Littoral Sedimentary Processes- — I nman, Gayman and Cox 
129 
ACKNOWLEDGMENTS 
This paper represents, in part, results of re- 
search carried out by the University of California 
under contract with the Office of Naval Re- 
search. The original field work was performed in 
November and December 1955. Supplementary 
field study in January 1959 was supported by the 
LI hue Plantation Company, Kauai. Valuable ad- 
vice and field assistance during the supplemen- 
tary study was given by J. T. Orrick and S. L. 
Keala, Jr., of the Lihue Plantation. Since this 
study, North Kapaa Reef has been modified by 
dredging. Unfortunately the dredging was not 
performed entirely in accordance with plans 
based on the study of the littoral processes over 
the reef as outlined here. A north-south channel 
was dredged, which may intercept the sand sup- 
ply to the beaches and cause the beach to erode. 9 
Valuable suggestions and guidance during the 
course of the study were contributed by R. S. 
Arthur, E. D. Goldberg, F. P. Shepard, E. W. 
Fager, and M. N. Bramlette of the University 
| of Califoria. Suggestions leading to the section 
- on exposure to waves and wind were made by 
P. L. Horrer of Marine Advisers, La Jolla. Idem 
| tification of foraminifera was made by Ruth 
Todd of the U. S. Geological Survey, Washing- 
ton. In addition, the writers wish to express their 
appreciation to H. S. Ladd and J. I. Tracey, Jr., 
I also of the U. S. Geological Survey, for their 
; careful reading of the manuscript, and to Edith 
Haselwood of the Hawaiian Sugar Planters’ As- 
| sociation for her editorial criticism. 
APPENDIX I 
DERIVATION OE SEDIMENT TRANSPORT 
EQUATION 
x = x, p x=x 2 
BEACH ; y> j 
LONGSHORE ........ + 
CURRENT V | 
- A,, » 
© 
o 
1 
* Ax * 
OCEAN rr 
ri 
B; while the sediment Q, transported longshore 
consists of two components, a terrigenous frac- 
tion T, and a biogenous fraction B = 1 — T If 
complete mixing takes place within a coastal 
segment, having boundaries xi and X 2 , a distance 
Ax apart, then T is a function of the longshore 
distance x and can be written T ( x ) . The above 
assumptions permit the budget for the fraction 
of terrigenous material to be written: 
Q • T( Xl ) = Q • T(x 2 ) + F 0 T(xi +Lr) Ax 
^ Q T(xi) T(x 2 ) , , Ax, 
0= x + F 0 T(xi. d — - ) 
Ax 2 
but in the limit as Ax 
-> o 
~ dT 
° =Q 
F„T(x) 
and integration gives 
lnT= — ^-x + k 
where In is the base of natural logarithms and k 
■ is a constant of integration. The relation may be 
written in terms of B = 1 — T as: 
A small segment of shoreline (see figure) is 
! assumed to be in a state of equilibrium, such 
i that the rate of longshore transport of material 
into the segment (the longshore influx) is con- 
stant and equal to the outflux, Qi = Q 0 - Also, the 
onshore influx and outflux are constant and 
equal, F| l- F 0 . The sediment influx from offi 
; shore, F :> consists of 100% biogenous material, 
9 Comparison of surveys of 1959 and 1962 indicate 
| a net erosion of beach immediately westward of the 
dredging area (approximately stations 51-57, Fig. 8) 
! of about 2,500 cubic yd per year. 
I n B= -q - x + k 
REFERENCES 
Arthur, R. S. 1948. Forecasting Hawaiian swell 
from January 2 to 5, 1947. Bull. Amer. Me- 
teor. Soc. 29:395-400. 
BlEN, G. S. 1952. Chemical analysis methods. 
Scripps Inst. Oceanogr. Ref. 52-58. 
