Selection of dune orientation

In this example, we show how the calculation of the elonagtion direction and MGBNT orientation are selected in the model of COurrech du Pont et al 2014.

[1] Courrech du Pont, S., Narteau, C., & Gao, X. (2014). Two modes for dune orientation. Geology, 42(9), 743-746.

import numpy as np
import matplotlib.pyplot as plt
from pydune.physics import courrechdupont2014 as CDP


theta = np.array([0, 120])
Q0 = np.array([5, 1])
alpha = np.arange(0, 361)

Elongation direction

flux_perp = CDP.resultant_flux_perp_crest_at_crest(alpha[:, None], theta[None, :], Q0[None, :])
flux_aligned = CDP.resultant_flux_aligned_crest_at_crest(alpha[:, None], theta[None, :], Q0[None, :])
alpha_E = CDP.elongation_direction(theta, Q0)

fig, ax = plt.subplots(1, 1, constrained_layout=True)
ax.plot(alpha, flux_perp, label='Flux perp. to crest')
ax.plot(alpha, flux_aligned, label='Flux aligned with crest')
ax.axhline(0, color='k', ls='--', lw=1)
ax.axvline(alpha_E, color='k', ls='--', lw=1)
ax.set_xlim(0, 360)
ax.set_xlabel('Crest orientation [deg.]')
ax.set_ylabel('Fluxes [-]')
ax.legend()
fig.show()

MGBNT orientation

alpha = np.arange(0, 181)

sigma = CDP.growth_rate(alpha[:, None], theta[None, :], Q0[None, :])
alpha_MGBNT = CDP.MGBNT_orientation(theta, Q0)

fig, ax = plt.subplots(1, 1, constrained_layout=True)
ax.plot(alpha, sigma)
ax.axhline(sigma.max(), color='k', ls='--', lw=1)
ax.axvline(alpha_MGBNT, color='k', ls='--', lw=1)
ax.set_xlim(0, 180)
ax.set_xlabel('Crest orientation [deg.]')
ax.set_ylabel(r'Growth rate [-]')
fig.show()