Friction Laws

Friction Laws for calculating bottom shear stress. More...

Description

Friction laws calculate the stress between the flowing fluid and the bottom, which is called bottom shear stress. The bottom shear stress is needed to calculate on the one hand the loss of momentum due to bottom friction and on the other hand the bedload transport rate. The following laws can be implemented by deriving from the abstract base class, where the LET mobility model by Lomeland et al. [54] can be employed to introduce an artificial water depth, which helps to limit friction in scenarios with small water depths.

Manning

This friction law calculates the stress between the flowing fluid and the bottom, which is called bottom shear stress, using the Manning friction law:

${\tau }_x=\frac{g}{(\frac{h^{1/6}}{n}{)}^2}u\sqrt{u^2+v^2}$ and ${\tau }_y=\frac{g}{(\frac{h^{1/6}}{n}{)}^2}v\sqrt{u^2+v^2}$

with the gravity constant $\mathrm{g}$ in $[\mathrm{m}/{\mathrm{s}}^2]$, the water depth $\mathrm{h}$ in $[\mathrm{m}]$ and the Manning friction coefficient $\mathrm{n}$ in $[\mathrm{s}/{\mathrm{m}}^{1/3}]$.

The bottom shear stress is needed to calculate on the one hand the loss of momentum due to bottom friction and on the other hand the bedload transport rate.

The LET mobility model is used to limit the friction for small water depths if a roughness height > 0.0 is provided (default roughnessHeight = 0.0).

Nikuradse

This friction law calculates the stress between the flowing fluid and the bottom, which is called bottom shear stress, using the Nikuradse [60] friction law

${\tau }_x=\frac{{\kappa }^2}{(ln\frac{12h}{ks}{)}^2}u\sqrt{u^2+v^2}$ and ${\tau }_y=\frac{{\kappa }^2}{(ln\frac{12h}{ks}{)}^2}v\sqrt{u^2+v^2}$

with the dimensionless Karman's constant $\kappa$, the quivalent sand roughness $\mathrm{ks}$ in $[\mathrm{m}]$ and the water depth $\mathrm{h}$ in $[\mathrm{m}]$.

The bottom shear stress is needed to calculate on the one hand the loss of momentum due to bottom friction and on the other hand the bedload transport rate.

The LET mobility model is used to limit the friction for small water depths if a roughness height > 0.0 is provided (default roughnessHeight = 0.0).

No Friction

This friction law sets the stress between the flowing fluid and the bottom, which is called bottom shear stress, to zero. The bottom shear stress is needed to calculate on the one hand the loss of momentum due to bottom friction and on the other hand the bedload transport rate.

Viscous No-Slip

This friction law assumes thin film flow with a parabolic velocity profile in depth (for the depth-averaged shallow water equations). The velocity profile and associated bottom shear stress can be derived from plane Poiseuille flow with a free surface boundary condition on top and a no-slip boundary condition on the bottom.

Files
file	frictionlaw.hh
	Implementation of the abstract base class for friction laws.
file	manning.hh
	Implementation of the friction law after Manning.
file	nikuradse.hh
	Implementation of the abstract base class for friction laws.
file	nikuradse.hh
	Implementation of the abstract base class for friction laws.
file	nofriction.hh
	A pseudo friction law with no bottom friction.
file	viscousnoslip.hh
	Implementation of a viscous no-slip bottom friction law.

Classes
class	Dumux::FrictionLaw< VolumeVariables >
	Implementation of the abstract base class for friction laws. More...
class	Dumux::FrictionLawManning< VolumeVariables >
	Implementation of the friction law after Manning. More...
class	Dumux::FrictionLawNikuradse< VolumeVariables >
	Implementation of the friction law after Nikuradse. More...
class	Dumux::FrictionLawNoFriction< VolumeVariables >
	A pseudo friction law with no bottom friction. More...
class	Dumux::FrictionLawViscousNoSlip< VolumeVariables >
	Implementation of a viscous no-slip bottom friction law. More...