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Sedimentation and detrital gold 229
4.19 Internal structure of natural turbulent flow, where J is the flow depth, t
the fluid density, o the temporal mean velocity, S the bed slope surface, the
thickness of the viscous sublayer, and K the height of roughness elements (after
Slingerland and Smith, 1986). (Reprinted, with permission, from the Annual
Review of Earth and Planetary Sciences, Volume 14, 1986 by Annual Reviews
www.annualreviews.org).
Because it cannot be measured directly, the average shear velocity U * need only
be considered as a surrogate or convenience variable for tractive shear stress
since this is always much smaller. A parameter used in certain problems in fluid
mechanics is defined as:
p
U * = f gJS 4.21
o
For smooth boundaries, the thickness of the viscous sublayer, , depends upon
shear velocity and viscosity:
4.22
cv=U *
where c is a constant. For a ratio of bottom roughness size to sublayer thickness,
K= , substituting from eqn 4.19 gives:
4.23
k= U * k=cv constant R *
The dimensionless quantity is the boundary Reynolds number R * . The value of
R * 5 is commonly accepted today as a reflection of the degree to which the
distribution of fluid forces acting on grains can be expected to be a reasonable
function of that value. A fully rough boundary has a value of R * 70.
Suspended load
The suspended load may be subdivided into:
