pydune.physics.dune.bedinstability_1D

Dune flat bed instability under a unidirectional wind (1D – no spanwise direction). Here, ‘temporal’ and ‘spatial’ functions refer to the temporal and spatial version of the dune instability (see Gadal et al. 2020).

This theory is developped assuming a quadratic transport law of the form

\[q_{\rm sat}/Q_{*} = \omega \left[1 - (u_{\rm th}/u_{*})^{2}\right],\]

where \(Q_{*}\) is a characteristic sand flux, \(\omega\) a dimensional constant, \(u_{*}\) the wind shear velocity and u_{rm th} the threshold velocity for sediment transport.

In the following, all quantities are made non dimensional:

- length scales by the saturation length \(L_{\rm sat}\).

- time scales by \(L_{\rm sat}^{2}/Q_{*}\).

References

[1] Gadal, C., Narteau, C., Ewing, R. C., Gunn, A., Jerolmack, D., Andreotti, B., & Claudin, P. (2020).

Spatial and temporal development of incipient dunes. Geophysical Research Letters, 47(16), e2020GL088919.

Functions

complex_pulsation	Dispersion relation as the output of the temporal dune instability:
complexe_wavenumer	Dispersion relation as the output of the spatial dune instability:
spatial_growth_rate	Dune instability spatial growth rate - imaginary part of the complex wavenumber \(k_{+}\).
spatial_wavenumber	Dune instability spatial wavenumber - real part of the complex wavenumber \(k_{+}\).
temporal_growth_rate	Dune instability temporal growth rate - imaginary part of the complex pulsation where \(\mathcal{A} = \mathcal{A}_{0}\) and \(\mathcal{B} = \mathcal{B}_{0} - 1/(r^{2}\mu)\), taking into account slope effects.
temporal_pulsation	Dune instability temporal pulsation - real part of the complex pulsation.
temporal_velocity	Dune instability temporal velocity - real part of the complex pulsation divided by the wavenumber.