pipe sections with opposite flow direction, from which head-loss readings 
could be obtained and correlated with flow rate and sediment concentration; 
and a Venturi meter, in which the pressure drop was again measured and 
correlated with sediment concentration, 
A further report "Sand Movement on Coastal Dunes" was given limited 
distribution by the University as Institute of Engineering Research Tech- 
nical Report HEL-2-3, and is also being published in the Proceedings of 
the Federal Interagency Sedimentation Conference in Jackson, Mississippi, 
28 January - 1 February 1963. This report summarizes the results of 
laboratory studies of sand movement by wind, discussed more fully in the 
report, “Sand Movement by Wind", and its appendix discussed above. 
A further report, "Transportation of Bed Material Due to Wave Action" 
was given limited distribution by the University as Institute of Engineer- 
ing Research Technical Report HEL-2-4, and is now being published as a 
Beach Erosion Board Technical Memorandum, This report discusses the 
mechanism of sediment transport in a layer immediately adjacent to the 
ocean floor for long waves of small amplitude in relatively deep water. 
The fundamental principle of the supporting theory is that at equilibrium 
the submerged weight of the solid particle is balanced by the vertical 
component of the resultant hydrodynamic force exerted on the particle by 
the flow above. Effects of both the unsteady mean flow velocity and the 
turbulent fluctuations are taken into account. The distribution of the 
lift forces associated with the former was determined experimentally, 
while a statistical approach based on experience with the same phase of 
the problem in a steady mean flow was used to determine the latter. 
IV, University of California, Contract DA-49-055-civ-eng-63-5. Wave 
Diffraction and Refraction Studies, (Old Contract DA-49-055-eng-44, 
"Laboratory Study of Wave Refraction") 
’ Work previously carried out under Contract DA-49-055-eng-44 was con- 
tinued under a new contract, Contract DA-49-055-civ-eng-63-5, "Wave Dif- 
fractiofxand Refraction Studies". A report, "Higher Approximation to 
Non-Linear Water Waves and the Limiting Heights of Cnoidal, Solitary, and 
Stokes* Waves", was supported partially under this contract and published 
as Technical Memorandum 133 of the Board. This report presents a mathe- 
matical description of some of the higher approximations to non-linear 
water waves and is particularly important in indicating limiting heights. 
First and second approximations to solitary and cnoidal waves are obtained 
by carrying the shallow water expansion method of Friedrichs and Keller 
to the fourth order, The rigorous first approximation to these finite 
amplitude waves of permanent form is identical to earlier solutions. The 
second approximation, however, results in new expressions for predicting 
behavior of long waves in shallow water. The limiting height for solitary 
waves is found to be 8/llths of the free water depth. The third approxi- 
mation to Stokes’ waves in water of finite depth is verified by use of 
classical small-perturbation expansion methods, For finite amplitude waves 
the series expansion is found to be in terms of a parameter that is most 
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