# 6.9.1: Choice of formulations

- Page ID
- 16368

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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)The quantitative description of sediment transport is still largely empirical (e.g. Fredsøe and Deigaard (1992) and Van Rijn (1989)). There is a variety of transport formulas and models, each with its own strong points and weaknesses. Note that all the models discussed in this chapter are geared towards describing the sub-aqueous (‘underwater’) transport. Aeolian transport (by wind) and transport in the swash zone around the water line are not considered. They can however be important in a sediment balance.

Results of sediment transport computations often show large discrepancies compared with actual measurements. A factor 2 to 5 too large or too small is certainly not exceptional. Many researchers are trying to improve the results, for instance by proposing better and more reliable descriptions of various elements in a formula. For practical problems in coastal engineering however, the simpler models (e.g. Bijker (Sect. 6.5.4), Bailard (Sect. 6.7.2) are still the ones to beat.

A. G. Davies et al. (2002) present a very interesting intercomparison study of various research and practical sand transport models. They summarise their study as follows:

“A series of model intercomparisons, and model comparisons with field data, was carried out as part of the EU MASTIII SEDMOC Project (1998-2001). Initially, seven ‘research’ models were intercompared over a wide range of wave and current conditions, corresponding to both plane and rippled sand beds. These models included both one-dimensional vertical (1DV) formulations, varying in complexity from eddy viscosity and mixing length models to a full two-phase flow formulation, and two-dimensional vertical (2DV) formulations capable of representing vortex shedding above sand ripples. The model results showed greatest convergence for cases involving plane beds, with predicted sand transport rates agreeing to well within an order of magnitude, and greatest divergence for cases involving rippled beds. A similar intercomparison involving (mainly) practical sand transport models, carried out over wide wave and current parameter ranges, also showed greatest variability for cases involving rippled beds. Finally, (mainly) practical models were compared with field data obtained at five contrasting field sites. The results showed that suspended sand concentrations in the bottom metre of the flow were predicted within a factor of 2 of the measured values in 13% to 48% of the cases considered, and within a factor of 10 in 70% to 83% of the cases, depending upon the model used. Estimates of the measured alongshore component of suspended sand transport yielded agreement to within a factor of 2 in 22% to 66% of cases, and within a factor of 10 in 77% to 100% of cases. *The results suggest that, at the present stage of research, considerable uncertainty should be expected if untuned models are used to make absolute predictions for field conditions. The availability of some measurements on site still appears to be a necessary requirement for high-accuracy sand transport predictions. However, for morphological modellers, the results may be viewed as more encouraging, since many of the present models exhibit agreement in their relative behaviour over wide ranges of wave and current conditions, which is a prerequisite to obtaining correct morphodynamic predictions*.”