import numpy as np
import scipy.io as sio
import matplotlib.pyplot as plt
# load y+ and u+ data (ascii file with 2 columns: y+ & u+, at 2 Re-tau)
temp1=np.loadtxt('u-profile-Retau1000.dat')
y1=temp1[:,0];  u1=temp1[:,1]
temp2=np.loadtxt('u-profile-Retau5200.dat')
y2=temp2[:,0];  u2=temp2[:,1]
kappa=0.38; B=4.2; # log-law model parameters.  
c1=12.0;  c2=(1/kappa)*np.log(c1)+B # composite model parameters.  
# log and linear law:
ym1=np.array(list(range(1,5000)));  um1=(1/kappa)*np.log(ym1)+B
ym2=np.array(list(range(1,100)));   um2=ym2
# composite function:
ym3=ym1;  um3=((1/kappa)*np.log(c1+ym3)+B)*(1+(ym3/c2)**(-2))**(-1/2)
# create semilog mean velocity profile plot
fig, ax = plt.subplots()
CS = ax.plot(y1, u1, '-r',y2, u2, '-g')
CS = ax.plot(ym1, um1, '--k', ym2, um2, ':k',ym3,um3,'-.b')
plt.xlim(1,7000);  plt.ylim(0,30)
plt.title('Mean velocity',fontsize=15)
plt.xlabel(r'$y^+=y u_{\tau}/~\nu$',fontsize=18)
plt.xticks(fontsize=16);   plt.yticks(fontsize=16)
plt.ylabel(r'$\overline{u}^+=\overline{u}~ / ~ u_{\tau}$',fontsize=18)
ax.set_xscale('log')