Thank you for reading my question.
My question is that can we cancel out the porosity in the equation.
The detailed description is in the file.
I think your derivation is right. The density (or sediment concentration) variation in the momentum equation is generally ignored (the so-called Boussinesq approximation) but in high density flows with erosion and sedimentation (f.i. in dredging or in turbidity currents) it may be significant. See f.i.
Winterwerp, J.C., Bakker, W.T., Mastbergen, D.R. and Van
Rossum, H. (1992) Hyperconcentrated sand-water mixture
flows over erodible bed. J. Hydraul. Eng., 118, 1508–1525.
Mastbergen, D.R.; Van den Berg, J.H. (2003) Breaching in fine sands and the generation of sustained turbidity currents in submarine canyons. Sedimentology, 50, 625–637.
A decrease in density (sedimentation) results in an acceleration term and vice versa.
Thank you for answering my question Dick R. Mastbergen
I am studying internal erosion/suffusion with numerical methods.
Do you mean that the derivative of porosity with respect to space and time is zero?
No as you already mentioned and as described in the papers the gradient of density (or concentration) is not negligible in high density flows. Note concentration by volume is equal to 1 - porosity. in suspended sediment flows we generally use concentration and in static soil description porosity.
- Badges
- Science topic