STORM SURGE SIMULATION IN TRANSFORMED COORDINATES 



Volume I. Theory and Application 



by 



John J. Wanstrath, Robert E. Whitaker, 

 Robert 0. Reid, and Andrew C. Vastano 



I . INTRODUCTION 

 1 . Background . 



Storm surges are transient fluctuations in the sea level induced 

 by atmospheric disturbances, notably those due to extra-tropical 

 storms and hurricanes and to a less frequent extent pressure jumps 

 associated with line squalls. The rise of the water and circulation 

 caused by a hurricane can be considerable and is of special practi- 

 cal importance with respect to loss of lives and property not only 

 adjacent to the coast but also well inland. Statistical studies of 

 hurricanes of record provide a means of predicting the surge height 

 along an open coast. The empirical formulas developed from these 

 studies relate the maximum expected surge height to meteorological 

 parameters and effective coastal bathymetry (Donn, 1958). However, 

 all such studies do not provide the time history or even the time 

 scale of the forcing function which is necessary as input for bay- 

 response studies (Reid and Bodine, 1968). 



More recently, time-dependent models based upon the physics of 

 the storm surge phenomena have been developed to study the generation 

 or modification of the surge as it leaves deep water and moves over 

 the Continental Slope and Shelf. These models, like the one proposed 

 herein, involve the vertically integrated equations of motion and 

 mass continuity. The greatest difficulty in utilizing these models 

 has been the manner in which the shoreline has been portrayed and the 

 application of realistic boundary conditions at the specified shore. 

 Jelesnianski (1967, 1972) takes the shoreline as a vertical plane of 

 infinite height, thereby facilitating the mathematical representa- 

 tion of the shore boundary. More general portrayal of the shoreline 

 is achieved by the schemes of Miyazaki (1963) and Platzman (1963) in 

 which the coastline is represented as a series of straight-line seg- 

 ments connected at right angles. Specifying the shoreline in this 

 stairstep manner results in greater numerical programing complexity 

 for the shore boundary condition in that the algorithm must possess 

 the ability to search for and substantiate the location of land. A 

 more serious objection is that this approximation may inject spurious 

 oscillations into the calculations. This adverse effect is more than 

 academic since the concentration of energy is near its maximum at the 

 coast, and further, this is precisely the region from which water 

 level observations are usually available for model verification. 



