APPENDIX B 



VELOCITY DISTRIBUTION IN OSCILLATORY BOUNDARY LAYER 



This section contains the description of the experimental method 

 and the results obtained in the phase of the study which had as its 

 objective the derivation of an expression describing the velocity dis- 

 tribution in an oscillatory boundary layer. The linearized equation of 

 motion from classical hydrodynamics may be used to describe the flow field 

 in the interior. Within the boundary layer as long as the flow is laminar 

 the velocity field can be described to the first approximation by an ex- 

 pression of the form 



u = u js incut - e sin (uut-(3y) j- 



(B-l) 



where u is defined as the amplitude of the velocity at the wall from 

 irrotational theory. 



When the flow in the boundary layer becomes unstable the only way 

 the field can be described is by empirical methods. The experimental work 

 involved may be extremely difficult; however, it becomes much simpler if 

 one postulated that the unsteady mean flow in this case can be described 

 by an expression of the form 



u = u a .jsinuot-f jCy) sin cut-f 2 (y) r 

 in analogy with the stable solution. 

 Equation (B-2) may be written as 



(B-2) 



where 



u l 



= 1 



I up r ~i 



sincut — — sin UJt-f^(y) 

 I u o I L J 



^ i = f,(y) 



(B-3) 



and 



The purpose therefore of the tests was to determine the functions fi(y) 

 and f2(y). The structure of equation (B-2) suggested the possibility of 

 determining these functions by the convenient method of measuring the 

 velocity amplitude and the phase shift in a flume where the bed oscillates 

 with an harmonic motion of the form u^ = u Q sincut relative to the water 

 at rest. 



The flume and the rest of the equipment used in these tests has been 

 described in detail elsewhere, Li (1954), Manohar (1955), Kalkanis (1957). 

 In Appendix A we gave a brief description of the main apparatus and in 

 this section we will give the necessary information regarding the opera- 

 tion of the additional equipment used in the tests. 



B-l 



