Introduction to the fluid mechanics of meso-scale flow fields

Abstract

Meso-scale airflows are essentially characterised by a horizontal length scale of a few tens of kilometres. Many of them, particularly those of importance to the distribution of pollutants, are relatively shallow (a few kilometres at most) and are significantly influenced by the nature of the underlying earth’s surface. This chapter is concerned with clarifying the term ‘meso-scale’ and presenting the basic fluid mechanics of meso-scale airflows, bearing in mind the above characteristics. It starts with a consideration of the observational and theoretical background to the idea of a meso-scale of atmospheric flows and then investigates the equations that aid understanding of the mechanics of these flows. Presentation of the basic equations is followed by elucidation of how they may be averaged, thus revealing the turbulent transfer terms. This is followed by a consideration of four approximations that may be made in the momentum and continuity equations, identifying those of most importance to meso-scale airflows. The need for and procedures involved in specifying turbulence closure follows. Much of the analysis of meso-scale airflows now involves solution of the momentum and other conservation equations in numerical models, so the notions of a model domain, grid volumes and sub-grid scale processes underlie the treatment in this chapter. Readers will find of value the books by Garratt (1992) and Stull (1988) for full treatments of the atmospheric boundary layer and that by Pielke (1984) for its treatment of the modelling of meso-scale airflows.