in a turning of the height contours of the lake surface. However, the 

 turning of the contours lagged behind the wind so that for a time the 

 wind blew parallel to the water level contours instead of perpendicular 

 to them. Contour lines of the lake surface from 1800 hours on 26 August 

 to 0600 hours on 27 August 1949 are shown in Figure 3-57. The map con- 

 tours for 2300 hours on 26 August show the wind blowing parallel to the 

 highest contours at two locations. (Haurwitz, 1951), (Saville, 1952), 

 (Sibul, 1955), (Tickner, 1957), and (U.S. Army, Corps of Engineers, 1955).) 



Recorded examples of wind setup on the Great Lakes are available from 

 the U.S. Lake Survey, National Ocean Survey, and NOAA. These observations 

 have been used for the development of theoretical methods for forecasting 

 water levels during approaching storms and for the planning and design of 

 engineering works. As a result of the need to predict unusually high 

 stages on the Great Lakes, numerous theoretical investigations have been 

 made of wind setup for that area. (Harris, 1953), (Harris and Angelo, 

 1962), (Platzman and Rao, 1963), (Jelesnianski, 1958), (Irish and 

 Platzman, 1962), and (Platzman, 1958, 1963, 1965, and 1967),) 



Water level variations in an enclosed basin cannot be estimated satis- 

 factorily if a basin is irregularly shaped, or if natural barriers such as 

 islands affect the horizontal water motions. However, if the basin is 

 simple in shape and long compared to width, then water level elevations 

 may be reasonably calculated using the hydrodynamic equations in one 

 dimension. Thus if the motion is considered only along the x-axis (major 

 axis), and advection of momentum, pressure deficit, astronomical effects 

 and precipitation effects are neglected, then Equations 3-50 and 3-52 

 reduce to 



3U 98 1 



9s aiu 



at ~ ax 



(3-80) 



If it is further assumed that steady state exists, then Equation 3-79 becomes 



dS 1 



dx pgD 



i^s+'^b) (3-81) 



The bottom stress is taken in the same direction as the wind stress, since 

 for equilibrium conditions the flow near the bottom is opposite to flow 

 induced by winds in the upper layers. Theoretical development of this 

 wind setup equation was given by Hellstrom (1941), Keulegan (1951), and 

 others. The mechanics of the various determinations have differed some- 

 what, but the resultant equation has been about the same. This wind 

 setup equation is expressed as: 



k'np^W'F 



AS = COS0 (3-82) 



PgD 



3-128 



