exploratory feasibility studies to point out specific problem areas within 

 a large study area. This knowledge allows a physical modeler to study in 

 detail and at larger scale only those specific areas and might again pre- 

 clude much model construction and testing effort. Rather simplified mathe- 

 matical models have also been used to calculate and control tidal and 

 salinity inputs to physical scale models (Simmons, Harrison, and Huval, 

 1971). 



Physical scale models have been used to provide input to mathematical 

 models. In a general way, observations of a physical model running under 

 test conditions often lead to ideas and correct conclusions which would 

 not have been realized under another set of circumstances. Most empiri- 

 cally based computation formulas (such as Manning's equation) have been 

 derived as a result of laboratory testing. Scale models also provide 

 boundary and initial conditions as well as discharge coefficients for a 

 mathematical model. In addition, physical scale modeling is used to 

 obtain dispersion coefficients which are then used in mathematical models 

 to simulate tidal transport phenomena. Mathematical models are often 

 easily verified by using hydraulic scale models (Simmons, Harrison, and 

 Huval, 1971). 



Table 3-3 summarizes (in a simplified listing) some of the chief 

 advantages and disadvantages of the two types of models. However, in 

 deciding which modeling technique (if any) is appropriate for solution 

 of specific problems, experienced investigators should be consulted. 



Table 3-3. Physical models versus mathematical models.' 



Advantages 



Disadvantages 



Physical models 



Best description of three-dimensional flow 



High cost 



Extensive operational experience 



Difficulty of modification 



Ease of visualization 



Distortion effects 



Best simulation of salinity effects 



Limited long-range development 



Ability to reproduce several phenomena in 



Measurement difficulty 



a single model 





Mathematical models 



High repeatability and precision of 



Cannot reproduce three-dimensional density 



measurements 



gradients 



Data and model storage and retrievability 



Storage grid-size limitations 



Computational speed 



High computer cost 



Compatibility with other models 



Computational stability problems 



Ability to expand and improve models 



Boundary condition definition 



Verification and modification simplicity 



Integration limits— time and scale 



Low cost after development 



High initial development cost 





Mathematical equation formulation problem 



Simmons, Harrison, and Huval, 1971. 



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