140 



recently, fully three-dimensional models have been developed. These models 

 have been applied to a study of New York Harbor'^. 



9.3 PHYSICAL PRINCIPLES 



Analytic approaches to solve the problem of saltwater intrusion depend 

 upon whether the estuary can be treated as stratified, or as partially 

 mixed or fully mixed. Thus, for example, an estuary is classified as "well 

 mixed" if the salinity over any flow cross section does not vary by more 

 than 10%; otherwise it is classified as partially mixed (Ippen, 1966). In 

 a fully stratified estuary the salt is contained almost entirely in the 

 lower layer (the wedge). A further quantitative means of classifying and 

 comparing estuaries, and one which requires salinity and velocity only, is 

 due to Hansen and Rattray (1966). Their commonly used diagram relates, for 

 different types of estuaries, a stratification parameter, 5s/sq, defined as 

 the ratio of the surface to bottom difference in salinity, 5s, divided by 

 the mean cross -sectional salinity, Sq, and a circulation parameter, Ug/uf, 

 the ratio of net surface current, Ug to the mean cross -sectional velocity, 



Uf. 



The penetration of salt water into fresh is strongly influenced by 

 density differences, since salt water is the heavier of the two fluids. 

 Consider a barrier which separates two fluids, one of density p (water) 

 with zero salinity (s = 0) and another of density p + pA (salt water) , 

 salinity Sq. As shown in Fig. 9.1a, if the barrier were lifted at time t = 

 0, a saltwater gravity front (current) would penetrate fresh water at the 

 bottom, and an equal volume of fresh water would be displaced per unit time 

 into salt water, at the top. If now a freshwater flow of velocity, Uq, 

 were imposed as shown in Fig. 9.1b, the intrusion of gravity current would 

 be arrested at some position where the pressure and drag forces in both 

 directions balance. This is the basic mechanism which operates within 

 estuaries, where sea-driven tides are an additional factor. In cases where 

 the mixing potential of the incoming tidal energy is relatively high, the 

 estuary will be well mixed in terms of vertical salinity structure. If 



^Allen Teeter, Waterways Experiment Station, Vicksburg, Mississippi, 

 personal communication. 



