Physical and Geological Perspective
Sediment transport in the marine environment is driven by fluid motion. Some important transport mechanisms are depicted in Figure 1 in the context of the continental shelf:
Different regimes exist across the continental shelf:
Figure 342
Context for Study of Boundary Layers
A boundary layer exhibits a velocity profile connecting a background oceanographic flow and a noslip, zero velocity condition at a solid boundary.
Figure 343
Transfer of momentum toward the boundary imposes a shear stress; when it is sufficient (i.e., exceeds a critical value), it can cause transport of sediment either as bedload or suspended load.
We begin by considering how a moving fluid interacts with a solid boundary and the nature of the velocity profile.
Shear Stress
Stress, denoted t, is a force applied to a plane surface per unit area. Dimensionally:
Eq 341
Consider a volume element. Each of the three surfaces can have three forces acting on it, so there are nine components in all. They are denoted where the i subscript describes the surface (e.g., z would indicate the surface perpendicular to the zaxis) and the j subscript describes the direction of the force (e.g., x would indicate the force acting in the direction of the xaxis).
Figure 344
Eq 342
Of the remaining six components, we are interested in the two acting in the x and y directions on the plane perpendicular to the zaxis :
Eq 343
At the seabed these stresses are denoted and .
For simplicity we will consider flow in the xdirection that is steady () and uniform () so henceforth we denote as and the stress at the boundary as .
Consider the case of laminar flow (no turbulence) between a fixed surface and a plate of area A, separated by a height h, and moving at a steady velocity u (such that the applied force is opposed equally by the drag of the solid surface).
Figure 345
Eq 344:
For laminar flow (of a Newtonian fluid, see below), the velocity profile would be linear:
Eq 345:
The gradient of velocity which appears in this equation is called the shear. Since the stress is the force per unit area, we use Eq 344 and 345 to write:
Eq 346:
The proportionality constant µ is the absolute viscosity and is a measure of the resistance to deformation of a fluid. Dimensionally the stress has units of force per unit area (g cm/s)/(cm) and the velocity gradient units of (s) so the viscosity has units of g/(cm s). One g/(cm s) is one poise. In seawater the viscosity depends on temperature and salinity:

Fresh Water 
Seawater, S=35 o/oo 

Temperature 
Density 
Absolute Viscosity 
Kinematic Viscosity 
Density 
Absolute Viscosity 
Kinematic Viscosity 
° C 
g/cm^{3} 
centipoise 
cm^{2}/s (x 10^{2}) 
g/cm^{3} 
centipoise 
cm^{2}/s (x 10^{2}) 
0 
1.0000 
1.52 
1.52 
1.028 
1.61 
1.57 
10 
.9997 
1.31 
1.31 
1.027 
1.39 
1.35 
15 
.9991 
1.14 
1.14 
1.026 
1.22 
1.19 
20 
.9982 
1.005 
1.00 
1.025 
1.07 
1.05 
30 
.9956 
0.801 
0.804 
1.022 
0.87 
0.85 
An alternative way of thinking about the stress due to shear is as a transfer of momentum in a direction perpendicular to the surface on which the stress is acting. Multiplying the numerator and denominator by r :
Eq 347
The stress is the product of the gradient of fluid momentum and a constant n, the kinematic viscosity.
The discussion to this point pertains to a laminar flow and is for a Newtonian fluid. We say a fluid is Newtonian when the viscosity as defined by the proportionality in Eq 346 is a constant.
Figure 346
Oceanography 540 Pages Pages Maintained by Russ McDuff (mcduff@ocean.washington.edu) Copyright (©) 19942001 Russell E. McDuff and G. Ross Heath; Copyright Notice Content Last Modified 1/2/2001  Page Last Built 1/2/2001 