
graphes.plt.colorbar()
figs.update(
graphes.legende('$x$ (mm)',
'$y$ (mm)',
'Vorticity after pre-processing',
cplot=True))
graphes.color_plot(x, y, E, vmin=0, vmax=50000, fignum=3)
graphes.plt.colorbar()
figs.update(
graphes.legende('$x$ (mm)',
'$y$ (mm)',
'Energy after pre-processing',
cplot=True))
### Gaussian filter
omega_filt = filters.gaussian_filter(omega, sigma=2.) #[...,0]
graphes.color_plot(x, y, omega_filt, vmin=0, vmax=80, fignum=5)
graphes.plt.colorbar()
figs.update(
graphes.legende('$x$ (mm)',
'$y$ (mm)',
'Vorticity after gaussian smoothing',
cplot=True))
graphes.save_figs(figs, savedir=savedir)