pydune.physics.dune.bedinstability_2D

Dune flat bed instability taking into account two spatial direction (x and y), under unidirectional, bidirectional and multidirectional wind regimes. Here, only the temporal instability is derived, following Gadal et al. 2019.

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

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., Du Pont, S. C., Rozier, O., & Claudin, P. (2019). Incipient bedforms in a bidirectional wind regime. Journal of Fluid Mechanics, 862, 490-516.

[2] Andreotti, B., Claudin, P., Devauchelle, O., Durán, O., & Fourrière, A. (2012). Bedforms in a turbulent stream: ripples, chevrons and antidunes. Journal of Fluid Mechanics, 690, 94-128.

Functions

celerity_bidi	Celerity \(\sigma\) of sinusoidal periodic dunes of wavenumber \(k\) and orientation \(\alpha\) induced by a bidirectional wind whose orientation alternates regularly between \(-\theta/2\) and \(+\theta/2\).
cosd	Cosine element-wise np.cos with an input in degree.
growth_rate_bidi	Temporal growth rate \(\sigma\) of sinusoidal periodic dunes of wavenumber \(k\) and orientation \(\alpha\) induced by a bidirectional wind whose orientation alternates regularly between \(-\theta/2\) and \(+\theta/2\).
sind	Trigonometric sine using np.sin, element-wise with an input in degree.
temporal_celerity	Temporal celerity \(c = \omega/k\) of sinusoidal periodic dunes of wavenumber \(k\) and orientation \(\alpha\) induced by a unidirectional constant wind through the linear dune instability.
temporal_celerity_multi	Temporal celerity \(c\) of sinusoidal periodic dunes of wavenumber \(k\) and orientation \(\alpha\) induced by succesion of winds of various orientations and strengths.
temporal_growth_rate	Temporal growth rate of sinusoidal periodic dunes of wavenumber \(k\) and orientation \(\alpha\) induced by a unidirectional constant wind through the linear dune instability.
temporal_growth_rate_multi	Temporal growth rate \(\sigma\) of sinusoidal periodic dunes of wavenumber \(k\) and orientation \(\alpha\) induced by succesion of winds of various orientations and strengths.
temporal_pulsation	Temporal pulsation \(\omega\) of sinusoidal periodic dunes of wavenumber \(k\) and orientation \(\alpha\) induced by a unidirectional constant wind through the linear dune instability.