2M_45eta_Figure3.ipynb

Kernel: Python 3 (system-wide)

import math
import numpy as np
import pandas as pd
import matplotlib.colors as colors
from matplotlib import pyplot as plt

KHMH = pd.read_hdf('../Data/2M_database.h5', 'data')

KHMH

# Specify variables
Cascade_phi = np.array(KHMH['Phi'].tolist())
Cascade_pi  = np.array(KHMH['Pi'].tolist())
k_sf        = np.array(KHMH['Du2'].tolist())
k_sgs       = 0.5*(np.array(KHMH['Tau11'].tolist()) + np.array(KHMH['Tau22'].tolist()) + np.array(KHMH['Tau33'].tolist()))
Eps         = 1.3668 
dx          = 2*np.pi/8192
R           = 15*dx #radius

# Normalization
Cascade_phi = Cascade_phi/Eps
Cascade_pi  = Cascade_pi/Eps
k_sgs = k_sgs / ((Eps*30*dx)**(2/3))
k_sf  = k_sf  / ((Eps*30*dx)**(2/3))

# Joint PDFs of Ksgs and Ksf
fig = plt.figure(figsize =(10, 7))
ax = fig.add_axes([0.2, 0.2, 0.7, 0.7])
h, ex, ey = np.histogram2d(k_sf, k_sgs,
                           bins=(np.linspace(0, 10, 200), np.linspace(0, 10, 200)), normed=True)
eex =(ex[1:]+ex[:-1])/2
eey =(ey[1:]+ey[:-1])/2

plt.contour(eex, eey, h.T, np.r_[0.01, 0.03, 0.1, 0.3, 1, 3], colors='k')

plt.ylim([-0.1,6])
plt.xlim([-0.1,6])


plt.ylabel(r'$k_{sgs,\ell} / (\langle \epsilon \rangle \ell)^{(2/3)} $', fontsize = 30)
plt.xlabel(r'$k_{sf,\ell} / (\langle \epsilon \rangle \ell)^{(2/3)}$', fontsize = 30)

ax.tick_params(axis='both', which='major', labelsize=30)

# Joint PDFs of Pi and Phi
fig = plt.figure(figsize =(10, 7))
ax = fig.add_axes([0.2, 0.2, 0.7, 0.7])
h, ex, ey = np.histogram2d(Cascade_phi, Cascade_pi,
                           bins=(np.linspace(-30, 30, 300), np.linspace(-30, 30, 300)), density = True)
eex =(ex[1:]+ex[:-1])/2
eey =(ey[1:]+ey[:-1])/2
plt.contour(eex, eey, h.T, np.r_[ 0.003, 0.01, 0.03, 0.1, 0.3, 1], colors='k')

plt.plot(eex,eex,'--r')
plt.ylim([-3.5,6])
plt.xlim([-3.5,6])

plt.ylabel(r'$\Pi_{\ell}/\langle \epsilon \rangle$', fontsize = 30)
plt.xlabel(r'$\Phi_{\ell}/\langle \epsilon \rangle$', fontsize = 30)

ax.tick_params(axis='both', which='major', labelsize=30)