The corresponding velocity components are obtained by differentiation 
with respect to time of the above equations to give: 
u= (3) w {cosh [k (y+d) ]/sinh(k d)} sin(k x - w t) (3) 
= (3) w {sinh [k(y+d) ]/sinh(k d)} cos(k x - wt) (4) 
From these equations it is evident that the vertical component of the 
displacement and velocity becomes smaller as the distance from the sur- 
face increases. At the bottom, where y = -d, the motion degenerates into 
a simple harmonic oscillation in the x-direction. It is this horizontal 
harmonic oscillation which is of first-order importance in producing tur- 
bulence and suspension of sediment. The equations also indicate that the 
magnitudes of the horizontal displacement and velocity change slightly 
with depth near the ocean bottom and can therefore be considered constant 
in the region of sediment suspension. For example, consider a 5-foot-high 
wave with a wavelength of 150 feet and a period of 10 seconds in a water 
depth of 50 feet. Equation (3) indicates the horizontal velocity at 
y = -d is u = 0.393 sin(kx-wt) feet per second and that for y = -d+ 5 
(S feet above the bed), the horizontal velocity is u = 0.401 sin(kx-wt). 
The sediment suspension measurements which will be discussed later indi- 
cate that the regime of measurable sediment concentrations is well with- 
in the bottom 5 feet of water depth for this typical wave condition. 
(Measurable sediment concentrations were actually found within 1 foot 
of ‘the bed.) The change in horizontal velocity in the bottom 5 feet of 
water depth is only 2 percent. Therefore, to design an experimental 
apparatus to simulate the flow conditions near the ocean floor, the hori- 
zontal flow velocity above the boundary layer can be considered constant 
and equal to the value given by equation (3) for y = -d. Equation (4) 
indicates that for the wave condition discussed above the vertical flow 
velocity at y = -d is zero, and at an elevation of 5 feet above the bed 
is 0.082 cos (kx-wt). The fact that the vertical velocity only increases 
slightly in the 5 feet above the bed and that its motion is symmetrical 
Suggests that the vertical velocity has no effect on the suspension of 
sediment. 
With the above assumptions of a constant horizontal oscillating 
velocity and zero vertical oscillating velocity above the boundary layer, 
the turbulent flow conditions which exist near the ocean floor are easily 
approximated. By superimposing a constant velocity equal to that given 
by equation (3) for y = -d but opposite in sign, there would be no motion 
in the fluid above the boundary layer, the distribution of velocities in 
the boundary layer would be inverted, and the bed would be oscillating at 
the simple harmonic given by equation (3) for y = -d. 
It is now only necessary that the physical apparatus which duplicates 
these flow conditions contains a water depth greater than the thickness 
of the boundary layer. Kalkanis (1957) made velocity distribution measure- 
ments in a flume containing a still body of water with an oscillating 
