Mathematical Modeling and Computation of Channel Flow over Discrete Structures

In this paper mathematical modeling and computation of channel flow over small discrete structures are carried out under some reasonable conditions. A mathematical model for such a flow problem, which is based on a relevant system of partial differential equations and Fourier analysis, is studied using perturbation and nonlinear stability methods, and the resulting flow solutions over two types of discrete structures are computed under both stable and unstable conditions. It was found, in particular, that for a subcritical domain with the Reynolds number R slightly less than its critical value R-c, which is defined as the value below which no disturbances are linearly unstable, the structure leads to a stable steady flow whose modal representations have horizontal scale(s) that are due to those of the structure. On the limiting boundary between the stable and unstable flow, the flow is oscillatory with length scales due to the structure and the critical flow. Larger height of the structure affects the flow more significantly by reducing the subcritical domain for the induced steady flow.