Section II. PRELIMINARY CONSIDERATIONS 



A. Bar Jormation: — If an experimental beach be assumed having 

 initially a smooth sand surface of constant slope and subject to the 

 action of waves, the part of the beach which lies between the point of 

 impending wave break and that of reformation following the breaker 

 is the area of most active change. This region may be called the 

 bar environment since it is here that the bar is ultimately formed. 

 As will be discussed more fully later, the breaker is the most important 

 element of the region and is the genetic cause of the bar itself. 



The deformation of the beach surface is in the form of a ridge, 

 which is relatively flat in the initial stages and moves toward the 

 shore in an observable manner. In the course of time the ridge is 

 enlarged, its form is established or stabilized and its motion decreases 

 to an imperceptible value. When the changes in the position and 

 shape of the bar become minute, the bar can be considered relatively 

 stable. Thus, beginning with an initial smooth beach of slope i at 

 time ^=0, the bar will reach a stable position and assume a stable 

 shape at time U, such that after that time the changes in the bar 

 position and the bar shape take place at an imperceptible rate. 

 Hence, ti may be said to be the time required for the bar to become 

 relatively stable. The first problem in studying bar formation 

 therefore is to determine the factors which affect the position of the 

 bar at the time that it becomes relatively stable. 



The dimension defining the position of bars in a hydrodynamical 

 sense must necessarily be selected. Inasmuch as the types of bars 

 considered here are associated with breaking waves, the relevant 

 dimension is the depth of the bar with respect to the undisturbed water 

 surface rather than the distance between the bar and the shore. 

 The depth of the bar can be represented by the bar base, defined as 

 the straight line joining the seaward and shoreward toes of the bar 

 (fig. 1.) The depth of the bar base is measured from the undisturbed 

 water surface to the point directly below the crest, C. This depth will 

 be denoted by H'b when the bar is in the process of formation and 

 by Hb after the bar becomes relatively stable. 



Suppose that the variables affecting H' b are the deep water wave 

 length Xo, wave height ao, time t, the sand size doM, the sand size 

 distribution coefficient a^ (Krumbein notation), the kinematic 

 viscosity v, the sand and water densities Ps and Py,, respectively, and 

 the slope of beach i. The usual considerations of dimensional analysis 

 then lead to the general relation: 



