6. Limitations of Reduced Equations 



The Bathystrophic equations reveal that the time-dependent surge can 

 be determined only spatially along the x-axis or a single line, often 

 referred to as the traverse line. Orientation of this line becomes very 

 important for valid computations due to the restrictions brought about by 

 the simplifications of the resulting formulas. Since all transport along 

 the X-axis is neglected, the computational axis must be oriented peirpen- 

 dicular to the bed contours. The onshore wind stress is then assumed 

 to give an instantaneous setup of water where the deep basin beyond the 

 Continental Shelf acts as a relatively infinite reservoir for replenishing 

 the volume being set up. The orientation of the traverse line for shelves 

 that have contours which are straight and parallel to the coastline pre- 

 sents no problems. Actual shelf formations do not have such a simple 

 configuration; many are quite complex in shape. If the shelf configura- 

 tions are not unusually complex, particularly in the shallow nearshore 

 regions, it appears that a reasonable estimate might be obtained by 

 orienting the traverse line which on the average would be perpendicular 

 to the bed contours, and by giving special weight to those contours in 

 the nearshore region. It is emphasized that a line along which numerical 

 computations are made rrust always be taken straight and perpendicular on 

 the average to the bed contours for valid resolution. 



There are also restrictions for placement of the traverse line with 

 respect to the storm system. Use of the Bathystrophic approximation is 

 invalid for estimating storm surge in the left quadrants of the hurricane, 

 because of the water motions due to the offshore wind components coupled 

 with the effects of earth's rotation. Furthermore, the formula is gener- 

 ally not considered appropriate for traverses to the left of the region 

 of maximum winds. A traverse line can be taken at the region of maximum 

 winds and anywhere to the right of this position, although previous 

 studies indicate that surge predictions are not too reliable if the 

 traverse line is selected in the vicinity of the outskirts of the storm. 

 Care is needed in computing the surge along a traverse line when a storm 

 moves over the Shelf with a large crossing angle. Consequently, it is 

 seen that one can only investigate the dispersion of the surge at and to 

 the right of maximum winds when using the Bathystrophic formulas. 



Generally, in connection with storm- surge problems, predicting the 

 height of the water surface is of primary interest; predicting the associ- 

 ated volume transport or current velocities is of only casual interest. 

 The simplified prediction technique covered here neglects all x-component 

 transport, and only partially describes the y-component of transport. 

 Thus, the Bathystrophic relations should be used only for predicting the 

 height of the water surface. 



This prediction scheme is considered more appropriate for determining 

 storm surge for slow moving hurricanes, because of the resulting quasi- 

 steady state relation. More specifically, 8U/9t is neglected while 9V/8t 

 is retained. For fast-moving hurricanes, inertial effects become important, 

 and can contribute significantly to the total setup at the shore. 



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