pydune.physics.dune.bedinstability_1D.complexe_wavenumer#

complexe_wavenumer(w, A, B)[source]#

Dispersion relation as the output of the spatial dune instability:

avec \(\Delta = \omega(4(\mathcal{A} + i\mathcal{B}) - \omega)\). Note that only the branch \(k_{+}\) corresponds to spatially growing waves in the flow direction.

Parameters:

  • w (scalar, numpy array) – non dimensional pulsation \(\omega\).

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

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

Returns:

  • kplus (scalar, numpy array) – \(k_{+}\) branch.

  • kminus (scalar, numpy array) – \(k_{-}\) branch.

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
>>> w = np.linspace(0.001, 1, 1000)
>>> A, B = 3.5, 2
>>> kplus, kminus = complexe_wavenumer(w, A, B)