Figure-8.ipynb

Kernel: Python 3 (system-wide)

import matplotlib.pyplot as plt
import xarray as xr
import numpy as np
plt.rcParams.update({'font.size': 18})
plt.rc('text', usetex=True)
plt.rc('text.latex',preamble=r"\usepackage{amsmath}")
plt.rc('font', family='serif')

# Loading in datasets
ds5 = xr.open_dataset('../Data/solver_lowpass_x_t_omega_2_Nint_100_strat_3_T_5_Ttotal_42.3.nc')
ds10 = xr.open_dataset('../Data/solver_lowpass_x_t_omega_2_Nint_100_strat_3_T_10_Ttotal_44.8.nc')
ds20 = xr.open_dataset('../Data/solver_lowpass_x_t_omega_2_Nint_100_strat_3_T_20_Ttotal_49.8.nc')
ds30 = xr.open_dataset('../Data/solver_lowpass_x_t_omega_2_Nint_100_strat_3_T_30_Ttotal_54.8.nc')
ds40 = xr.open_dataset('../Data/solver_lowpass_x_t_omega_2_Nint_100_strat_3_T_40_Ttotal_59.8.nc')

# Initialising figure
fig = plt.figure(figsize = (15,8))
ax0 = plt.subplot2grid((12, 6), (3, 0), colspan=1,rowspan=6)
ax1 = plt.subplot2grid((12, 6), (0, 1), colspan=1,rowspan=6)
ax2 = plt.subplot2grid((12, 6), (0, 2), colspan=1,rowspan=6)
ax3 = plt.subplot2grid((12, 6), (0, 3), colspan=1,rowspan=6)
ax4 = plt.subplot2grid((12, 6), (0, 4), colspan=1,rowspan=6)
ax5 = plt.subplot2grid((12, 6), (0, 5), colspan=1,rowspan=6)
ax6 = plt.subplot2grid((12, 6), (6, 1), colspan=1,rowspan=6)
ax7 = plt.subplot2grid((12, 6), (6, 2), colspan=1,rowspan=6)
ax8 = plt.subplot2grid((12, 6), (6, 3), colspan=1,rowspan=6)
ax9 = plt.subplot2grid((12, 6), (6, 4), colspan=1,rowspan=6)
ax10 = plt.subplot2grid((12, 6), (6, 5), colspan=1,rowspan=6)
axcb = plt.subplot2grid((12, 6), (10, 0), colspan=1,rowspan=1)

# Plotting
vmin = -1
vmax = 1
axes = [ax1,ax2,ax3,ax4,ax5,ax6,ax7,ax8,ax9,ax10]
p0 = ds10.z_inst.plot(ax=ax0,add_colorbar=False,vmin = vmin, vmax=vmax,cmap='RdBu_r')
ds5.z_LM_at_mean.plot(ax=ax1,add_colorbar=False,vmin = vmin, vmax=vmax,cmap='RdBu_r')
ds10.z_LM_at_mean.plot(ax=ax2,add_colorbar=False,vmin = vmin, vmax=vmax,cmap='RdBu_r')
ds20.z_LM_at_mean.plot(ax=ax3,add_colorbar=False,vmin = vmin, vmax=vmax,cmap='RdBu_r')
ds30.z_LM_at_mean.plot(ax=ax4,add_colorbar=False,vmin = vmin, vmax=vmax,cmap='RdBu_r')
ds40.z_LM_at_mean.plot(ax=ax5,add_colorbar=False,vmin = vmin, vmax=vmax,cmap='RdBu_r')
(ds5.z_inst_at_mean - ds5.z_LM_at_mean).plot(ax=ax6,add_colorbar=False,vmin = vmin, vmax=vmax,cmap='RdBu_r')
(ds10.z_inst_at_mean - ds10.z_LM_at_mean).plot(ax=ax7,add_colorbar=False,vmin = vmin, vmax=vmax,cmap='RdBu_r')
(ds20.z_inst_at_mean - ds20.z_LM_at_mean).plot(ax=ax8,add_colorbar=False,vmin = vmin, vmax=vmax,cmap='RdBu_r')
(ds30.z_inst_at_mean - ds30.z_LM_at_mean).plot(ax=ax9,add_colorbar=False,vmin = vmin, vmax=vmax,cmap='RdBu_r')
(ds40.z_inst_at_mean - ds40.z_LM_at_mean).plot(ax=ax10,add_colorbar=False,vmin = vmin, vmax=vmax,cmap='RdBu_r')
fig.colorbar(p0,cax=axcb,orientation='horizontal',label='Relative vorticity')

textposx = 0.4
textposy = 37.4
bbox=dict(facecolor='white', edgecolor='none', boxstyle='round')
ax0.text(textposx,textposy,'a) $\zeta$',bbox=bbox)
ax1.text(textposx,textposy,r'b) $\overline{\zeta}^\mathrm{L}$',bbox=bbox)
ax2.text(textposx,textposy,r'c) $\overline{\zeta}^\mathrm{L}$',bbox=bbox)
ax3.text(textposx,textposy,r'd) $\overline{\zeta}^\mathrm{L}$',bbox=bbox)
ax4.text(textposx,textposy,r'e) $\overline{\zeta}^\mathrm{L}$',bbox=bbox)
ax5.text(textposx,textposy,r'f) $\overline{\zeta}^\mathrm{L}$',bbox=bbox)
ax6.text(textposx,textposy,r'g) $\zeta_{\mathrm{L2}}^\mathrm{w}$',bbox=bbox)
ax7.text(textposx,textposy,r'h) $\zeta_{\mathrm{L2}}^\mathrm{w}$',bbox=bbox)
ax8.text(textposx,textposy,r'i) $\zeta_{\mathrm{L2}}^\mathrm{w}$',bbox=bbox)
ax9.text(textposx,textposy,r'j) $\zeta_{\mathrm{L2}}^\mathrm{w}$',bbox=bbox)
ax10.text(textposx,textposy,r'k) $\zeta_{\mathrm{L2}}^\mathrm{w}$',bbox=bbox)

# Formatting
[ax.axes.set_xticklabels([]) for ax in axes];
[ax.axes.set_yticklabels([]) for ax in axes];
[ax.set_xlabel('') for ax in axes];
[ax.set_ylabel('') for ax in axes];

ax0.axes.set_xticks([0,np.pi,2*np.pi])
labels = ['0','$\pi$','$2\pi$']
ax0.set_xticklabels(labels)
ax0.set_ylabel('$t^*$')
ax0.set_xlabel('$x$')
ax0.set_title('Instantaneous')
[ax.set_title('') for ax in [ax6,ax7,ax8,ax9,ax10]];
ax1.set_title(r'$2T = 5$')
ax2.set_title(r'$2T = 10$')
ax3.set_title(r'$2T = 20$')
ax4.set_title(r'$2T = 30$')
ax5.set_title(r'$2T = 40$')

plt.subplots_adjust(wspace=0.1, hspace=1)

fig.savefig('Figure-8.png',bbox_inches='tight',dpi=200)

Hovmöller diagrams of vorticity for a range of averaging interval times. a) instantaneous $\zeta$, (top row) Lagrangian mean $\overline{\zeta}^\mathrm{L}$, and (bottom row) L2 wave $\zeta_{\mathrm{L2}}^\mathrm{w}$.

More data variables are available in the xarray datasets:

ds20