Figure-5.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 datasets
ds_lp = xr.open_dataset('../Data/solver_lowpass_x_y_omega_2_Nint_1_strat_3_T_40.nc')

# Initialising figure
fig, axes = plt.subplots(4,3,figsize = (15,18),constrained_layout=True)

# Plotting
vmin = -1
vmax = 1
p0=axes[0,0].pcolormesh(ds_lp.z_inst,vmin = vmin, vmax = vmax,cmap = 'RdBu_r')
axes[0,1].pcolormesh(ds_lp.z_EM,vmin = vmin, vmax = vmax,cmap = 'RdBu_r')
axes[0,2].pcolormesh(ds_lp.z_inst - ds_lp.z_EM,vmin = vmin, vmax = vmax,cmap = 'RdBu_r')
axes[1,0].pcolormesh(ds_lp.z_inst,vmin = vmin, vmax = vmax,cmap = 'RdBu_r')
axes[1,1].pcolormesh(ds_lp.z_LM_at_mean,vmin = vmin, vmax = vmax,cmap = 'RdBu_r')
axes[1,2].pcolormesh(ds_lp.z_inst - ds_lp.z_LM_at_mean,vmin = vmin, vmax = vmax,cmap = 'RdBu_r')
axes[2,0].pcolormesh(ds_lp.z_inst,vmin = vmin, vmax = vmax,cmap = 'RdBu_r')
axes[2,1].pcolormesh(ds_lp.z_LM_at_mid,vmin = vmin, vmax = vmax,cmap = 'RdBu_r')
axes[2,2].pcolormesh(ds_lp.z_inst-ds_lp.z_LM_at_mid,vmin = vmin, vmax = vmax,cmap = 'RdBu_r')
axes[3,0].pcolormesh(ds_lp.z_inst_at_mean,vmin = vmin, vmax = vmax,cmap = 'RdBu_r')
axes[3,1].pcolormesh(ds_lp.z_LM_at_mean,vmin = vmin, vmax = vmax,cmap = 'RdBu_r')
axes[3,2].pcolormesh(ds_lp.z_inst_at_mean-ds_lp.z_LM_at_mean,vmin = vmin, vmax = vmax,cmap = 'RdBu_r')

fig.colorbar(p0,ax=axes[0,2],label='Relative vorticity')
fig.colorbar(p0,ax=axes[1,2],label='Relative vorticity')
fig.colorbar(p0,ax=axes[2,2],label='Relative vorticity')
fig.colorbar(p0,ax=axes[3,2],label='Relative vorticity')

textposx = 8
textposy = 234
bbox=dict(facecolor='white', edgecolor='none', boxstyle='round')
axes[0,0].text(textposx,textposy,r'a) $\zeta(\mathbf{x})$',bbox=bbox)
axes[0,1].text(textposx,textposy,r'b) $\overline{\zeta}^\mathrm{E}(\mathbf{x})$',bbox=bbox)
axes[0,2].text(textposx,textposy,r'c) $\zeta_\mathrm{E}^\mathrm{w} = \zeta(\mathbf{x}) - \overline{\zeta}^\mathrm{E}(\mathbf{x})$',bbox=bbox)
axes[1,0].text(textposx,textposy,r'd) $\zeta(\mathbf{x})$',bbox=bbox)
axes[1,1].text(textposx,textposy,r'e) $\overline{\zeta}^\mathrm{L}(\mathbf{x})$',bbox=bbox)
axes[1,2].text(textposx,textposy,r'f) $\zeta_\mathrm{S-E}^\mathrm{w} = \zeta(\mathbf{x}) - \overline{\zeta}^\mathrm{L}(\mathbf{x})$',bbox=bbox)
axes[2,0].text(textposx,textposy,r'g) $\zeta(\mathbf{x})$',bbox=bbox)
axes[2,1].text(textposx,textposy,r'h) $\zeta^*(\mathbf{x}) = \overline{\zeta}^\mathrm{L}(\boldsymbol{\Xi^{3 \mapsto 2}}(\mathbf{x}))$',bbox=bbox)
axes[2,2].text(textposx,textposy,r'i) $\zeta_\mathrm{L1}^\mathrm{w} = \zeta(\mathbf{x}) - \zeta^*(\mathbf{x})$',bbox=bbox)
axes[3,0].text(textposx,textposy,r'j) $\zeta((\boldsymbol{\Xi^{3 \mapsto 2}})^{-1}(\mathbf{x}))$',bbox=bbox)
axes[3,1].text(textposx,textposy,r'k) $\overline{\zeta}^\mathrm{L}(\mathbf{x})$',bbox=bbox)
axes[3,2].text(textposx,textposy,r'l) $\zeta_\mathrm{L2}^\mathrm{w} = \zeta((\boldsymbol{\Xi^{3 \mapsto 2}})^{-1}(\mathbf{x})) - \overline{\zeta}^\mathrm{L}(\mathbf{x})$',bbox=bbox)

# Formatting
[axes[i,j].set_aspect('equal') for i in range(4) for j in range(3)];
axes[0,0].set_ylabel('Eulerian wave decomposition (E)')
axes[1,0].set_ylabel('Semi-Eulerian wave decomposition (S-E)')
axes[2,0].set_ylabel(r'Lagrangian wave decomposition (L1)')
axes[3,0].set_ylabel(r'Lagrangian wave decomposition (L2)')
[axes[i,j].axes.set_xticklabels([]) for i in range(4) for j in range(3)];
[axes[i,j].axes.set_yticklabels([]) for i in range(4) for j in range(3)];

fig.savefig('Figure-5.png',dpi=200,bbox_inches='tight')

The four different wave decompositions: (top) Eulerian, (second row) semi-Eulerian, (third row) Lagrangian first definition, and (bottom) Lagrangian second definition. For each row, the middle 'mean' field is subtracted from the left 'instantaneous' field to give the right 'wave' field. The flow parameters are as for figure 2, and strategy 3 is used.

More data variables are available in the xarray dataset:

ds_lp