based on Newton's law, force = mass times acceleration. Equation (3) 

 is the expression for conservation of mass for an incompressible fluid, 

 generally referred to as the equation of continuity. 



4. The Bathystrophic Approximation 



The assumptions made by Freeman, Baer and Jung (1957) in the develop- 

 ment of the Bathystrophic Storm Tide Theory implied that: the volume 

 transport perpendicular to the shore could be neglected; the onshore winds 

 give an instantaneous rise of the sea surface; advection of momentum 

 (field acceleration) is negligible; the sea surface is uniform, and 

 parallel to the depth contours; and precipitation can be neglected. 

 These assumptions indicate that: 



3U ^,, SU ^bx „ u 4. 



-rr- , fU , -77— , -> 0, no onshore transport, 



9t * ' 9x ' p ' r J 



M , M , M ^0, momentum values neglected, 

 XX' yy' xy ' 



9S 9V 



-— , — - ^ 0, alongshore sea surface uniform, 



9y 9y 



P ->- 0, Precipitation neglected. 



95 9C Barometric effects are not considered here, but will be 

 9?c ' "dy accounted for from a separate source. This effect is 

 discussed later. 



Based on these assumptions. Equations (1) and (2) reduce to 



gD |i = f V + ^ (4) 



^ 9x p 



9t p 



and the continuity relation. Equation (3) , is disregarded in the Bathy- 

 strophic approximation because of the assumptions taken. Thus the reduced 

 equations are quasi-two-dimensional since computations are restricted to a 

 single axis, the x-axis; however, the rate of change of transport along 

 the y-axis is retained to account for the effects of earth's rotation. 



5. Bottom and Surface Stresses 



Relations are now introduced which describe approximately the stresses 

 that occur when there is water motion in the neighborhood of the seabed 

 and the interaction of the winds with the sea surface. Formulas based on 

 experiments and theoretical considerations have been introduced which give 



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