figure 18.ipynb

Kernel: Python 3 (system-wide)

import numpy as np
import h5py
import matplotlib.pyplot as plt
import seaborn as sns
import cmocean

# Aesthetics
sns.set_theme()
sns.set_style('ticks')
sns.set_context('paper')
plt.rc('mathtext', fontset='stix')
plt.rc('font', family='serif')
plt.rc('axes', grid=True)

import pandas as pd

Load energy budget data

df = pd.read_csv('../data/budget_data.csv')
df.head()

Set parameter-dependent figure aesthetics

def Pr_mark(Pr):
    if Pr==1:
        return 'o'
    elif Pr==4:
        return '^'
    else:
        return 'v'
        
camp = sns.color_palette('flare', as_cmap=True)
cspeed = cmocean.tools.crop_by_percent(cmocean.cm.tempo, 30, which='both', N=None)

def Re_col(lR):
    return camp((lR - 2.5)/1.5)

def Gr_col(lG):
    return cspeed((lG - 6)/2)

fig, axs = plt.subplots(2,2, figsize=(5.2,3.6), dpi=200, layout='constrained')
for Gr in df.Gr.unique():
    for Pr in df.Pr.unique():
        sdf = df[(df.Gr==Gr) & (df.Pr==Pr)].sort_values('Re')
        Ub = np.minimum(sdf.Re/Gr**0.5, 1)
        nu = np.minimum(Gr**-0.5, sdf.Re**-1)
        axs[0,0].loglog(sdf.Re, (sdf.Pu)/(Ub**3), marker=Pr_mark(Pr), color=Gr_col(np.log10(Gr)), markeredgecolor='k')
        axs[0,1].semilogx(sdf.Re, (sdf.Pu)/sdf.I, marker=Pr_mark(Pr), color=Gr_col(np.log10(Gr)), markeredgecolor='k')

Rr = 10**np.linspace(3.1,3.9,101)
axs[0,0].loglog(Rr, 0.1*(Rr/1e3)**-1, 'k--')
for ax in axs[0,:]:
    ax.set_xlabel('$Re$')
axs[0,0].set_ylabel('$\mathcal{P}_u/(U^3/H)$')
axs[0,1].set_ylabel('$\mathcal{P}_u/\mathcal{I}$')
axs[0,0].annotate('$Re^{-1}$', (5e3, 4e-2), rotation=0, ha='center', va='center')
axs[0,1].set_ylim([0.2,0.6])
axs[0,0].set_ylim([2e-3,1e-1])

for Gr in df.Gr.unique():
    for Pr in df.Pr.unique():
        sdf = df[(df.Gr==Gr) & (df.Pr==Pr)].sort_values('Re')
        nu = np.minimum(Gr**-0.5, sdf.Re**-1)
        Uf = np.minimum(Gr**0.5/sdf.Re, 1)
        U0 = sdf.Re0/np.maximum(Gr**0.5, sdf.Re)
        UL = sdf.UL
        axs[1,0].loglog(sdf.Re**2/sdf.Gr, (sdf.Pw)/(Uf**3), marker=Pr_mark(Pr), color=Gr_col(np.log10(Gr)), markeredgecolor='k')
        axs[1,1].semilogx(sdf.Re**2/sdf.Gr, (sdf.Pw)/sdf.qm, marker=Pr_mark(Pr), color=Gr_col(np.log10(Gr)), markeredgecolor='k')

for ax in axs[1,:]:
    ax.set_xlabel('$Re^2/Gr = Ri^{-1}$')
axs[1,0].set_ylabel('$\mathcal{P}_w/(U_f^3/H)$')
axs[1,1].set_ylabel('$\mathcal{P}_w/\overline{q}$')
axs[1,1].set_ylim([0.2,1])
axs[1,0].set_ylim([2e-3,1e-1])

alph = 'abcd'
for i, ax in enumerate(axs.flatten()):
    ax.annotate('$('+alph[i]+')$', (-0.05, 1.05), xycoords='axes fraction', ha='right', va='bottom')

# fig.savefig('mean_KE_budget.pdf')

plt.show()