python_codes.linear_theory#

Linear theory of a turbulent flow over a sinusoidal bottom.

References

[1] Fourrière, A. (2009). Morphodynamique des rivières: Sélection de la largeur, rides et dunes (Doctoral dissertation, Université Paris-Diderot-Paris VII).
[2] Fourriere, A., Claudin, P., & Andreotti, B. (2010). Bedforms in a turbulent stream: formation of ripples by primary linear instability and of dunes by nonlinear pattern coarsening. Journal of Fluid Mechanics, 649, 287-328.
[3] Andreotti, B., Fourriere, A., Ould-Kaddour, F., Murray, B., & Claudin, P. (2009). Giant aeolian dune size determined by the average depth of the atmospheric boundary layer. Nature, 457(7233), 1120-1123.
[4] 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

`Ax`	Calculate the hydrodynamic coefficient \(\mathcal{A}_{x}\) using the geometrical model:
`Ay`	Calculate the hydrodynamic coefficient \(\mathcal{A}_{y}\) using the geometrical model:
`Bx`	Calculate the hydrodynamic coefficient \(\mathcal{B}_{x}\) using the geometrical model:
`By`	Calculate the hydrodynamic coefficient \(\mathcal{B}_{y}\) using the geometrical model:
`Cisaillement_basal`	Calculate the basal shear stress over a two dimensional sinusoidal topography for a wind from left to right (along the \(x\)-direction):
`Cisaillement_basal_rotated_wind`	Calculate the basal shear stress over a two dimensional sinusoidal topography for an arbitrary wind direction.
`calculate_solution`	Solve the system and apply the boundary conditions.
`coeffA0`
`coeffB0`
`function_coeff`