User Guide 011

Notes: • The size classes are constant for the whole domain. • The fraction of each sediment size class in the bed describes the bed composition. • Increasing the number of sediment size classes increases the com-putational time because each size class requires its own governing equations. • If not size classes are specified, then a single transport grain size is used based on the mean of the median grain size diameter for the surface bed layer.

Recommendations: • It is NOT recommended to use more 8-9 sediment size classes, be-cause of the increased computational time. For most cases, 3-5 sediment size classes are sufficient. • A good and simple way of estimating the grain size classed based only on the size limits of the distribution is by distributing the di-ameters logarithmically: (2 22) where is the number of sediment size classes, indicates the sediment size class, and the subscript indicates the size class num-ber. This leads diameters more closely spaced in the finer grain sizes and more loosely spaced in the coarser grain sizes. Since the sediment transport is larger for the finer grain sizes, it makes sense to give more resolution near the finer grain sizes. • The size class diameter should be chosen carefully so that encom-pass the whole range of sediment sizes found in the bed.

A Matlab example how to select the sediment size classes based on a median grain size and geometric standard deviation is given in Appendix E.

Fall Velocity

The user may select one of several sediment size class fall velocity formulas to calculate the fall velocity. It is noted that the fall velocity should not be used as a calibration parameter. There are three options for the sediment fall velocity: 1. User-specified 2. Soulsby (1997) 3. Wu and Wang (2006) The options for the sediment fall velocity can be selected with within the Size Class section within the Sediment tab of the CMS-Flow Model Con-trol window (see figure below).

figure 2-84

The cards used to specify the sediment fall velocity are described in the table below.

table 2-74

The Soulsby (1997) formula is given by (2 23) where is the dimensionless grain size (2 24) where is the median grain size, is the sediment specific gravity, is the gravitational constant, is the kinematic viscosity. The Wu and Wang (2006) formula includes the effect of the sediment shape through and is given by (2 25) where , , . Here is the Corey shape factor defined as in which , , and are the diameters of the short, intermediate and long mutually perpendicular axes. Naturally worn quartz sands have a typical Corey shape factor of 0.7 and calcareous sand of about 0.55.

Notes: • For noncohesive sediments, it is NOT recommended to use the sediment fall velocity, or shape factor as calibration parameters. These parameters should be estimated using field or literature data. If not measurements are available then the default formula should be used. • For high sediment concentrations, the sediment fall velocity can be reduced. However, because the effects are important for high concentrations, the effect can usually be ignored. • Decreasing the shape factor decreases the sediment fall velocity.

Critical Shear Stress When using the Lund-CIRP or Watanabe transport formula, the option is given to modify the critical shear stress for incipient motion. In the case of the Soulsby-van Rijn, and van Rijn transport formula, the depth-averaged critical velocities are used and cannot be modified by the user. Therefore this section is only applicable to the Lund-CIRP and Watanabe transport formula. There are three options for the critical shear stress for incipient motion: 4. User-Specified 5. Soulsby (1997) 6. Wu and Wang (1999) The options for the sediment size class critical shear stress can be selected with within the Size Class section within the Sediment tab of the CMS-Flow Model Control window (see figure below).

figure 2-85

The cards used to specify the sediment size class critical shear stress are described in the table below.

table 2-75

The critical shear stress, , is related to the Shields parameter, , by (2 26) Soulsby (1997) proposed the following formula for the Shields parameter (2 27) The formula by Wu and Wang (1999) is given by (2 28

Notes: • For noncohesive sediments, it is NOT recommended to use the sediment fall velocity, or shape factor as calibration parameters. These parameters should be estimated using field or literature data. If not measurements are available then the default formula should be used.

Examples In the example below a single sediment size is specified. Since there is only one sediment size class, the bed sorting and gradation is not considered.

example 2-72

In the following example three sediment size classes are considered which allows the model to track the bed composition. It is noted that not the same input parameters have to be specified for all sediment size classes. Any parameters which are not specified are set the default value.

example 2-73

Transport Model There are currently three sediment transport models available in CMS: (1) Equilibrium total load, (2) Equilibrium bed load plus advection-diffusion for suspended load, and (3) Non-equilibrium total load. The first two models are selected by unchecking the checkbox which says "Use non-equilibrium transport" and selecting either "Total load" for the first model, or "Advection-diffusion" for the second next to input item named "Formulation". The third model is selected by checking the box "Use non-equilibrium transport". Table 2 76gives a description, default value, and range for the sediment transport models.

table 2-76

example 2-74

Notes: • When selecting the equilibrium total load model, the SED_TRAN_FORMULATION card is set to either WATANABE or LUND_CIRP depending on the transport formula chosen. When se-lecting the equilibrium A-D model, the transport formula is speci-fied through the concentration profile formula (described below). • All three sediment transport models are available with the explicit solver, while only the NET is available only with the implicit time stepping scheme. • Only the Nonequilibrium Total Load model is available in CMS versions 4.0 and greater at the moment. Plans are under way to in-clude the Equilibrium Bed plus Advection-Diffusion Suspended Load model as an option, but the Equilibrium Total Load model will likely be discontinued.

A description of each sediment transport model is described in the sec-tions below. Equilibrium Total load In this model, both the bed load and suspended load are assumed to be in equilibrium. The bed change is solved using a simple mass balance equation known as the Exner equation. Equilibrium Bed load plus Advection-Diffusion Suspended Load Calculations of suspended load and bed load are conducted separately. The bed load is assumed to be in equilibrium and is included in the bed change equation while the suspended load is solved through the solution of an advection-diffusion equation. Actually the advection diffusion equation is a non-equilibrium formulation, but because the bed load is assumed to be in equilibrium, this model is referred to the "Equilibrium A-D" model. Nonequilibrium Total Load In this approach, neither the bed nor suspended loads are assumed to be in equilibrium. The suspended- and bed-load transport equations are combined into a single equation and thus there is one less empirical pa-rameter to estimate (adaptation length).

Sediment Transport Formula The near bed sediment concentration or concentration capacity are calcu-lated with one of the following transport formula: • Lund-CIRP (2006) • Van Rijn (1998) • Watanabe (1987) • Soulsby-van Rijn (1997) (>=V4.0) Table 2 77 gives a description, default value, and range for the sediment transport formulae.

table 2-77