Plots of the dispersion relation for SGWs with added physics

surface-gravity-wave-dispersion.py

import numpy as np
import matplotlib.pyplot as plt

cs=1500
g=9.8
h=100
kappa = np.linspace(-0.08,0.08,100)

fig,ax=plt.subplots(1,4,figsize=(15,4))
plt.subplot(141)
for ky in (0,0.1):
    kx = kappa
    new_kappa = np.sqrt(kx**2 + ky**2)
    omega = np.sqrt(g*new_kappa * np.tanh(new_kappa*h))
    plt.plot(kx,omega)
plt.title('Varying incidence angle')


plt.subplot(142)
kappa = np.linspace(-1000,1000,100)
plt.plot(kappa,np.sqrt((g*kappa + 0.074/1000 * kappa**3)*np.tanh(kappa*h)))
plt.plot(kappa,np.sqrt((g*kappa)*np.tanh(kappa*h)))
plt.title('Capilary Effect')

plt.subplot(143)
kappa = np.linspace(-0.08,0.08,100)
plt.plot(kappa,np.sqrt(g*kappa*np.tanh(kappa*h)) + 1.0*kappa)
plt.plot(kappa,np.sqrt((g*kappa)*np.tanh(kappa*h)))
plt.title('Background current (1 m/s)')

plt.subplot(144)
omega = np.linspace(0,200,1000)
for n in (1,2):
    kagw = omega * np.sqrt(1/cs**2 - ((n - 1/2)*np.pi*omega/ (omega**2*h - g) )**2 +0j)
    k = np.real(kagw)
    plt.plot(k[k>0],omega[k>0],c=f'C{n-1}')
    plt.plot(-k[k>0],omega[k>0],c=f'C{n-1}')
plt.title('Acoustic Modes')
for axx in ax:
    axx.set_ylabel('Frequency (Hz)')
    axx.set_xlabel('Wavenumber (1/m)')
plt.tight_layout()
plt.show()