Boundary Layers

The idea of boundary layers can be illustrated very well using the example of sediment transport in suspension. If water in a river flows over a sandy bottom at sufficiently high velocity, sand will be picked up and carried with the flow, even though it tends to fall back. The process by which sediment particles are kept in suspension is turbulent diffusion. Just as in chapter 11, turbulence causes an effective transport from regions with high sand concentration (near the bottom) to those with low concentration (near the water surface). If you consider a steady-state situation, the mass balance for suspended sand is (14.1)$$u\frac{{\partial c}}{{\partial x}} + \frac{{\partial s}}{{\partial z}} = 0$$ in which the sediment flux in vertical direction is (14.2)$$s = {w_s}c - D\frac{{\partial c}}{{\partial z}}{\text{ }}$$ where x and z are the horizontal and vertical coordinates, D is the turbulent diffusion coefficient and w_s the settling velocity or fall velocity of the sand particles.