then a physical model may be cost-effective. A substantial amount of literature on physical models and

modeling is available. An extremely comprehensive source of information is Hudson et al. (1979).

(1) Introduction.

(a) Numerical hydrodynamic models generally fall into two solution scheme categories, finite difference

and finite element. Finite difference models use a rectangular orthogonal grid, although grid transformation

schemes permit the mapping of the grid to conform to curvilinear boundaries. Finite element models use a

variable-size, either triangular or rectangular, unstructured computational grid. The ability to define elements

of variable size gives the finite element method an advantage over finite difference schemes for accurately

representing areas of very complex geometry. However, both modeling techniques produce accurate results

when applied correctly. Both models are in common use, as is demonstrated in the following two examples

of numerical model applications to specific coastal and estuarine applications. These examples are intended

to demonstrate the capability and accuracy of numerical models to reproduce natural hydrodynamic systems

and generate an appreciation for the difficulty involved with applying them to specific flow-field situations.

(b) In addition to differences in computational schemes, hydrodynamic models are also categorized as

1-, 2-, and 3-dimensional. One-dimensional models provide a cross-sectional average solution to the

governing equations. This class of solution is well-suited to pipeline or river flow problems, but not

coastal/estuarine problems. Therefore, 1-D models are not addressed in this chapter because their solutions

provide little detailed flow-field information that cannot be computed from the formulas given in Part II-1,

"Water Wave Mechanics."

(c) Two-dimensional models are generally depth-integrated (depth-averaged); they provide a single

velocity vector corresponding to each horizontal cell of a computational domain representing large areas of

surface flow. Currents are defined at nodes or on cell faces, depending on the computational scheme used.

Two-dimensional models are generally used in situations where the modeled system is well-mixed, i.e.,

currents are approximately uniform throughout the water column. These models are appropriate for studies

in which changes in surface elevation are the primary concern. Typical examples include storm surge or lake

seiche studies.

(d) An additional class of two-dimensional models is the laterally averaged model. In this case, instead

of depth-averaged governing equations, a width-averaged set of equations is defined. In this form of solution,

currents are defined at multiple locations through the water column; however, no horizontal distribution

information is given. Laterally averaged models are generally used in conjunction with river flow, reservoir

operation, and/or salinity intrusion applications and these models are not described in this manual.

(e) Three-dimensional applications are used when the vertical structure of currents is not uniform and

the vertical distribution of currents is an important aspect of the study. Example applications include areas

exhibiting flow reversal situations where surface currents and bottom currents flow in opposite directions.

Included in this class of problems are cases in which vertical temperature and salinity gradients create density-

driven flows. Although these non-tidal flows can be small in comparison to the tidal ebb and flood currents,

they can contribute to residual circulation patterns that may affect the transport and dispersion of certain water

quality parameters such as dissolved oxygen. An additional example may include channel-deepening effects

on salinity intrusion.

Water Levels and Long Waves

II-5-55

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