Mathematical Modeling of Wind Forces

Abstract

This paper is divided into two parts. In the first part physical meanings and some other aspects of wind and the driving forces are reviewed. There includes types of driving forces, sources for wind production, boundary layer effects, roughness and surface structure effects, and the types of wind in the nature. In the second part we first focus on the effect of surface structure, roughness and surface waviness, and several experimental, computational and mathematical investigations that have been done by the present and other authors in the past for both laminar and turbulent shear flows, are reviewed. Next, a mathematical model of moderate wind over general types of surface structures is considered and studied under some reasonable conditions. This mathematical model, which is based on a relevant system of partial differential equations and Fourier analysis, is investigated briefly here using perturbation and weakly nonlinear methods, and the mathematical features and the qualitative results are then presented. It was found, in particular, that surface structures can have significant influences on various features of the wind such as stability, instability, amplitude, scales, patterns, mode excitation and resonance.