As opposed to analytical solutions of shoreline change, which simplify the equations used to predict beach

evolution, mathematical modeling facilitates generalization of these equations so that input parameters may

vary in time and in the longshore, and possibly cross-shore, dimensions. Also, numerical models become

necessary where difficult boundary conditions are encountered (say at groins or offshore breakwaters)

because of shoreline morphology or wave transformation. Numerical models of beach change perform best

when a perturbation is introduced to a system that is in equilibrium. The perturbation to the system might

be an introduction or removal of littoral material (e.g., beach fill, sand mining, release of sediment due to a

flooded river or landslide) or placement of a hardened structure (e.g., groins, detached breakwaters, seawalls,

revetments). Historical trends of beach change and knowledge of the littoral budget are typically used to

calibrate and verify the controlling equations, then forecasts may be simulated as a function of various

engineering alternatives and/or wave climate scenarios. Therefore, beach response as a function of complex

coastal processes may be readily examined in detail with mathematical models. However, the limitations

inherent in the controlling equations, and assumptions implied in developing "representative" parameters

require that model results be carefully interpreted, ideally within the context of other coastal engineering

analyses.

(1) Fully three-dimensional models.

(a) In nature, nearshore beach change due to waves, circulation patterns, and longshore currents varies

with time and location; therefore, equations to fully describe effects of these processes on beach evolution

must be three-dimensional and time-dependent. Development of these equations is still an area of active

research, and fully three-dimensional models are not available for routine engineering design.

(b) The intent of three-dimensional models is to describe bottom elevation changes which may vary in

the cross-shore and longshore directions. These models provide insight into wave transformations and

circulation for complicated bathymetry and in the vicinity of nearshore structures. However, they are less

useful for making long-term shoreline evolution calculations because they are computationally intensive.

These models also involve poorly known empirical coefficients such as those related to bottom friction,

turbulent mixing, and sediment transport. Integrating the calculated local distributions of sediment transport

over the cross-shore and for long time periods may lead to erroneous results because small local inaccuracies

will be amplified over a long simulation. Because of their intent to predict local process parameters (e.g.,

waves, currents, sediment transport), they require a detailed data set for calibration, verification, and

sensitivity testing, perhaps from a companion physical model study or field data collection.

(2) Schematic three-dimensional models. Schematic three-dimensional models simplify the controlling

equations of fully three-dimensional models by, for example, restricting the shape of the profile or calculating

global rather than point transport rates. Bakker (1968) has developed a two-line model which allows the

evolution of two contours to be independently simulated. From this model, Perlin and Dean (1983)

developed an n-line model that allows an arbitrary number of contour lines to represent the beach profile.

Most schematic multi-line models developed to date are restricted to monotomic profile representations. For

models that represent the profile by more than one contour, it is necessary to specify a relationship for cross-

shore sediment transport. Schematic three-dimensional models have not yet reached the stage of wide

application due to their complexity, requirement for considerable computational resources, and need for

expertise in operational applications.

III-2-78

Longshore Sediment Transport

Integrated Publishing, Inc. |