velocity may be ignored. This latter limitation would require that there be no abrupt significant depth changes

in the harbor. These equations are known as the long-wave equations (see Part II-5). Harris and Bodine

(1977) present a derivation of these equations and discuss their formulation for numerical solution.

(c) If the solute advection-diffusion equation is added to the numerical hydrodynamic model, the

movement and distribution of pollutants in the harbor can be computed. From this, the harbor exchange

coefficients and flushing efficiency can be determined. An interesting application of numerical modeling to

investigate harbor circulation, flushing, and variations in dissolved oxygen has been carried out by the

Waterways Experiment Station for Los Angeles and Long Beach Harbor in California (Vemulakonda, Chou,

and Hall 1991). Typical two-dimensional and a quasi-three-dimensional numerical model investigations

studied the impact of deepening channels and constructing landfills in the harbor.

(d) Chiang and Lee (1982), Spaulding (1984), and Falconer (1980, 1984, 1985) provide other examples

of applying the long-wave equations to calculate harbor hydrodynamics and adding the solute transport

equation to determine the flushing characteristics of harbors.

(e) These numerical models have a number of advantages - they are flexible in that it is easy to adjust

input tide and wind conditions as well as harbor bottom and lateral boundary conditions, and they do not have

some of the scale/distortion problems found in physical models. But they also have disadvantages - they are

a two-dimensional representation of the flow field in the harbor, and since calculations are done for a grid,

flow details that are smaller than the grid dimension are not represented. This latter disadvantage makes it

difficult to investigate, for example, the eddies generated by flow separation at the harbor entrance or at

internal structures. It can be overcome to some extent by decreasing the grid point spacing in key segments

of the harbor such as around the harbor entrance (Falconer and Mardapitta-Hadjipandeli 1986).

(f) Numerical models require that a number of empirical coefficients (e.g. surface wind stress and bottom

stress, eddy viscosity, and component diffusion coefficients) be defined in order to run the model. Thus,

confidence in the model can be significantly increased if field data are available to calibrate the model and

verify subsequent model results.

(2) Physical model studies.

(a) Physical model studies have been conducted to investigate flushing and circulation patterns for

existing and proposed harbors (Nece and Richey 1972, Schluchter and Slotta 1978, Nece 1985, Nece and

Layton 1989) and for basic planform patterns of idealized harbors (Nece, Falconer, and Tsutumi 1976; Jiang

and Falconer 1985).

(b) Physical models of harbors are designed to investigate tidal flushing, so they are based on Froude

similitude (Hudson et al. 1979). They typically have a distorted scale, with the vertical scale being larger than

the horizontal scale. Common model scale ratios that have been used are 1:30 to 1:50 for the vertical scale

and 1:300 to 1:500 for the horizontal scale. It is assumed that wind effects are negligible and that the water

column has no density stratification. Also, the effects of Coriolis acceleration are not modeled. Most harbors

are sufficiently small that Coriolis effects can be neglected.

(c) For models using water and having the typical harbor model/prototype scale ratios, Froude and

Reynolds similitude are incompatible. Consequently, model Reynolds numbers are underscaled. Thus,

inertial effects are scaled but turbulent diffusion is not scaled. To minimize these effects, some experimenters

have installed roughness strips at the model harbor entrance to generate turbulence. Thus, local diffusion-

dispersion of solutes is not accurately replicated but advective transport of solutes is replicated. The latter

typically dominates. Fine details of the internal flow circulation are not replicated, but gross circulation

patterns are.

II-7-52

Harbor Hydrodynamics

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