pydune.physics.dune.bedinstability_1D.complex_pulsation#

complex_pulsation(k, A, B)[source]#

Dispersion relation as the output of the temporal dune instability:

\[\omega = k^{2}\frac{\mathcal{A} + i\mathcal{B}}{1 + i k}.\]
Parameters:

  • k (scalar, numpy array) – non dimensional wavenumber \(k\).

  • A (scalar, numpy array) – hydrodynamic coefficient \(\mathcal{A}\) (in-phase).

  • B (scalar, numpy array) – hydrodynamic coefficient \(\mathcal{B}\) (in-quadrature).

Returns:

omega – complex pulsation.

Return type:

scalar, numpy array

Notes

Note that all quantities are made non dimensional:

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

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

Examples

>>> import numpy as np
>>> k = np.linspace(0.001, 1, 1000)
>>> A, B = 3.5, 2
>>> omega = complex_pulsation(k, A, B)