from Orr_Sommerfeld import OS
import numpy as np
import matplotlib
import matplotlib.pyplot as plt
matplotlib.rcParams['text.usetex'] = True
%matplotlib inline

Couette Flow

\begin{align*} U(y)=1-y^2 \end{align*}

#lampb0=np.loadtxt('validacion/Pob0.txt')
#lampb1=np.loadtxt('validacion/Pob1.txt')

lamcb0=np.loadtxt('validacion/Couetteb0.txt')
lamcb1=np.loadtxt('validacion/Couetteb1.txt')

Parametros de entrada

N=100
R=800
alp=1
b=0
n3d=2
n2d=0
Np=1 # couette
_,y=OS.cheb(N)
y=y[1:-1]

lamc,_,_,_=OS.Orr_Sommerfeld_Temporal(N,R,alp,0,n2d,Np)

lamc2,_,_,_=OS.Orr_Sommerfeld_Temporal(N,R,0.5,1,n2d,Np)

Validación autovalores

x_ = [ele.real for ele in lamc]
y_ = [ele.imag for ele in lamc]

plt.scatter(x_, y_, label="Scarafia")
plt.scatter(lamcb0[:,0],lamcb0[:,1],marker='^', label="Schmid")
plt.ylabel('Img($\lambda$)')
plt.xlabel('Re($\lambda$)')
plt.title(r'$Re=800$ ; $\alpha=1$ ; $\beta=0$')
plt.ylim(-2,0.1)
plt.xlim(-1,1)
plt.grid()
plt.legend()
plt.show()



x_ = [ele.real for ele in lamc2]
y_ = [ele.imag for ele in lamc2]

plt.scatter(x_, y_, label="Scarafia")
plt.scatter(lamcb1[:,0],lamcb1[:,1],marker='^',label="Schmid")
plt.ylabel('Img($\lambda$)')
plt.xlabel('Re($\lambda$)')
plt.title(r'$Re=800$ ; $\alpha=0.5$ ; $\beta=1$')
plt.ylim(-2,0.1)
plt.xlim(-1,1)
plt.grid()
plt.legend()
plt.show()