text: import matplotlib.pyplot as plt
  import numpy as np
  
  npts = 200
  t = np.linspace(0,1,npts)
  u_mean = np.full(npts, 1)
  # u_fluc = 0.5*np.random.rand(npts)+0.75
  denom = 4
  u_fluc = np.random.uniform(u_mean-u_mean/denom, u_mean+u_mean/denom, npts)
  
  print(len(t))
  # print(len(u_mean))
  print(len(u_fluc))
  
  fig, ax = plt.subplots()
  
  ax.plot(t, u_fluc)
  ax.plot(t, u_mean)
  ax.legend(( "u'", "$\\bar{u}$"))
  
  ax.set(xlabel='Time (s)', ylabel='Flow Velocity (m/s)',
         title='Mean Velocity vs. Velocity Fluctuations')
  ax.set_ylim((0,2))
  
  fig.savefig("mean-vs-fluc.png")
  # plt.show()
  
  
  ################################################################################
  
  npts = 200
  d = np.linspace(0,1,npts)
  u_mean = d/(d+0.05)
  max_fluc = 0.05
  u_fluc = np.random.uniform(u_mean-max_fluc, u_mean+max_fluc, npts)
  
  fig, ax = plt.subplots()
  
  ax.plot(u_fluc, d)
  ax.plot(u_mean, d)
  ax.legend(( "u'", "$\\bar{u}$"))
  
  ax.set(xlabel='Flow Velocity (m/s)', ylabel='Distance from Wall (m)',
         title='Mean Velocity vs. Velocity Fluctuations')
  ax.set_xlim((0, 1.5))
  
  fig.savefig("mean-vs-fluc-wall.png")
  plt.show()
  