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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 Find the best $\alpha$ for $p = 7, N_y = 256, N_z = 2048$
Step1:  Find the best $\alpha$ for $p = 15, N_y = 128, N_z = 1024$
Step2:  Find the best $\alpha$ for $p = 31, N_y = 64, N_z = 512$
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Python Code:
alphs = list(np.linspace(0,pi/2, 16, endpoint=False))
Re=2000;
N = 7
Nl = 257
Nz = 2049
yms = []; y1s = []; y10s = []; zms = []
for alph in alphs:
    yl=mesh(alph, Nl)
    ym, y1, y10, zm, cm = wall_units(yl,Nz, N,Re)
    yms.append(ym)
    y1s.append(y1)
    y10s.append(y10)
    zms.append(zm)
alpha = 0.1
plot_units(yms, y1s, y10s, zms, alpha)
yl=mesh(alpha, Nl)
ym, y1, y10, zm, cm = wall_units(yl,Nz, N,Re)
print("Final values:", ym, y1, y10, zm, cm)
yl=mesh(.1, 257)
plt.figure(figsize=(256,1))
plot_mesh(yl)
plt.savefig('mesh_8.png')
print(yl)
Explanation: Find the best $\alpha$ for $p = 7, N_y = 256, N_z = 2048$
End of explanation
alphs = list(np.linspace(0,pi/2, 16, endpoint=False))
Re=2000;
N = 16
Nl = 129
Nz = 1025
yms = []; y1s = []; y10s = []; zms = []; cms = []
for alph in alphs:
    yl=mesh(alph, Nl)
    ym, y1, y10, zm, cm = wall_units(yl,Nz, N,Re)
    yms.append(ym)
    y1s.append(y1)
    y10s.append(y10)
    zms.append(zm)
    cms.append(cm)
alpha = 0.22
plot_units(yms, y1s, y10s, zms, alpha)
yl=mesh(alpha, Nl)
ym, y1, y10, zm, cm = wall_units(yl,Nz, N,Re)
print("Final values:", ym, y1, y10, zm, cm)
yl=mesh(0.22, 129)
plt.figure(figsize=(128,1))
plot_mesh(yl)
plt.savefig('mesh_16.png')
print(yl)
Explanation: Find the best $\alpha$ for $p = 15, N_y = 128, N_z = 1024$
End of explanation
alphs = list(np.linspace(0,pi/2, 16, endpoint=False))
Re=2000;
N = 31
Nl = 65
Nz = 513
yms = []; y1s = []; y10s = []; zms = []
for alph in alphs:
    yl=mesh(alph, Nl)
    ym, y1, y10, zm, cm = wall_units(yl,Nz, N,Re)
    yms.append(ym)
    y1s.append(y1)
    y10s.append(y10)
    zms.append(zm)
alpha = 0.36
plot_units(yms, y1s, y10s, zms, alpha)
yl=mesh(alpha, Nl)
ym, y1, y10, zm, cm = wall_units(yl,Nz, N,Re)
print("Final values:", ym, y1, y10, zm, cm)
yl=mesh(.36, 65)
plt.figure(figsize=(64,1))
plot_mesh(yl)
plt.savefig('mesh_32.png')
print(yl)
Explanation: Find the best $\alpha$ for $p = 31, N_y = 64, N_z = 512$
End of explanation
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