cut a terrace, the well-defined water depth, d^, at the seawardmost 

 stable point indicates the elevation of the terrace (Fig. 2) . Measured 

 values of dc from published profiles will be compared to dg , calcu- 

 lated using Figure 1 (eq. 5), because -dg has been hypothesized to 

 indicate the limit depth of intense bed agitation, revealed by the 

 nearly horizontal profile feature developed at the cut depth. 



Figure 3 plots the measured d^ against the calculated dg for 27 

 published profiles from 7 laboratory studies including tests with fine 

 sands (D<0.4 millimeter). (Twenty other profiles obtained in these 

 studies did not show an ideal terrace, although test conditions were 

 similar; see App. B,) There is some scatter, but the 27 pairs of cal- 

 culated and measured depths have a correlation coefficient of 0.936, im- 

 plying a linear relationship between da and dg is certain (Freund, 

 1962). On the average, the calculated limit depth is 3.6 percent greater 

 than the water depth at the cut into the initial slope. This good agree- 

 ment between calculation and measurement occurs for a wide range of wave 

 conditions, with 0.0039 £ H^/L^ £ 0.071 (see App. B for test conditions). 



The reduced scale of these laboratory tests, compared to natural pro- 

 totypes, should not be important for the present comparison, because the 

 threshold of intense bed agitation is evidently crossed in th.e terrace 

 zone of the laboratory tests. Also, the calculation procedure is based 

 on wave energy per unit sediment grain volume, and fine sand occurs both 

 in the laboratory tests and in the offshore region of natural beaches. 

 Limited verification of the unimportance of scale effects on the cut 

 depth in a plane sand slope is provided by several profiles obtained by 

 Saville (1957) in large-scale laboratory tests. Saville's test number 5 

 had the largest ratio of water depth to wavelength, with waves 4.8 feet 

 high in a 15-foot Stillwater depth and a 3. 75-second wave period; dg = 

 8.3 feet is obtained for this condition. Figure 4 shows the unpublished 

 profiles developed with sand of 0.22- and 0.46-millimeter diameter. Al- 

 though there is no clear terrace development, the initial slope is eroded 

 onshore of water depths from 7.0 to 8.8 feet, with offshore deposition 

 in both cases. Judging from this evidence, the calculation procedure 

 provides an accurate estimate for the limit depth of intense agitation 

 of a fine sand bed by waves. 



IV. APPLICATION TO NATURAL BEACHES 



The natural beach profile adjusts seasonally in response to wave 

 climate with relatively little loss of sand from the nearshore over an 

 average yearly cycle. Subaerial profile erosion by storm waves can be 

 notable, but most eroded sand remains in relatively shallow water and is 

 carried onshore by less steep waves. Bruun (1954) and Winant, Inman, and 

 Nordstrom (1975) analyzed southern California data showing that the sub- 

 marine profile beyond the 5- to 10-meter water depth is accurately 

 described throughout the year by a constant function. 



12 



