APPENDIX A 

 STABILITY OF AN OSCILLATORY BOUNDARY LAYER 



It has been shown in section 3 that the wave motion at the outer edge 

 of the boundary layer may be approximated by a simple harmonic motion. The 

 stability of this layer and its transition into turbulence plays an im- 

 portant role in the problem associated with the transportation of sediment. 

 In a laminar oscillating stream the predominant force induced by the flow 

 on the particle is a tangential drag. When this force becomes larger than 

 the force resisting motion the particle will begin to move. A criterion 

 of initiation of movement then can be set as 



T c = K (p - p f ) g tan 9 1 (A-l) 



where 9i is the angle of repose of the particle. The shear stress T at 

 any distance from the wall may be determined from equation (3-15). It is 

 evident that the maximum value of T occurs at the wall so that 



T = p, |^ = \i&u n (A-2) 



max ^ dy | y=o o 



Therefore the criterion of motion in a laminar boundary layer can be set 

 as 



-,2/3 



_ pC (p s -Pf) gD tan 9! 1 (A _ 3) 



a p f v 

 This is Manohar's (1955) equation (19). 



In an unstable boundary layer on the other hand the predominant force, 

 as we have seen in section 4, is the hydrodynamic lift which is associated 

 both with the mean unsteady flow and the turbulent perturbations. The 

 mechanism through which motion is induced is not only different in character 

 for the two cases but also in the unstable case it is more intense by several 

 orders of magnitude. 



The purpose of Li's investigation (Li, Huon 1954) was to determine the 

 factors and relationships governing the transition of an oscillatory laminar 

 layer over smooth and rough beds. The mathematical model being so complex, 

 a theoretical approach was ruled out from the outset. The effort therefore 

 was concentrated to obtain empirical results experimentally. The study in 

 the laboratory of the boundary layer created by a surface wave would re- 

 quire equipment of very large size. It was instead considered expedient 

 to investigate the stability of the boundary layer near an oscillating wall 

 in a body of water at rest. It is apparent of course that the patterns of 

 flow on the prototype and in such a model are by no means identical but 

 the reasoning was that the critical values of the governing parameters 



