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

Jet Bickley Flow

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

Parametros de entrada

N=200
n=0 # mas inestable
Np=3 #jet
_,y=OS.cheb(N)
y=y[1:-1]

lamJET,u,v,w=OS.Orr_Sommerfeld_Temporal(N,1,1,0,n,Np)

Espectro autovalores

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

plt.scatter(x_, y_,)
plt.scatter(lamJET[0].real,lamJET[0].imag, color='red', label="Más inestable")
plt.ylabel('$Img(\lambda)$')
plt.xlabel('$Re(\lambda)$')
plt.title(r'Espectro Jet Bickely $\alpha=1$ ; $\beta=0$')
#plt.ylim(-1,0.1)
#plt.xlim(-0.2,2)
plt.grid()
plt.legend()
#plt.savefig('poiseuille_Re2000a1b0.png', dpi=1000)
plt.show()

Autofunciones

plt.plot(u.real,OS.mapping(y,Np),label= "$u_r(y)$")
plt.plot(u.imag,OS.mapping(y,Np),label= "$u_i(y)$")
plt.xlabel('$v$')
plt.ylabel('$y$')
plt.title('Perfil de la perturbación $u_{2D}(y)$')
plt.grid()
plt.legend()
plt.show()

plt.plot(v.real,OS.mapping(y,Np),label= "$v_r(y)$")
plt.plot(v.imag,OS.mapping(y,Np),label= "$v_i(y)$")
plt.xlabel('$v$')
plt.ylabel('$y$')
plt.title('Perfil de la perturbación $v_{2D}(y)$')
plt.grid()
plt.legend()
plt.show()