def EEF_U0(set_, pi):
# For every U0 value in U0_set,
un = len(set_)
EEF_array = np.zeros((un, 6, 2))
for ui in range(
0,
un): # ui indexes the local EEF_array (i.e. computational domain)
# Redefine U0 and H0 in each run.
for j in range(0, N):
U0[j] = set_[ui]
H0[j] = -(U0[j] / g) * (f0 * y[j] + beta * y[j]**2 / 2) + Hflat
U0_nd = U0 / U
H0_nd = H0 / chi
a1, a2, a3, a4, b4, c1, c2, c3, c4 = solver.SOLVER_COEFFICIENTS(
Ro, Re, K_nd, f_nd, U0_nd, H0_nd, omega_nd, gamma_nd, dy_nd, N)
solution = solver.FREE_SLIP_SOLVER(a1, a2, a3, a4, f_nd, b4, c1, c2,
c3, c4, Ro * Ftilde1_nd,
Ro * Ftilde2_nd, Ftilde3_nd, N, N2)
utilde_nd, vtilde_nd, etatilde_nd = solver.extractSols(
solution, N, N2, BC)
u, v, h = solver.SPEC_TO_PHYS(utilde_nd, vtilde_nd, etatilde_nd, T_nd,
dx_nd, omega_nd, N)
# Take real part.
u = np.real(u)
v = np.real(v)
h = np.real(h)
# Normalise all solutions by the (non-dimensional) forcing amplitude.
u = u / AmpF_nd
v = v / AmpF_nd
h = h / AmpF_nd
# In order to calculate the vorticities of the system, we require full (i.e. BG + forced response) u and eta.
h_full = np.zeros((N, N, Nt))
u_full = np.zeros((N, N, Nt))
for j in range(0, N):
h_full[j, :, :] = h[j, :, :] + H0_nd[j]
u_full[j, :, :] = u[j, :, :] + U0_nd[j]
PV_prime, PV_full, PV_BG = PV.potentialVorticity(
u, v, h, u_full, h_full, H0_nd, U0_nd, N, Nt, dx_nd, dy_nd, f_nd,
Ro)
uq, Uq, uQ, UQ, vq, vQ = PV.fluxes(u, v, U0_nd, PV_prime, PV_BG, N, Nt)
P, P_xav = PV.footprint(uq, Uq, uQ, UQ, vq, vQ, x_nd, T_nd, dx_nd,
dy_nd, N, Nt)
EEF_array[ui, :], l_array[ui, :] = PV.EEF(P_xav, y_nd, y0_nd, y0_index,
dy_nd, N)
filename = 'EEF_array_' + str(pi)
np.save(filename, EEF_array)
def EEF_main(set_,pi):
NU = len(set_)
# Initialise output arrays
Ef_av_array = np.zeros((NU,N,N))
Ed_av_array = np.zeros((NU,N,N))
# Now start the loop over each forcing index.
for ui in range(0,NU):
#print(ui)
# Redefine U0 and H0
#sigma = set_[ui]
Umag = set_[ui]
U0, H0 = BG_state.BG_uniform(Umag,Hflat,f0,beta,g,y,N)
U0_nd = U0 / U
H0_nd = H0 / chi
# Solution
a1,a2,a3,a4,b4,c1,c2,c3,c4 = solver.SOLVER_COEFFICIENTS(Ro,Re,K_nd,f_nd,U0_nd,H0_nd,omega_nd,gamma_nd,dy_nd,N)
solution = solver.FREE_SLIP_SOLVER(a1,a2,a3,a4,f_nd,b4,c1,c2,c3,c4,Ro*Ftilde1_nd,Ro*Ftilde2_nd,Ftilde3_nd,N,N2)
utilde_nd, vtilde_nd, etatilde_nd = solver.extractSols(solution,N,N2,BC)
u, v, h = solver.SPEC_TO_PHYS(utilde_nd,vtilde_nd,etatilde_nd,T_nd,dx_nd,omega_nd,N)
# Take real part. Don't normalise by forcing ampltiude, as we want to compare energy input by forcing.
u = np.real(u)
v = np.real(v)
h = np.real(h)
# Calculate full flow quantities.
u_full = diagnostics.fullFlow(u,U0_nd)
h_full = diagnostics.fullFlow(h,H0_nd)
#==
# Energy budget terms.
Ed, Ed_av_array[ui,] = energy.budgetDissipation3(U0_nd,H0_nd,u,v,h,Ro,Re,gamma_nd,dx_nd,dy_nd,T_nd,Nt,N)
Ef, Ef_av_array[ui,] = energy.budgetForcing(u_full,v,h_full,F1_nd,F2_nd,F3_nd,Ro,N,T_nd,omega_nd,Nt)
# End loop.
np.save('Ed_av_array'+str(pi),Ed_av_array)
np.save('Ef_av_array'+str(pi),Ef_av_array)
S = np.load('time_series1.npy');
#Om = np.fft.fftfreq(Nt,dt_nd);
S_tilde = np.fft.fft(S);
for wi in range(1,Nt):
print(wi);
# Coefficients
a1,a2,a3,a4,b4,c1,c2,c3,c4 = solver.SOLVER_COEFFICIENTS(Ro,Re,K_nd,f_nd,U0_nd,H0_nd,omega_nd,gamma_nd,dy_nd,N)
# Solver
if BC == 'NO-SLIP':
solution = solver.NO_SLIP_SOLVER(a1,a2,a3,a4,f_nd,b4,c1,c2,c3,c4,S_tilde[wi]*Ro*Ftilde1_nd,S_tilde[wi]*Ro*Ftilde2_nd,S_tilde[wi]*Ftilde3_nd,N,N2);
if BC == 'FREE-SLIP':
solution = solver.FREE_SLIP_SOLVER(a1,a2,a3,a4,f_nd,b4,c1,c2,c3,c4,S_tilde[wi]*Ro*Ftilde1_nd,S_tilde[wi]*Ro*Ftilde2_nd,S_tilde[wi]*Ftilde3_nd,N,N2)
u[:,:,wi], v[:,:,wi], h[:,:,wi] = solver.extractSols(solution,N,N2,BC);
u, v, h = solver.SPEC_TO_PHYS_STOCH(u,v,h,dx_nd,N);
# Normalise all solutions by the (non-dimensional) forcing amplitude.
u = u / AmpF_nd;
v = v / AmpF_nd;
h = h / AmpF_nd;
mass = sum(sum(h[:,:,ts]))/N**2
print(mass)
plt.contourf(h[:,:,ts]);
plt.colorbar()
plt.show()
def EEF_y0(y0_set, pi):
# For every y0 value in y0_set all forcing parameters must be redefined.
from inputFile_1L import *
yn = len(y0_set)
EEF_array = np.zeros((yn, 6, 2))
for yi in range(
0,
yn): # yi indexes the local EEF_array (i.e. computational domain)
ii = y0_set[yi]
# ii indexes arrays defined over global domain
print(ii)
if EEF_array[
yi, 0,
0] == 0: # Check if any of the array has been updated after initialisation.
y0 = y[ii]
# Redefine y0 and the forcing in each run.
y0_nd = y0 / L
# Forcing
if FORCE_TYPE == 'CTS':
F1_nd, F2_nd, F3_nd, Ftilde1_nd, Ftilde2_nd, Ftilde3_nd = forcing.forcing_cts(
x_nd, y_nd, K_nd, y0_nd, r0_nd, N, FORCE, AmpF_nd, f_nd,
f0_nd, dx_nd, dy_nd)
elif FORCE_TYPE == 'DCTS':
F1_nd, F2_nd, F3_nd, Ftilde1_nd, Ftilde2_nd, Ftilde3_nd = forcing.forcing_dcts(
x_nd, y_nd, K_nd, y0_nd, r0_nd, N, FORCE, AmpF_nd, f_nd,
f0_nd, dx_nd, dy_nd)
else:
sys.exit('ERROR: Invalid forcing option selected.')
# Solver
if BC == 'NO-SLIP':
solution = solver.NO_SLIP_SOLVER(a1, a2, a3, a4, f_nd, b4, c1,
c2, c3, c4, Ftilde1_nd,
Ftilde2_nd, Ftilde3_nd, N, N2)
if BC == 'FREE-SLIP':
solution = solver.FREE_SLIP_SOLVER2(a1, a2, a3, a4, f_nd, b4,
c1, c2, c3, c4, Ftilde1_nd,
Ftilde2_nd, Ftilde3_nd, N,
N2)
utilde_nd, vtilde_nd, etatilde_nd = solver.extractSols(
solution, N, N2, BC)
u, v, h = solver.SPEC_TO_PHYS(utilde_nd, vtilde_nd, etatilde_nd,
T_nd, dx_nd, omega_nd, N)
# Take real part.
u = np.real(u)
v = np.real(v)
h = np.real(h)
# Normalise all solutions by the (non-dimensional) forcing amplitude.
u = u / AmpF_nd
v = v / AmpF_nd
h = h / AmpF_nd
# In order to calculate the vorticities of the system, we require full (i.e. BG + forced response) u and eta.
h_full = np.zeros((N, N, Nt))
u_full = np.zeros((N, N, Nt))
for j in range(0, N):
h_full[j, :, :] = h[j, :, :] + H0_nd[j]
u_full[j, :, :] = u[j, :, :] + U0_nd[j]
# Calculate PV fields and PV fluxes.
PV_prime, PV_full, PV_BG = PV.potentialVorticity(
u, v, h, u_full, h_full, H0_nd, U0_nd, N, Nt, dx_nd, dy_nd,
f_nd)
uq, Uq, uQ, UQ, vq, vQ = PV.fluxes(u, v, U0_nd, PV_prime, PV_BG, N,
Nt)
# Do footprints
P, P_xav[yi, :] = PV.footprint_1L(u_full, v, h_full, PV_full,
U0_nd, U, Umag, x_nd, y_nd, T_nd,
dx_nd, dy_nd, dt_nd, AmpF_nd,
FORCE, r0, nu, BG, Fpos, ts,
period_days, N, Nt, GAUSS)
EEF_array[yi, :], l_array[yi, :] = PV.EEF(P_xav[yi, :], y_nd,
y0_nd, dy_nd, omega_nd,
N)
filename = 'EEF_array_' + str(pi)
np.save(filename, EEF_array)
# Solver
if BC == 'NO-SLIP':
solution = solver.NO_SLIP_SOLVER(a1, a2, a3, a4, b1, b4, c1, c2, c3,
c4, c5, d1, d3, d4, d5, e4, e5, f1,
f2, f3, f4, Ro * Ftilde1,
Ro * Ftilde2, Ftilde3, Ro * Ftilde4,
Ro * Ftilde5, Ftilde6, N, N2)
if BC == 'FREE-SLIP':
solution = solver.FREE_SLIP_SOLVER(a1, a2, a3, a4, b1, b4, c1, c2, c3,
c4, c5, d1, d3, d4, d5, e4, e5, f1,
f2, f3, f4, Ro * Ftilde1,
Ro * Ftilde2, Ftilde3, Ro * Ftilde4,
Ro * Ftilde5, Ftilde6, N, N2)
utilde, vtilde, htilde = solver.extractSols(solution, N, N2, BC)
u, v, h = solver.SPEC_TO_PHYS(utilde, vtilde, htilde, T, Nt, dx, omega, N)
# Before taking real part, can define an error calculator to call here.
u = np.real(u)
v = np.real(v)
h = np.real(h)
# For use in PV and footprint calculations: the 'full' zonal velocities and interface thicknesses.
u_full = np.zeros((N, N, Nt, 2))
h_full = np.zeros((N, N, Nt, 2))
for j in range(0, N):
u_full[j, :, :, 0] = u[j, :, :, 0] + U1[j]
u_full[j, :, :, 1] = u[j, :, :, 1] + U2[j]
h_full[j, :, :, 0] = h[j, :, :, 0] + H1[j]
def RSW_main():
# Forcing
#plotting.forcingPlot_save(x_grid,y_grid,F3_nd[:,0:N],FORCE,BG,Fpos,N);
#F1_nd, F2_nd, F3_nd = forcing.forcingInv(Ftilde1_nd,Ftilde2_nd,Ftilde3_nd,x_nd,y_nd,dx_nd,N);
#F12, F22 = forcing.F12_from_F3(F3_nd,f_nd,dx_nd,dy_nd,N,N);
#plotting.forcingPlots(x_nd[0:N],y_nd,Ro*F1_nd,Ro*F2_nd,F3_nd,Ftilde1_nd,Ftilde2_nd,Ftilde3_nd,N);
# Coefficients
a1, a2, a3, a4, b4, c1, c2, c3, c4 = solver.SOLVER_COEFFICIENTS(
Ro, Re, K_nd, f_nd, U0_nd, H0_nd, omega_nd, gamma_nd, dy_nd, N)
# Solver
if BC == 'NO-SLIP':
solution = solver.NO_SLIP_SOLVER(a1, a2, a3, a4, f_nd, b4, c1, c2, c3,
c4, Ro * Ftilde1_nd, Ro * Ftilde2_nd,
Ftilde3_nd, N, N2)
if BC == 'FREE-SLIP':
#solution = solver.FREE_SLIP_SOLVER(a1,a2,a3,a4,f_nd,b4,c1,c2,c3,c4,Ro*Ftilde1_nd,Ro*Ftilde2_nd,Ftilde3_nd,N,N2)
solution = solver.FREE_SLIP_SOLVER4(a1, a2, a3, a4, f_nd, b4, c1, c2,
c3, c4, Ro * Ftilde1_nd,
Ro * Ftilde2_nd, Ro * Ftilde3_nd,
N, N2)
utilde_nd, vtilde_nd, etatilde_nd = solver.extractSols(solution, N, N2, BC)
#utilde_nd, vtilde_nd, etatilde_nd = diagnostics.selectModes(utilde_nd,vtilde_nd,etatilde_nd,6,False,N)
u, v, h = solver.SPEC_TO_PHYS(utilde_nd, vtilde_nd, etatilde_nd, T_nd,
dx_nd, omega_nd, N)
# Take real part
u = np.real(u)
v = np.real(v)
h = np.real(h)
# Normalise all solutions by the (non-dimensional) forcing amplitude.
u = u / AmpF_nd
v = v / AmpF_nd
h = h / AmpF_nd
#np.save('u.npy',u)
#np.save('v.npy',v)
#np.save('h.npy',h)
#sys.exit()
# In order to calculate the vorticities/energies of the system, we require full (i.e. BG + forced response) u and eta.
u_full = diagnostics.fullFlow(u, U0_nd)
h_full = diagnostics.fullFlow(h, H0_nd)
#====================================================
# Energy
if doEnergy:
KE_BG, KE_BG_tot, PE_BG, PE_BG_tot = energy.energy_BG(
U0_nd, H0_nd, Ro, y_nd, dy_nd, N)
KE, KE_tot = energy.KE(u_full, v, h_full, x_nd, y_nd, dx_nd, dy_nd, N)
PE, PE_tot = energy.PE(h_full, Ro, x_nd, y_nd, dx_nd, dy_nd, N)
E = KE + PE
#E_tot = KE_tot + PE_tot
Ef, Ef_av = energy.budgetForcing(u_full, v, h_full, F1_nd, F2_nd,
F3_nd, Ro, N, T_nd, omega_nd, Nt)
#Ef, Ef2_av = energy.budgetForcing2(U0_nd,H0_nd,u,v,h,F1_nd,F2_nd,F3_nd,Ro,N,T_nd,omega_nd,Nt)
#Ed, Ed_av = energy.budgetDissipation(u_full,v,h_full,Ro,Re,gamma_nd,dx_nd,dy_nd,T_nd,Nt)
Ed, Ed_av = energy.budgetDissipation2(U0_nd, H0_nd, u, v, h, Ro, Re,
gamma_nd, dx_nd, dy_nd, T_nd, Nt,
N)
Eflux, Eflux_av, uEflux_av, vEflux_av = energy.budgetFlux(
u_full, v, h_full, Ro, dx_nd, dy_nd, T_nd, Nt)
print(np.sum(Ef_av))
print(np.sum(Ed_av))
plt.subplot(221)
plt.contourf(Ef_av)
plt.grid()
plt.colorbar()
plt.subplot(222)
plt.contourf(Ed_av)
plt.grid()
plt.colorbar()
plt.subplot(223)
plt.contourf(vEflux_av)
plt.grid()
plt.colorbar()
plt.subplot(224)
plt.contourf(-Ed_av - Ef_av)
plt.grid()
plt.colorbar()
plt.show()
#uE, vE = energy.flux(KE,u,v)
#Econv, Econv_xav = energy.conv(uE,vE,T_nd,Nt,x_nd,dx_nd,y_nd,dy_nd)
#vE_av = diagnostics.timeAverage(vE,T_nd,Nt)
#plt.contourf(vE_av); plt.colorbar(); plt.show()
#plt.subplot(121); plt.contourf(Econv); plt.colorbar();
#plt.subplot(122); plt.plot(Econv_xav); plt.show()
#quit()
#====================================================
if doCorr:
M = corr.M(u, v, T_nd)
N_ = corr.N(u, v, T_nd)
K = corr.K(u, v, T_nd)
D = corr.D(u, v, 1, dx_nd, dy_nd)
Curl_uD = corr.Curl_uD(u, v, D, T, dx_nd, dy_nd)
theta = corr.orientation(M, N_)
Mnorm = corr.Mnorm(u, v, T_nd)
Nnorm = corr.Nnorm(u, v, T_nd)
Dv, Du = corr.Curl_uD_components(u, v, D, T, dx_nd, dy_nd)
#corr.plotComponents(x_nd,y_nd,M,N_,K,Du)
plotting_bulk.plotKMN(K, Mnorm, Nnorm, x_grid, y_grid, N, 0, 2, '')
plt.show()
#N_ /= diagnostics.domainInt(K,x_nd,dx_nd,y_nd,dy_nd)
N_av = np.trapz(diagnostics.extend(N_), x_nd, dx_nd, axis=1)
Nyy = diagnostics.diff(diagnostics.diff(N_, 0, 0, dy_nd), 0, 0, dy_nd)
Nyy_av = np.trapz(diagnostics.extend(Nyy), x_nd, dx_nd, axis=1)
Curl_uD_av = np.trapz(diagnostics.extend(Curl_uD), x_nd, dx_nd, axis=1)
#np.save('M',M); np.save('N',N_); np.save('Nyy',Nyy)
lim = np.max(np.abs(N_)) / 2.
plt.figure(figsize=[12, 6])
plt.subplot(121)
plt.pcolor(x_grid, y_grid, N_, cmap='bwr', vmin=-lim, vmax=lim)
plt.xlim(-0.1, 0.1)
plt.ylim(-.1, 0.1)
plt.text(-0.08, 0.08, 'N', fontsize=18)
plt.xlabel('x', fontsize=18)
plt.ylabel('y', fontsize=18)
plt.grid()
plt.colorbar()
plt.subplot(122)
plt.plot(N_av, y_nd)
plt.ylim(-.1, .1)
plt.xlabel('<N>', fontsize=18)
plt.grid()
plt.tight_layout()
plt.show()
#plt.figure(figsize=[12,6])
#plt.subplot(121)
#plt.contourf(x_nd[0:N],y_nd,Nyy)
#plt.xlim(-0.1,0.1)
#plt.ylim(-0.1,0.1)
#plt.colorbar()
#plt.subplot(122)
#plt.plot(Nyy_av,y_nd)
#plt.show()
#corr.plotOrientation(theta,K,x_nd,y_nd)
#uav = np.trapz(diagnostics.extend(Du),x_nd,dx_nd,axis=1)
#vav = np.trapz(diagnostics.extend(Dv),x_nd,dx_nd,axis=1)
#plt.plot(uav,label='u')
#plt.plot(vav,label='v')
#plt.plot(Curl_uD_av,label='full')
#plt.legend()
#plt.show()
# Correlation.
# Central half?
#cs = N / 4;
#ce = N - N / 4;
#corr = corr.arrayCorrTime(u[cs:ce,cs:ce,:],v[cs:ce,cs:ce,:]);
#print corr
#quit()
#====================================================
# Error - if calculated, should be done before real part of solution is taken
if errorPhys:
e1, e2, e3 = diagnostics.error(u, v, h, dx_nd, dy_nd, dt_nd, U0_nd,
H0_nd, Ro, gamma_nd, Re, f_nd, F1_nd,
F2_nd, F3_nd, T_nd, ts, omega_nd, N)
e = np.sqrt((e1**2 + e2**2 + e3**2) / 3.0)
print 'Error = ' + str(e) + '. Error split = ' + str(e1) + ', ' + str(
e2) + ', ' + str(e3)
if errorSpec:
error_spec = np.zeros((3, N))
# An array to save the spectral error at each wavenumber for each equation.
for i in range(0, N):
error_spec[:,i] = diagnostics.specError(utilde_nd[:,i],vtilde_nd[:,i],etatilde_nd[:,i],Ftilde1_nd[:,i],Ftilde2_nd[:,i],Ftilde3_nd[:,i],a1[:,i],a2,a3,a4[i],\
b4,c1[:,i],c2,c3,c4[:,i],f_nd,Ro,K_nd[i],H0_nd,y_nd,dy_nd,N)
for eq in range(0, 3):
error = sum(error_spec[eq, :]) / N
print('Error' + str(int(eq + 1)) + '=' + str(error))
#====================================================
# Momentum footprints
#====================================================
if doMomentum:
uu, uv, vv = momentum.fluxes(u, v)
Mu, Mv, Mu_xav, Mv_xav = momentum.footprint(uu, uv, vv, x_nd, T_nd,
dx_nd, dy_nd, N, Nt)
#plotting.MomFootprints(Mu,Mv,Mu_xav,Mv_xav);
Mumax = np.max(Mu_xav)
plt.plot(Mu_xav / Mumax, y_nd, linewidth=2., color='k')
plt.text(-0.4, 0.4, str(Mumax))
plt.xlabel('Zonal mom. flux convergence', fontsize=18)
plt.ylabel('y', fontsize=18)
plt.ylim([-.5, .5])
plt.yticks((-1. / 2, -1. / 4, 0, 1. / 4, 1. / 2))
plt.grid()
plt.show()
if False:
plt.subplot(121)
plt.pcolor(x_grid, y_grid, Mu, cmap='bwr', vmin=-.5, vmax=.5)
plt.xticks((-1. / 2, -1. / 4, 0, 1. / 4, 1. / 2))
plt.yticks((-1. / 2, -1. / 4, 0, 1. / 4, 1. / 2))
plt.xlabel('x', fontsize=16)
plt.ylabel('y', fontsize=16)
plt.axis([x_grid.min(),
x_grid.max(),
y_grid.min(),
y_grid.max()])
plt.grid(b=True, which='both', color='0.65', linestyle='--')
plt.colorbar()
plt.subplot(122)
plt.plot(Mu_xav, y_nd)
plt.xlabel('y')
plt.show()
plt.subplot(121)
plt.pcolor(x_grid, y_grid, Mv, cmap='bwr', vmin=-1., vmax=1.)
plt.xticks((-1. / 2, -1. / 4, 0, 1. / 4, 1. / 2))
plt.yticks((-1. / 2, -1. / 4, 0, 1. / 4, 1. / 2))
plt.xlabel('x', fontsize=16)
plt.ylabel('y', fontsize=16)
plt.axis([x_grid.min(),
x_grid.max(),
y_grid.min(),
y_grid.max()])
plt.grid(b=True, which='both', color='0.65', linestyle='--')
plt.subplot(122)
plt.plot(Mv_xav, y_nd)
plt.tight_layout()
plt.show()
EEF_u, EEF_v = momentum.EEF_mom(Mu_xav, Mv_xav, y_nd, y0_nd, y0_index,
dy_nd, omega_nd, N)
#print(EEF_u, EEF_v);
# PV and PV footprints
#====================================================
# Calculate PV fields, footprints and equivalent eddy fluxes (EEFs)
if doPV:
PV_prime, PV_full, PV_BG = PV.potentialVorticity(
u, v, h, u_full, h_full, H0_nd, U0_nd, N, Nt, dx_nd, dy_nd, f_nd,
Ro)
#PV_prime1, PV_prime2, PV_prime3 = PV.potentialVorticity_linear(u,v,h,H0_nd,U0_nd,N,Nt,dx_nd,dy_nd,f_nd,Ro)
uq, Uq, uQ, UQ, vq, vQ = PV.fluxes(u, v, U0_nd, PV_prime, PV_BG, N, Nt)
# Keep these next two lines commented out unless testing effects of normalisation.
# uq, Uq, uQ, UQ, vq, vQ = uq/AmpF_nd**2, Uq/AmpF_nd**2, uQ/AmpF_nd**2, UQ/AmpF_nd**2, vq/AmpF_nd**2, vQ/AmpF_nd**2
# PV_prime, PV_full = PV_prime/AmpF_nd, PV_full/AmpF_nd
if doFootprints:
if footprintComponents:
P, P_uq, P_uQ, P_Uq, P_vq, P_vQ, P_xav, P_uq_xav, P_uQ_xav, P_Uq_xav, P_vq_xav, P_vQ_xav = PV.footprintComponents(
uq, Uq, uQ, vq, vQ, x_nd, T_nd, dx_nd, dy_nd, N, Nt)
#plotting.footprintComponentsPlot(uq,Uq,uQ,vq,vQ,P,P_uq,P_Uq,P_uQ,P_vq,P_vQ,P_xav,P_uq_xav,P_uQ_xav,P_Uq_xav,P_vq_xav,P_vQ_xav,x_nd,y_nd,N,Nt);
#plotting.plotPrimaryComponents(P_uq,P_vq,P_uq_xav,P_vq_xav,x_nd,y_nd,FORCE,BG,Fpos,N);
else:
P, P_xav = PV.footprint(uq, Uq, uQ, UQ, vq, vQ, x_nd, T_nd,
dx_nd, dy_nd, N, Nt)
if doEEFs:
from scipy.ndimage.measurements import center_of_mass
iii = center_of_mass(np.abs(P_xav))[0]
i1 = int(iii)
i2 = int(i1 + 1)
r = iii - i1
#print(iii,i1,i2,r)
com = y_nd[int(iii)]
#print(y0_index-iii)
if footprintComponents:
EEF_array = PV.EEF_components(P_xav, P_uq_xav, P_uQ_xav,
P_Uq_xav, P_vq_xav, P_vQ_xav,
y_nd, y0_nd, y0_index, dy_nd,
omega_nd, N)
# This returns EEF_array, an array with the following structure:
# EEF_array = ([EEF_north,EEF_south],[uq_north,uq_south],[Uq_north,Uq_south],[uQ_north,uQ_south],[vq_north,vq_south],[vQ_north,vQ_south]).
EEF_north = EEF_array[0, 0]
EEF_south = EEF_array[0, 1]
else:
EEF, l = PV.EEF(P_xav, y_nd, com, int(iii), dy_nd, N)
# These lines for Gaussian EEFs, when com jumps from 1 grid point to next, need to smooth EEF.
#EEF1, l = PV.EEF(P_xav,y_nd,y_nd[i1],i1,dy_nd,N)
#EEF2, l = PV.EEF(P_xav,y_nd,y_nd[i2],i2,dy_nd,N)
#EEF_ = (1 - r) * EEF1 + r * EEF2
EEF_north = EEF[0]
EEF_south = EEF[1]
EEF = EEF_north - EEF_south
print(EEF)
Pmax = np.max(abs(P_xav))
plt.plot(P_xav / Pmax, y_nd, linewidth=2., color='k')
plt.text(-0.4, 0.4, str(Pmax))
plt.xlabel('PV flux convergence', fontsize=18)
plt.ylabel('y', fontsize=18)
plt.ylim([-.5, .5])
plt.yticks((-1. / 2, -1. / 4, 0, 1. / 4, 1. / 2))
plt.grid()
plt.show()
# Buoyancy footprints
#====================================================
if doThickness:
# Should these be zero, according to conservation of mass?
Pb, Pb_xav = thickness.footprint(u_full, v, h_full, x_nd, y_nd, T_nd,
dx_nd, dy_nd, dt_nd, N, Nt)
#output.ncSave(utilde_nd,vtilde_nd,etatilde_nd,u,v,h,x_nd,y_nd,K_nd,T_nd,PV_full,PV_prime,PV_BG,Pq,EEFq,N,Nt);
#sys.exit()
#====================================================
# Plots
#====================================================
#====================================================
# Call the function that plots the forcing in physical and physical-spectral space.
if plotForcing:
plotting.forcingPlots(x_nd, y_nd, F1_nd, F2_nd, F3_nd, Ftilde1_nd,
Ftilde2_nd, Ftilde3_nd, N)
#forcing_1L.forcingInv(Ftilde1_nd,Ftilde2_nd,Ftilde3_nd,x_nd,y_nd,dx_nd,N); # For diagnostic purposes
# Background state plots (inc. BG SSH, BG flow, BG PV)
if plotBG:
plotting.bgPlots(y_nd, H0_nd, U0_nd, PV_BG)
# Soltuion Plots
if plotSol:
plotting.solutionPlots(x_nd, y_nd, u, v, h, ts, FORCE, BG, Fpos, N,
x_grid, y_grid, True)
#plotting.solutionPlots_save(x_nd,y_nd,u,v,h,ts,FORCE,BG,Fpos,N,x_grid,y_grid,True);
#plotting.solutionPlotsDim(x,y,u,v,eta,ts,L,FORCE,BG,Fpos,N);
# Plots of PV and zonally averaged PV
if doPV:
if plotPV:
#plotting.pvPlots(PV_full,PV_prime,x_nd,y_nd);
plotting.pvPlots_save(PV_full, PV_prime, P, P_xav, x_nd, y_nd, ts,
FORCE, BG, Fpos, N, U0_str, x_grid, y_grid,
True)
if plotPV_av:
plotting.PV_avPlots(x_nd, y_nd, PV_prime, PV_BG, PV_full, ts,
FORCE, BG, Fpos, N)
if doFootprints:
if plotFootprint:
plotting.footprintPlots(x_nd, y_nd, P, P_xav, Fpos, BG, FORCE,
nu, r0, period_days, U0_nd, U, N)
# Phase and amplitude
if plotPhaseAmp:
plotting.solutionPlotsAmp(x_nd, y_nd, u, v, h, ts, FORCE, BG, Fpos, N)
plotting.solutionPlotsPhase(x_nd, y_nd, u, v, h, ts, FORCE, BG, Fpos,
N)
def EEF_main(set_, pi):
NU = len(set_)
# Initialise output arrays
EEF_array = np.zeros((NU, nn, 2))
com = np.zeros((NU, nn))
E_array = np.zeros((NU))
M_array = np.zeros((NU, N, N))
N_array = np.zeros((NU, N, N))
# Now start the loop over each forcing index.
for ui in range(0, NU):
# Redefine U0 and H0.
#sigma = set_[ui]
#Umag = set_[ui]
#U0, H0 = BG_state.BG_Gaussian(Umag,sigma,JET_POS,Hflat,f0,beta,g,y,L,N)
#U0_nd = U0 / U;
#H0_nd = H0 / chi;
# r0
#r0 = set_[ui]
#r0_nd = r0 / L
# period
period_days = set_[ui]
period = 3600. * 24. * period_days
omega = 1. / (period)
T = np.linspace(0, period, Nt + 1)
dt = T[1] - T[0]
t = T[ts]
omega_nd = omega * T_adv
t_nd = t / T_adv
T_nd = T / T_adv
dt_nd = dt / T_adv
# k
#nu = set_[ui]
#Re = L * U / nu
a1, a2, a3, a4, b4, c1, c2, c3, c4 = solver.SOLVER_COEFFICIENTS(
Ro, Re, K_nd, f_nd, U0_nd, H0_nd, omega_nd, gamma_nd, dy_nd, N)
for yi in range(0, nn):
y0 = y0_set[yi]
# Redefine y0 and the forcing in each run.
y0_index = y0_index_set[yi]
y0_nd = y0 / L
# Forcing
F1_nd, F2_nd, F3_nd, Ftilde1_nd, Ftilde2_nd, Ftilde3_nd = forcing.forcing_cts2(
x_nd, y_nd, K_nd, y0_nd, r0_nd, N, FORCE, AmpF_nd, f_nd, f0_nd,
bh, dx_nd, dy_nd)
solution = solver.FREE_SLIP_SOLVER(a1, a2, a3, a4, f_nd, b4, c1,
c2, c3, c4, Ro * Ftilde1_nd,
Ro * Ftilde2_nd, Ftilde3_nd, N,
N2)
utilde_nd, vtilde_nd, etatilde_nd = solver.extractSols(
solution, N, N2, BC)
u, v, h = solver.SPEC_TO_PHYS(utilde_nd, vtilde_nd, etatilde_nd,
T_nd, dx_nd, omega_nd, N)
# Take real part.
u = np.real(u)
v = np.real(v)
h = np.real(h)
# Normalise all solutions by the (non-dimensional) forcing amplitude.
u = u / AmpF_nd
v = v / AmpF_nd
h = h / AmpF_nd
# In order to calculate the vorticities of the system, we require full (i.e. BG + forced response) u and eta.
h_full = np.zeros((N, N, Nt))
u_full = np.zeros((N, N, Nt))
for j in range(0, N):
h_full[j, :, :] = h[j, :, :] + H0_nd[j]
u_full[j, :, :] = u[j, :, :] + U0_nd[j]
#==
# Correlations (can do before or after energy)
M_array[ui, :, :] = corr.M(u, v, T_nd)
N_array[ui, :, :] = corr.N(u, v, T_nd)
#==
# Energy
#KE_BG, KE_BG_tot, PE_BG, PE_BG_tot = energy.energy_BG(U0_nd,H0_nd,Ro,y_nd,dy_nd,N)
#KE, KE_tot = energy.KE(u_full,v,h_full,x_nd,y_nd,dx_nd,dy_nd,N)
#PE, PE_tot = energy.PE(h_full,Ro,x_nd,y_nd,dx_nd,dy_nd,N)
#E_tot = KE_tot + PE_tot - KE_BG_tot - PE_BG_tot
# Use time-mean KE omitting h for now. Find a better way to do this
KE = u**2 + v**2
KE_tot = np.zeros(Nt)
for ti in range(0, Nt):
KE_tot[ti] = diagnostics.domainInt(KE[:, :, ti], x_nd, dx_nd,
y_nd, dy_nd)
E_array[ui] = diagnostics.timeAverage1D(KE_tot, T_nd, Nt)
#import matplotlib.pyplot as plt
#plt.plot(KE_tot);plt.show()
# Normalise by energy
u = u / np.sqrt(E_array[ui])
v = v / np.sqrt(E_array[ui])
h = h / np.sqrt(E_array[ui])
#==
# Calculate PV fields and PV fluxes.
PV_prime, PV_full, PV_BG = PV.potentialVorticity(
u, v, h, u_full, h_full, H0_nd, U0_nd, N, Nt, dx_nd, dy_nd,
f_nd, Ro)
uq, Uq, uQ, UQ, vq, vQ = PV.fluxes(u, v, U0_nd, PV_prime, PV_BG, N,
Nt)
P, P_xav = PV.footprint(uq, Uq, uQ, UQ, vq, vQ, x_nd, T_nd, dx_nd,
dy_nd, N, Nt)
com[ui, yi] = center_of_mass(np.abs(P_xav))[0]
i1 = int(com[ui, yi])
i2 = int(i1 + 1)
r = com[ui, yi] - i1
# For Gaussian flows, need to calculate EEF about new center of mass.
# This requires calculation of EEF at two grid points to aid continuity.
#EEF1, l_PV = PV.EEF(P_xav,y_nd,y_nd[i1],i1,dy_nd,N)
#EEF2, l_PV = PV.EEF(P_xav,y_nd,y_nd[i2],i2,dy_nd,N)
#EEF_array[ui,yi,:] = (1 - r) * EEF1 + r * EEF2
EEF_array[ui, yi, :], l_PV = PV.EEF(P_xav, y_nd, y_nd[y0_index],
y0_index, dy_nd, N)
filename = 'EEF_array' + str(pi)
np.save(filename, EEF_array)
filename_com = 'com' + str(pi)
np.save(filename_com, com)
def EIG_PROJ_main(dim):
'''
This function projects the SW solution onto eigenmodes as outputted by EIG.py.
The aim is to look at the number of modes required for certain levels of accuracy.
To do this we can look at the error in the whole solution (x,y), or look at the
error at specific wavenumbers (e.g. wavenumbers where there is a lot of weight).
'''
# Dimensions
Nm = dim # How many modes to use in the decomposition at each wavenumber (dim is maximum).
Nk = N
Ke = 10 # Wavenumber to look at error in spectral space.
Np = 50 # Number of modes to keep in decomposition.
# The 1L SW solution
#====================================================
I = np.complex(0.0, 1.0)
a1, a2, a3, a4, b4, c1, c2, c3, c4 = solver.SOLVER_COEFFICIENTS(
Ro, Re, K_nd, f_nd, U0_nd, H0_nd, omega_nd, gamma_nd, dy_nd, N)
# Define the solution in (k,y)-space - can be from FILE or a NEW run.
solution = solver.FREE_SLIP_SOLVER(a1, a2, a3, a4, f_nd, b4, c1, c2, c3,
c4, Ro * Ftilde1_nd, Ro * Ftilde2_nd,
Ftilde3_nd, N, N2) / AmpF_nd
utilde_nd, vtilde_nd, etatilde_nd = solver.extractSols(solution, N, N2, BC)
u, v, h = solver.SPEC_TO_PHYS(utilde_nd, vtilde_nd, etatilde_nd, T_nd,
dx_nd, omega_nd, N)
u = np.real(u)
v = np.real(v)
h = np.real(h)
print('solved')
#====================================================
# Perform decomposition and build projection.
#====================================================
theta = np.zeros((dim, N), dtype=complex)
theta_abs = np.zeros((dim, N))
proj = np.zeros((dim, N), dtype=complex)
projk = np.zeros((dim), dtype=complex)
for i in range(233, 234):
print(i)
k = K_nd[i]
# Load modes
path = '/home/mike/Documents/GulfStream/RSW/DATA/1L/EIG/256/04/'
#path = ''
ncFile = path + 'RSW1L_Eigenmodes_k' + str(int(k)) + '_N257.nc'
val, vec, count = output_read.ncReadEigenmodes(ncFile)
Phi = solution[:,
i] # 1. Assign the solution corresponding to wavenumber k=K_nd[ii].
theta_tmp = np.linalg.solve(vec, Phi) # 2.
theta_abs_tmp = np.abs(theta_tmp)
dom_index = np.argsort(
-theta_abs_tmp
) # 3. The indices of the modes, ordered by 'dominance'.
theta[:, i] = theta_tmp[dom_index]
theta_abs[:, i] = np.abs(theta[:, i])
vec = vec[:, dom_index]
# Now loop over each mode (at wavenumber k)
plt.plot(np.abs(theta[:, i]))
plt.show()
np.save('mode1', vec[:, 0])
np.save('mode2', vec[:, 1])
np.save('mode3', vec[:, 2])
np.save('mode4', vec[:, 3])
theta0123 = theta[0:4, i]
np.save('theta0123', theta0123)
for mi in range(0, 100):
proj[:, i] = proj[:, i] + theta[mi, i] * vec[:, mi]
theta_abs_tot = np.sum(theta_abs, axis=0)
utilde_proj = np.zeros((N, N), dtype=complex)
vtilde_proj = np.zeros((N, N), dtype=complex)
etatilde_proj = np.zeros((N, N), dtype=complex)
# Separate projection into flow components.
for j in range(0, N):
utilde_proj[j, :] = proj[j, :]
etatilde_proj[j, :] = proj[N + N2 + j, :]
for j in range(0, N2):
vtilde_proj[j + 1, :] = proj[N + j, :]
u_proj, v_proj, eta_proj = solver.SPEC_TO_PHYS(utilde_proj, vtilde_proj,
etatilde_proj, T_nd, dx_nd,
omega_nd, N)
u_proj = np.real(u_proj)
v_proj = np.real(v_proj)
eta_proj = np.real(eta_proj)
c = np.corrcoef(u[:, :, ts].reshape(N**2), u_proj[:, :,
ts].reshape(N**2))[0, 1]
print(c)
#====================================================
# Plot
#====================================================
if True:
plt.plot(utilde_proj[:, 3])
plt.plot(utilde_nd[:, 3])
plt.show()
plt.subplot(121)
plt.contourf(u[:, :, ts])
plt.colorbar()
plt.subplot(122)
plt.contourf(u_proj[:, :, ts])
plt.colorbar()
plt.show()
# Compare projection with solution.
#====================================================
corrk = np.zeros(N)
#for i in range(1,N):
# corrk[i] = np.corrcoef(utilde_nd[:,i],utilde_proj[:,i])[0,1]
return u, v, h, u_proj, v_proj, eta_proj
def EEF_main(set_, pi):
NU = len(set_)
# Initialise output arrays
EEF_array = np.zeros((NU, 2))
E_array = np.zeros((NU))
M_array = np.zeros((NU, N, N))
N_array = np.zeros((NU, N, N))
Mu_array = np.zeros((NU, N))
Munorm_array = np.zeros((NU, N))
# Now start the loop over each forcing index.
for ui in range(0, NU):
# Redefine U0 and H0
#sigma = set_[ui]
Umag = set_[ui]
U0, H0 = BG_state.BG_uniform(Umag, Hflat, f0, beta, g, y, N)
U0_nd = U0 / U
H0_nd = H0 / chi
# Solution
a1, a2, a3, a4, b4, c1, c2, c3, c4 = solver.SOLVER_COEFFICIENTS(
Ro, Re, K_nd, f_nd, U0_nd, H0_nd, omega_nd, gamma_nd, dy_nd, N)
solution = solver.FREE_SLIP_SOLVER(a1, a2, a3, a4, f_nd, b4, c1, c2,
c3, c4, Ro * Ftilde1_nd,
Ro * Ftilde2_nd, Ftilde3_nd, N, N2)
utilde_nd, vtilde_nd, etatilde_nd = solver.extractSols(
solution, N, N2, BC)
u, v, h = solver.SPEC_TO_PHYS(utilde_nd, vtilde_nd, etatilde_nd, T_nd,
dx_nd, omega_nd, N)
# Take real part.
u = np.real(u)
v = np.real(v)
h = np.real(h)
# Normalise all solutions by the (non-dimensional) forcing amplitude.
u = u / AmpF_nd
v = v / AmpF_nd
h = h / AmpF_nd
# In order to calculate the vorticities of the system, we require full (i.e. BG + forced response) u and eta.
#h_full = np.zeros((N,N,Nt))
#u_full = np.zeros((N,N,Nt))
#for j in range(0,N):
# h_full[j,:,:] = h[j,:,:] + H0_nd[j]
# u_full[j,:,:] = u[j,:,:] + U0_nd[j]
#==
# Correlations (can do before or after energy)
#M_array[ui,:,:] = corr.M(u,v,T_nd)
#N_array[ui,:,:] = corr.N(u,v,T_nd)
#==
# Energy
#KE_BG, KE_BG_tot, PE_BG, PE_BG_tot = energy.energy_BG(U0_nd,H0_nd,Ro,y_nd,dy_nd,N)
#KE, KE_tot = energy.KE(u_full,v,h_full,x_nd,y_nd,dx_nd,dy_nd,N)
#PE, PE_tot = energy.PE(h_full,Ro,x_nd,y_nd,dx_nd,dy_nd,N)
#E_tot = KE_tot + PE_tot - KE_BG_tot - PE_BG_tot
# Use time-mean KE omitting h for now. Find a better way to do this
KE = u**2 + v**2
KE_tot = np.zeros(Nt)
for ti in range(0, Nt):
KE_tot[ti] = diagnostics.domainInt(KE[:, :, ti], x_nd, dx_nd, y_nd,
dy_nd)
E_array[ui] = diagnostics.timeAverage1D(KE_tot, T_nd, Nt)
# Momentum
#==========
uu, uv, vv = momentum.fluxes(u, v)
Mu, Mv, Mu_array[ui, :], Mv_xav = momentum.footprint(
uu, uv, vv, x_nd, T_nd, dx_nd, dy_nd, N, Nt)
#import matplotlib.pyplot as plt
#plt.plot(KE_tot);plt.show()
# Normalise by energy
#u = u / np.sqrt(E_array[ui]); v = v / np.sqrt(E_array[ui]); h = h / np.sqrt(E_array[ui])
#==
# Calculate PV fields and PV fluxes.
#PV_prime, PV_full, PV_BG = PV.potentialVorticity(u,v,h,u_full,h_full,H0_nd,U0_nd,N,Nt,dx_nd,dy_nd,f_nd,Ro)
#uq, Uq, uQ, UQ, vq, vQ = PV.fluxes(u,v,U0_nd,PV_prime,PV_BG,N,Nt)
#P, P_xav = PV.footprint(uq,Uq,uQ,UQ,vq,vQ,x_nd,T_nd,dx_nd,dy_nd,N,Nt)
#EEF_array[ui,:], l_PV = PV.EEF(P_xav,y_nd,y_nd[y0_index],y0_index,dy_nd,N)
#==
# Repeat process with normalised velocities.
u = u / np.sqrt(E_array[ui])
v = v / np.sqrt(E_array[ui])
h = h / np.sqrt(E_array[ui])
uu, uv, vv = momentum.fluxes(u, v)
Mu, Mv, Munorm_array[ui, :], Mv_xav = momentum.footprint(
uu, uv, vv, x_nd, T_nd, dx_nd, dy_nd, N, Nt)
# In order to calculate the vorticities of the system, we require full (i.e. BG + forced response) u and eta.
#h_full = np.zeros((N,N,Nt))
#u_full = np.zeros((N,N,Nt))
#for j in range(0,N):
# h_full[j,:,:] = h[j,:,:] + H0_nd[j]
# u_full[j,:,:] = u[j,:,:] + U0_nd[j]
#==
# Calculate PV fields and PV fluxes.
#PV_prime, PV_full, PV_BG = PV.potentialVorticity(u,v,h,u_full,h_full,H0_nd,U0_nd,N,Nt,dx_nd,dy_nd,f_nd,Ro)
#uq, Uq, uQ, UQ, vq, vQ = PV.fluxes(u,v,U0_nd,PV_prime,PV_BG,N,Nt)
#P, P_xav = PV.footprint(uq,Uq,uQ,UQ,vq,vQ,x_nd,T_nd,dx_nd,dy_nd,N,Nt)
#EEFnorm_array[ui,:], l_PV = PV.EEF(P_xav,y_nd,y_nd[y0_index],y0_index,dy_nd,N)
#np.save('EEF_array'+str(pi),EEF_array)
#np.save('EEFnorm_array'+str(pi),EEFnorm_array)
#np.save('M_array'+str(pi),M_array)
#np.save('N_array'+str(pi),N_array)
np.save('E_array' + str(pi), E_array)
np.save('Mu_array' + str(pi), Mu_array)
np.save('Munorm_array' + str(pi), Munorm_array)
def RSW_main():
# Coefficients
a1, a2, a3, a4, b1, b4, c1, c2, c3, c4, c5, d1, d3, d4, d5, e4, e5, f1, f2, f3, f4 = solver.SOLVER_COEFFICIENTS(
Ro, Re, K, f, U1, U2, H1, H2, rho1_nd, rho2_nd, omega, gamma, dy, N)
# Solver
if BC == 'NO-SLIP':
solution = solver.NO_SLIP_SOLVER(a1, a2, a3, a4, b1, b4, c1, c2, c3,
c4, c5, d1, d3, d4, d5, e4, e5, f1,
f2, f3, f4, Ro * Ftilde1,
Ro * Ftilde2, Ftilde3, Ro * Ftilde4,
Ro * Ftilde5, Ftilde6, N, N2)
if BC == 'FREE-SLIP':
solution = solver.FREE_SLIP_SOLVER4(a1, a2, a3, a4, b1, b4, c1, c2, c3,
c4, c5, d1, d3, d4, d5, e4, e5, f1,
f2, f3, f4, Ro * Ftilde1,
Ro * Ftilde2, Ftilde3,
Ro * Ftilde4, Ro * Ftilde5,
Ftilde6, N, N2)
#===================================================
utilde, vtilde, htilde = solver.extractSols(solution, N, N2, BC)
u, v, h = solver.SPEC_TO_PHYS(utilde, vtilde, htilde, T, Nt, dx, omega, N)
# Before taking real part, can define an error calculator to call here.
u = np.real(u)
v = np.real(v)
h = np.real(h)
#u = u / AmpF_nd
#v = v / AmpF_nd
#h = h / AmpF_nd
# For use in PV and footprint calculations: the 'full' zonal velocities and interface thicknesses.
u_full = np.zeros((N, N, Nt, 2))
h_full = np.zeros((N, N, Nt, 2))
for j in range(0, N):
u_full[j, :, :, 0] = u[j, :, :, 0] + U1[j]
u_full[j, :, :, 1] = u[j, :, :, 1] + U2[j]
h_full[j, :, :, 0] = h[j, :, :, 0] + H1[j]
h_full[j, :, :, 1] = h[j, :, :, 1] + H2[j]
# Call function calculate PV in each layer.
q = np.zeros((N, N, Nt, 2))
q_full = np.zeros((N, N, Nt, 2))
Q = np.zeros((N, 2))
q[:, :, :,
0], q_full[:, :, :,
0], Q[:, 0] = PV.vort(u[:, :, :, 0], v[:, :, :, 0], h[:, :, :,
0],
u_full[:, :, :, 0], h_full[:, :, :, 0],
H1, U1, N, Nt, dx, dy, f)
q[:, :, :,
1], q_full[:, :, :,
1], Q[:, 1] = PV.vort(u[:, :, :, 1], v[:, :, :, 1], h[:, :, :,
1],
u_full[:, :, :, 1], h_full[:, :, :, 1],
H2, U2, N, Nt, dx, dy, f)
# Calculate footprints using previously calculated PV. Most interseted in the upper layer.
P, P_xav = PV.footprint(u_full[:, :, :, 0], v[:, :, :, 0],
q_full[:, :, :, 0], x, y, dx, dy, T, Nt)
# PLOTS
#====================================================
plt.contourf(u[:, :, 0, 1])
plt.colorbar()
plt.show()
quit()
plotting.solutionPlots(x, y, x_grid, y_grid, u, v, h, ts, N, False)
plotting.footprintPlots(x, y, P, P_xav)
def EEF_main(set_, pi):
NU = len(set_)
# Initialise output arrays
EEF_array = np.zeros((NU, 2))
# Now start the loop over each forcing index.
for ui in range(0, NU):
# Redefine U0 and H0.
#sigma = set_[ui]
Umag1 = set_[ui]
U1, U2, H1, H2 = BG_state.BG_uniform_none(Umag1, H1_flat, H2_flat,
rho1_nd, rho2_nd, f0, beta,
g, y, N)
U1 = U1 / U
U2 = U2 / U
H1 = H1 / chi
H2 = H2 / chi
# Solver coeffs depend on BG state.
a1, a2, a3, a4, b1, b4, c1, c2, c3, c4, c5, d1, d3, d4, d5, e4, e5, f1, f2, f3, f4 = solver.SOLVER_COEFFICIENTS(
Ro, Re, K, f, U1, U2, H1, H2, rho1_nd, rho2_nd, omega, gamma, dy,
N)
# Solve.
solution = solver.FREE_SLIP_SOLVER(a1, a2, a3, a4, b1, b4, c1, c2, c3,
c4, c5, d1, d3, d4, d5, e4, e5, f1,
f2, f3, f4, Ro * Ftilde1,
Ro * Ftilde2, Ftilde3, Ro * Ftilde4,
Ro * Ftilde5, Ftilde6, N, N2)
# Extract flow components.
utilde, vtilde, htilde = solver.extractSols(solution, N, N2, BC)
u, v, h = solver.SPEC_TO_PHYS(utilde, vtilde, htilde, T, Nt, dx, omega,
N)
# Take real part.
u = np.real(u)
v = np.real(v)
h = np.real(h)
# For use in PV and footprint calculations: the 'full' zonal velocities and interface thicknesses.
u_full = np.zeros((N, N, Nt, 2))
h_full = np.zeros((N, N, Nt, 2))
for j in range(0, N):
u_full[j, :, :, 0] = u[j, :, :, 0] + U1[j]
u_full[j, :, :, 1] = u[j, :, :, 1] + U2[j]
h_full[j, :, :, 0] = h[j, :, :, 0] + H1[j]
h_full[j, :, :, 1] = h[j, :, :, 1] + H2[j]
# Call function calculate PV in upper layer.
q = np.zeros((N, N, Nt, 2))
q_full = np.zeros((N, N, Nt, 2))
Q = np.zeros((N, 2))
q[:, :, :,
0], q_full[:, :, :,
0], Q[:, 0] = PV.vort(u[:, :, :, 0], v[:, :, :, 0],
h[:, :, :, 0], u_full[:, :, :, 0],
h_full[:, :, :,
0], H1, U1, N, Nt, dx, dy, f)
# Calculate footprints using previously calculated PV.
P, P_xav = PV.footprint(u_full[:, :, :, 0], v[:, :, :, 0],
q_full[:, :, :, 0], x, y, dx, dy, T, Nt)
# EEF
EEF_array[ui, :], l = PV.EEF(P_xav, y, y0, y0_index, dy, N)
# End loop.
# Save output from processor pi.
np.save('EEF_array' + str(pi), EEF_array)
def RSW_main(): # Forcing #plotting.forcingPlot_save(x_grid,y_grid,F3_nd[:,0:N],FORCE,BG,Fpos,N); #F1_nd, F2_nd, F3_nd = forcing.forcingInv(Ftilde1_nd,Ftilde2_nd,Ftilde3_nd,x_nd,y_nd,dx_nd,N); #F1_nd, F2_nd = forcing.F12_from_F3(F3_nd,f_nd,dx_nd,dy_nd,N,N); #plotting.forcingPlots(x_nd[0:N],y_nd,Ro*F1_nd,Ro*F2_nd,F3_nd,Ftilde1_nd,Ftilde2_nd,Ftilde3_nd,N); # sys.exit(); # Coefficients a1,a2,a3,a4,b4,c1,c2,c3,c4 = solver.SOLVER_COEFFICIENTS(Ro,Re,K_nd,f_nd,U0_nd,H0_nd,omega_nd,gamma_nd,dy_nd,N) # Solver if BC == 'NO-SLIP': solution = solver.NO_SLIP_SOLVER(a1,a2,a3,a4,f_nd,b4,c1,c2,c3,c4,Ro*Ftilde1_nd,Ro*Ftilde2_nd,Ftilde3_nd,N,N2) if BC == 'FREE-SLIP': #solution = solver.FREE_SLIP_SOLVER(a1,a2,a3,a4,f_nd,b4,c1,c2,c3,c4,Ro*Ftilde1_nd,Ro*Ftilde2_nd,Ftilde3_nd,N,N2) solution = solver.FREE_SLIP_SOLVER4(a1,a2,a3,a4,f_nd,b4,c1,c2,c3,c4,Ro*Ftilde1_nd,Ro*Ftilde2_nd,Ro*Ftilde3_nd,N,N2) utilde_nd, vtilde_nd, etatilde_nd = solver.extractSols(solution,N,N2,BC); u, v, h = solver.SPEC_TO_PHYS(utilde_nd,vtilde_nd,etatilde_nd,T_nd,dx_nd,omega_nd,N); PP = np.zeros(N) EEF = 0. for iji in range(0,N): print(iji) ut = np.zeros((N,N),dtype=complex) vt = np.zeros((N,N),dtype=complex) ht = np.zeros((N,N),dtype=complex) ut[:,iji] = utilde_nd[:,iji] vt[:,iji] = vtilde_nd[:,iji] ht[:,iji] = etatilde_nd[:,iji] u, v, h = solver.SPEC_TO_PHYS(ut,vt,ht,T_nd,dx_nd,omega_nd,N); u = np.real(u) v = np.real(v) h = np.real(h) # Normalise all solutions by the (non-dimensional) forcing amplitude. u = u / AmpF_nd v = v / AmpF_nd h = h / AmpF_nd # In order to calculate the vorticities/energies of the system, we require full (i.e. BG + forced response) u and eta. h_full = np.zeros((N,N,Nt)) u_full = np.zeros((N,N,Nt)) for j in range(0,N): h_full[j,:,:] = h[j,:,:] + H0_nd[j] u_full[j,:,:] = u[j,:,:] + U0_nd[j] PV_prime, PV_full, PV_BG = PV.potentialVorticity(u,v,h,u_full,h_full,H0_nd,U0_nd,N,Nt,dx_nd,dy_nd,f_nd,Ro) uq, Uq, uQ, UQ, vq, vQ = PV.fluxes(u,v,U0_nd,PV_prime,PV_BG,N,Nt) P, P_xav = PV.footprint(uq,Uq,uQ,UQ,vq,vQ,x_nd,T_nd,dx_nd,dy_nd,N,Nt) PP += P_xav from scipy.ndimage.measurements import center_of_mass iii = center_of_mass(np.abs(P_xav))[0] com = y_nd[int(iii)] EEF, l = PV.EEF(P_xav,y_nd,com,int(iii),dy_nd,N) EEF_north = EEF[0]; EEF_south = EEF[1]; EEF_tmp = EEF_north - EEF_south; EEF += EEF_tmp plt.plot(PP) plt.show() print(EEF)