Page under construction

...

1. Description computational model

The applied model for the turbidity current HMBreach is a 1DH 2-layer model for stationary non-uniform depth averaged flow. It was developed at WL | Delft Hydraulics for dredging applications and validated with flume tests. The slope development and stability during sand suction (“breaching”) in specific sand layers from a bore hole is predicted. The model was applied to turbidity currents in submarine canyons (Scripps Canyon) in collaboration with University of Utrecht. Ref. [Mastbergen & Van Den Berg, 2003]

...

A semi – empirical Erosion model / formula is applied see [Winterwerp et al, 1992] and the improved and more general version see [Mastbergen and Van den Berg, 2003] with permeability / d15 that defines the net bed erosion velocity v erosion . This expression includes hindered erosion and hindered settling effects and are validated with flume measurements in Oeverstabiliteit bij verdieping waterbodems  DC 04 43 11  september 2009 Rekenmodel HMBreach Deltares 1 9 antiin anti-dunes and in dredging experiments for sand grain size 100 – 200 ?m occuring only during short time. The maximum erosion rate is restricted due to high volumetric concentration with a supplemental empirical formula see [Winterwerp et al, 1992]. The critical value for erosion and the power are different, so computations were performed with both erosion model options.

2. Model equations

4 equations . to be solved with variables u, h, b and c

Extension of 1DH model

2.1 Momentum equation:

? ? ?

with bed and internal friction shear stress ? ? ? and f i = 0.33 f0

Momentum term, the left hand side of the Momentum equation reads:

? ?

Pressure term, the first term at the righ hand side of the Momentum Eq. reads:

 ? ? ? ?

Note: considering d???/ds means that the effect of density gradient on momentum is taken into account and the Boussinesq approximation is not applied as usually done.

Mixture density ? ?

with relative sediment density difference  ? ? ?

? ? ?

2.2 Continuity of water equation:

 ? ? ? ?

2.3 Continuity of sediment equation

 ? ?

Substitution results in the following equations for the gradients of u, c and h

 ? ?

? ? ?

? ? ?

with :

densiometric Froude number ? ?

with relative density flow difference  ? ? ?

? ?

? ?

? ?

2.4 Fanning gravity currents (optional):

? ?

 or b = b(s) by geometry.

The 4 equations can be solved with a simple straight forward solution scheme, that is stable and accurate for Fr > 1 and for instance a 0.5 m step length.

Approval criterion for breaching

...