CALCULATING A YEARLY LIMIT DEPTH TO THE ACTIVE BEACH PROFILE 



by 

 Robert J. EaLlevmeiev 



I. INTRODUCTION 



Certain coastal zone activities require setting a seaward limit to 

 the very active (littoral) zone of a sand beach; e.g., sediment budget 

 calculations, submarine placement of beach fill, and design of coastal 

 structures such as jetties. In principle, repetitive measurements of 

 waves and bathymetry can define the seaward limit at a site by establish- 

 ing the water depth beyond which bottom changes caused by wave action are 

 negligible. However, these data are costly and rare, so an estimate of 

 the limit depth must often be obtained from other evidence or experience. 



Silvester (1974) discussed physical data showing that extreme surface 

 waves occasionally move bottom sands in water depths up to about 100 

 meters; i.e., over much of the continental shelves. However, reviewing 

 geomorphological evidence, Dietz and Fairbridge (1968) concluded that 

 waves intensively work fine, nearshore sands into a somewhat concave 

 equilibrium profile extending to a water depth of 10 to 20 meters. This 

 depth is the seaward limit to the active profile, supposedly related to 

 wave climate for a particular site. Offshore of this depth lies a zone 

 of less important sand transport by waves. 



For these coastal zone activities, a calculation procedure using 

 knovm wave climate might provide a useful estimate of this limit depth, 

 in case definitive data are lacking. This report proposes a procedure 

 giving a minimum value for the limit depth to the seasonal onshore- 

 offshore transport cycle on sand beaches. The development is based on 

 dimensional reasoning of the energetics of wave agitation of a sand bed, 

 without detailed examination of sand transport processes. Although some- 

 what speculative, this approach arrives at a simple calculation procedure 

 giving a limit depth for a shoaling two-dimensional wave with a certain 

 height and period. Calculated depths agree with the published laboratory 

 and field evidence considered in Sections III and IV. 



II. DEVELOPMENT OF THE CALCULATION PROCEDURE 



This development considers wave energy density in terms of two dimen- 

 sionless parameters. The first parameter (eq. 1) has documented perti- 

 nence to the onset of sediment movement as a bedload. A second parameter 

 (eq. 2) , similar in form but numerically smaller, is hypothesized to 

 describe the onset of intense bed agitation, characterized by sediment 

 entrainment into the wave flow beyond a thin near-bed layer. 



Silvester (1974) presented the empirical expressions derived by var- 

 ious investigators of the motion threshold on a flat sediment bed. An 

 important factor in each expression is the sediment mobility parameter: 



