Hierarchy of Mesoscale Flow Assumptions and Equations

The present research proposes a standard nomenclature for mesoscale meteorological concepts and integrates existing concepts of atmospheric space scales, flow assumptions, governing equations, and resulting motions into a hierarchy useful in categorization of mesoscale models. New dynamically based mesoscale time- and space-scale boundaries are proposed, consistent with the importance of the Coriolis force. In the proposed flow-class classification, the starting point is the complete (no approximations) set of mesoscale equations for non-Boussinesq flows. In the subsequent scale analysis. the deep and shallow Boussinesq flow divisions of Dutton and Fichtl are kept, as is the shallow-flow subdivisions of Mahrt In addition, the scale analysis approach of Mahrt is extended to deep Boussinesq motions. Limits of applicability of each derived flow-class equation set (with respect to atmospheric phenomena that can be simulated) are also discussed. The proposed hierarchy of atmospheric motions is organized into hydrostatic versus nonhydrostatic flow types and then into non-Boussinesq, deep, and shallow Boussinesq motions. Criteria used to differentiate each resulting flow class are discussed, while resulting governing thermodynamic and dynamic equations for each motion type are given. Separate graphical representations during stable and unstable conditions of the spatial limits of each Boussinesq mesoscale flow subclass are constructed from order of magnitude estimates for the various length and flow-class separation criteria. A summary of the consensus in the literature concerning the equation sets necessary to reproduce characteristics associated with specific atmospheric flow phenomenon is given. Comparative modeling studies are required to test the quantitative aspects of many of the ideas put forth in this paper.