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from IPython.core.display import HTML
with open('../../common/creativecommons.html', 'r') as f:
html = f.read()
with open('../../common/custom.css', 'r') as f:
styles = f.read()
HTML(styles)
text = 'Check this post at'
uri = 'http://nbviewer.ipython.org/urls/raw.github.com/ocefpaf/python4oceanographers/master/content/downloads/notebooks'
name = get_notebook_name()
link = """<p>%s <a href="%s/%s"><em>nbviewer</em>.</a></p>""" % (text, uri, name)
html += str(link)
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import numpy as np
import matplotlib.pyplot as plt
Longwave dispersion relationship: $\omega = k\sqrt{gh}$
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L = 10500 # Lambda [m].
H = 500. # Water column depth [m].
N0 = 10 # Wave amplitude [m].
K = 2 * np.pi / L # Wavenumber [m^{-1}].
g = 9.8 # Aceleration of gravity [m s^{-2}]
w = np.sqrt(g * K ** 2 * H) # Longwave dispersion [rad s^{-1}].
T = 2 * np.pi / w # Period [s].
t = np.arange(0, 2 * T) # Two waves.
x = 0.0
z000, z100, z200, z300, z400, z500 = 0, -100, -200, -300, -400, -500
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HoL = H/L
if HoL < 1./20:
print("H/L = %s, Longwave!" % HoL)
else:
print("H/L = %s, This is not a longwave :(" % HoL)
The code below solve the following equations (Check them out in the course notes!):
Free surface displacement: $\eta = N_o\cos({kx - \omega t})$
x displacement: $\chi = -\frac{\eta_o}{kH}\sin({kx - \omega t})$
z displacement: $\zeta = \frac{\eta_o}{H}(z + H)\cos({kx - \omega t})$
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X = -(N0 / K * H) * np.sin((K * x) - (w * t))
N = N0 * np.cos((K * x) - (w * t))
Z000 = ((N0 / H) * (z000 + H)) * np.cos((K * x) - (w * t)) + z000
Z100 = ((N0 / H) * (z100 + H)) * np.cos((K * x) - (w * t)) + z100
Z200 = ((N0 / H) * (z200 + H)) * np.cos((K * x) - (w * t)) + z200
Z300 = ((N0 / H) * (z300 + H)) * np.cos((K * x) - (w * t)) + z300
Z400 = ((N0 / H) * (z400 + H)) * np.cos((K * x) - (w * t)) + z400
Z500 = ((N0 / H) * (z500 + H)) * np.cos((K * x) - (w * t)) + z500
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# Figure.
fig, ax = plt.subplots(figsize=(4, 4))
ax.plot(X, Z000, 'k',
X, Z100, 'k',
X, Z200, 'k',
X, Z300, 'k',
X, Z400, 'k',
X, Z500, 'k')
ax.set_title(u'Ondas de águas rasas (ou ondas longas)')
ax.set_xlabel(u'Distância [m]')
ax.set_ylabel('Profundidade [m]')
x = np.linspace(-X.max()*6, X.max()*6, N.size)
ax.plot(x, N, 'k:')
ax.set_ylim(-520, 90)
ax.grid(True)
ax.annotate(r'$\eta$', xy=(x[-20], N[-20]), xycoords='data',
xytext=(20, 20), textcoords='offset points',
arrowprops=dict(arrowstyle="->", connectionstyle="arc3,rad=0.2"))
fig.tight_layout()
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HTML(html)