Shallow layer modelling of dense gas clouds

摘要

The motivation for making shallow layer models is that they can deal with the dynamics of gravity driven flow in complex terrain at a modest computational cost compared to 3d codes. The main disadvantage is that the air-cloud interactions still have to be added 'by hand', where 3d models inherit the correct dynamics from the fundamental equations. The properties of the inviscid shallow water equations are discussed, focusing on existence and uniqueness of solutions. It is demonstrated that breaking waves and fronts pose severe problems, that can only be overcome if the hydrostatic approximation is given up and internal friction is added to the model. A set of layer integrated equations is derived starting from the Navier-Stokes equations. The various steps in the derivation are accompanied by plausibility arguments. These form the scientific basis of the model. The principle of least action is introduced as a means of generating consistent models, and as a tool for making discrete equations for numerical models, which automatically obey conservation laws. A numerical model called SLAM (Shallow LAyer Model) is presented. SLAM has some distinct features compared to other shallow layer models: A Lagrangian, moving grid; Explicit account for the turbulent kinetic energy budget; The entrainment rate is estimated on the basis of the local turbulent kinetic energy; Non-hydrostatic pressure; and Numerical methods respect conservation laws even for coarse grids. Thorney Island trial 8 is used as a reference case model tuning. The model reproduces the doughnut shape of the cloud and yield concentrations in reasonable agreement with observations, even when a small number of cells (e.g. 16) is used. It is concluded that lateral exchange of matter within the cloud caused by shear is important, and that the model should be improved on this point. (au) 16 ills., 38 refs.