The horizontally homogeneous model equations of incompressible atmospheric flow in general orthogonal coordinates

The goal of this brief report is to express the model equations for an incompressible flow which is horizontally homogeneous. It is intended as a computationally inexpensive starting point of a more complete solution for neutral atmospheric flow overcomplex terrain. This idea was set forth by Ayotte and Taylor (1995) and in the work of Beljaars et al. (1987). Unlike the previous models, the present work uses general orthogonal coordinates. Strong conservation form of the model equations is employedto allow a robust and consistent numerical procedure. An invariant tensor form of the model equations is utilized expressing the flow variables in a transformed coordinate system in which they are horizontally homogeneous. The model utilizes the k - emodel with limited mixing length by Apsley and Castro (1997). This turbulence closure reflects the fact that the atmosphere is only neutral up to a certain height. The horizontally homogeneous flow model is a part of a perturbation solver underdevelopment which is hoped to be more accurate than the current standard program WAsP by Troen and Petersen (1989) while achieving a high speed of execution.