where 



n = number density of grains at elevation z 



n a = the reference number density at a reference elevation 



w f = fall velocity of particles 



v r = eddy viscosity 



For example, if v r is constant, the distribution is exponential, and if v T 

 increases linearly with z, the vertical profile follows a power-law. When 

 using v T = k u. z, where k is the von Karman constant taken as 0.4 and u, is 

 the bottom friction velocity, the vertical distribution is represented by 



— =f-l 

 n„ z„ 



where 



z a = a reference elevation (cm) 

 n a = the reference concentration at z a (cm' 3 ) 

 r = -w f /u. k 



Typically, the smaller the magnitude of r (higher agitation or smaller parti- 

 cles), the more uniform the concentration distribution. Some initial insight 

 can be gained by interpreting the present admittedly time-dependent cases in 

 light of steady profiles. First, it is plausible to assume that u» is proportional 

 to w' so that the ratio r is proportional to w { / u\ The ratio r as computed 

 from this formulation would be 4.1, 0.78, and 0.73 for the three 3-sec waves, 

 and 1.08, 1.08, and 1.20 for the three 8-sec waves, arranged in the order of 

 ascending wave amplitude. Using magnitudes of u' at the lowest levels, the 

 magnitude of the exponent r would be expected to decrease, producing more 

 nearly constant profiles, as turbulence intensity increases. The measured 

 exponent r for the 3-sec cases (excluding Run S0314B) was approximately 

 1.5, and for the 8-sec cases it was approximately 1.0. The latter is in good 

 agreement with the theoretical prediction. The former is off by a factor of 

 two. The discrepancy may be caused by the steady model used or by the 

 presence of relatively few non-sand particles producing measurements (see 

 absence of a concentration gradient in Figure ll-7b, 3-sec, 0.2-m case). 

 These bear further examination. In any case, it is evident that the present 

 technique promises to produce non-invasive field estimates of sediment 

 concentration C at a reference height above bed z r . 



Sediment flux in the boundary layer 



Sediment flux profiles can be expected to begin at a magnitude of zero at 

 the bed in the absence of bed load, or a non-zero magnitude when bed-load 

 transport occurs. In the absence of bed load, the flux would reach a 

 maximum in the boundary layer before decaying to zero outside it, where no 

 suspended mass reaches. The active bed-load case will probably have a 



Chapter 1 1 LDV in the Bottom Boundary Layer 



227 



