python_codes.linear_theory.Cisaillement_basal#
- Cisaillement_basal(x, y, alpha, A0, B0, AR)[source]#
Calculate the basal shear stress over a two dimensional sinusoidal topography for a wind from left to right (along the \(x\)-direction):
\[\Tau_{x} = \Re\left(1 + (\mathcal{A}_{x}(\alpha, \mathcal{A}_{0}) + i\mathcal{B}_{x}(\alpha, \mathcal{B}_{0}))k\xi\exp^{i\cos\alpha x + \sin\alpha y}\right) \Tau_{y} = \Re\left((\mathcal{A}_{y}(\alpha, \mathcal{A}_{0}) + i\mathcal{B}_{y}(\alpha, \mathcal{B}_{0}))k\xi\exp^{i\cos\alpha x + \sin\alpha y}\right)\]- Parameters
x (array, scalar) – Streamwise coordinate, non-dimensional (\(kx\)).
y (array, scalar) – Spanwise coordinate, non-dimensional (\(ky\)).
alpha (array, scalar) – Dune orientation with respect to the perpendicular to the flow direction (in degree).
A0 (array, scalar) – value of the in-phase hydrodynamic coefficient for \(\alpha = 0\), i.e. for a dune orientation perpendicular to the flow direction.
B0 (array, scalar) – value of the in-quadrature hydrodynamic coefficient for \(\alpha = 0\), i.e. for a dune orientation perpendicular to the flow direction.
AR (array, scalar) – dune aspect ratio, \(k\xi\).
- Returns
Taux (array, scalar) – Streamwise component of the non-dimensional shear stress.
Tauy (array, scalar) – Spanwise component of the non-dimensional shear stress