The hydraulic model has been developed and used to solve many estua- 

 rine problems involving physical processes. Only the hydraulic model is 

 presently capable of simulating fluid flows with variable densities in 

 three dimensions. Many problems which cannot now be expressed mathe- 

 matically can be solved by the hydraulic model. Those problems which 

 can be expressed mathematically often require basic data to evaluate 

 coefficients in the equations which, in particular instances, may be 

 obtained at a far less cost and time in laboratory flumes or hydraulic 

 models than in nature. The hydraulic model study method has certain 

 other advantages. It is a highly useful method of visually demonstrating 

 alternative plans of improvement to the public and to representatives of 

 local. State and Federal agencies. The model has great value in decision- 

 making on estuary improvements, providing the necessary understandable 

 information by observation. The model can also be a research tool, and 

 imdefined problems or principles in the prototype can be discovered and 

 solved by operation of a hydraulic model (U.S. Department of the Army, 

 1969) . 



The hydraulic model has shortcomings, not the least of which is the 

 apparently great first cost for construction and verification. Changes 

 in conditions and alternative plans are more time consuming to study in 

 a physical model than in a mathematical model. The technique provides 

 little information on suspended-sediment concentrations in the estuary 

 or on patterns of resuspension of fine-grained sediments throughout the 

 estuary (U.S. Department of the Army, 1969). Phenomena which cannot be 

 reproduced in fixed-bed hydraulic models include shoreline erosion, 

 bottom scour, decay of pollutants , chemical interactions, turbidity, 

 flocculation, photosynthesis, respiration, evaporation, solar radiation, 

 refraction and diffraction (simultaneously) of short-period waves, and 

 biological processes. 



c. Complementarity of Scale and Mathematical Models . Extensive use 

 of both physical and mathematical models has shown that the two problem- 

 solving methodologies complement each other to a great extent. Although 

 the use of an existing well-verified mathematical model would probably 

 result in savings of time and money, physical scale modeling of tidal 

 phenomena is usually reliable in providing accurate values of decision 

 parameters for a wider range of problems than its mathematical modeling 

 counterpart. In some cases, the two modeling techniques have been 

 applied to the same prototype, an advantage of using different modeling 

 capabilities to perform given parts of the study in the most economical 

 manner (Simmons, Harrison, and Huval, 1971). 



Mathematical models are often used to provide input data for physical 

 scale models more economically than this input could be generated from 

 other sources (and vice versa). Mathematical models are also iised to 

 set the closed boundaries of physical models by establishing limits be- 

 yond which phenomena do not affect the problem areas or by providing 

 computed open-boundary conditions. Either approach would allow physical 

 modelers to reduce a model area at a commensurate savings in construction 

 and testing. Relatively simple mathematical models have been used for 



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