T. Allen

Large-Eddy Simulation Of Turbulent Separated Flow Over Rough Hills

Large-eddy simulations (LES) have been performed ofneutral turbulent flow over two-dimensional ridges steepenough to cause separation. Both periodic and isolated ridges havebeen considered. The results are compared with wind-tunnel observations and with the predictions of various turbulence closure models.For the periodic case the LES results are qualitatively reasonable,although the depth of the separated region appears to besensitive to the use of a distributed drag near the lower boundary.The isolated ridge results compare very favourably with the experimentaldata, with the LES performance appearing to be at least as good as that ofthe closure models.

Stochastic parametrization of multiscale processes using a dual-grid approach

Some speculative proposals are made for extending current stochastic sub-gridscale parametrization methods using the techniques adopted from the field of computer graphics and flow visualization. The idea is to emulate sub-filter-scale physical process organization and time evolution on a fine grid and couple the implied coarse-grained tendencies with a forecast model. A two-way interaction is envisaged so that fine-grid physics (e.g. deep convective clouds) responds to forecast model fields. The fine-grid model may be as simple as a two-dimensional cellular automaton or as computationally demanding as a cloud-resolving model similar to the coupling strategy envisaged in ‘super-parametrization’. Computer codes used in computer games and visualization software illustrate the potential for cheap but realistic simulation where emphasis is placed on algorithmic stability and visual realism rather than pointwise accuracy in a predictive sense. In an ensemble prediction context, a computationally cheap technique would be essential and some possibilities are outlined. An idealized proof-of-concept simulation is described, which highlights technical problems such as the nature of the coupling.

A deep non-hydrostatic compressible atmospheric model on a Yin-Yang grid

The singularity in the traditional spherical polar coordinate system at the poles is a major factor in the lack of scalability of atmospheric models on massively parallel machines. Overset grids such as the Yin-Yang grid introduced by Kageyama and Sato 1 offer a potential solution to this problem. In this paper a three-dimensional, compressible, non-hydrostatic atmospheric model is developed and tested on the Yin-Yang grid building on ideas previously developed by the authors on the solution of Elliptic boundary value problems and conservation on overset grids. Using several tests from the literature, it is shown that this model is highly stable (even with little off-centering), accurate, and highly efficient in terms of computational cost. The model also incorporates highly efficient and accurate approaches to achieve positivity, monotonicity and conservative transport, which are paramount requirements for any atmospheric model. The parallel scalability of this model, using in excess of 212 million unknowns and more than 6000 processors, is also discussed and shown to compare favourably with a highly optimised latitude-longitude model in terms of scalability and actual run times.

A moist Boussinesq shallow water equations set for testing atmospheric models

The shallow water equations have long been used as an initial test for numerical methods applied to atmospheric models with the test suite of Williamson et al. 1] being used extensively for validating new schemes and assessing their accuracy. However the lack of physics forcing within this simplified framework often requires numerical techniques to be reworked when applied to fully three dimensional models. In this paper a novel two-dimensional shallow water equations system that retains moist processes is derived. This system is derived from three-dimensional Boussinesq approximation of the hydrostatic Euler equations where, unlike the classical shallow water set, we allow the density to vary slightly with temperature. This results in extra (or buoyancy) terms for the momentum equations, through which a two-way moist-physics dynamics feedback is achieved. The temperature and moisture variables are advected as separate tracers with sources that interact with the mean-flow through a simplified yet realistic bulk moist-thermodynamic phase-change model. This moist shallow water system provides a unique tool to assess the usually complex and highly non-linear dynamics-physics interactions in atmospheric models in a simple yet realistic way. The full non-linear shallow water equations are solved numerically on several case studies and the results suggest quite realistic interaction between the dynamics and physics and in particular the generation of cloud and rain. Novel shallow water equations which retains moist processes are derived from the three-dimensional hydrostatic Boussinesq equations.The new shallow water set can be seen as a more general one, where the classical equations are a special case of these equations.This moist shallow water system naturally allows a feedback mechanism from the moist physics increments to the momentum via buoyancy.Like full models, temperature and moistures are advected as tracers that interact through a simplified yet realistic phase-change model.This model is a unique tool to test numerical methods for atmospheric models, and physics-dynamics coupling, in a very realistic and simple way.

On the monotonic and conservative transport on overset/Yin-Yang grids

In this paper, we outline a simple and a general methodology to achieve positivity, monotonicity and mass conservation with transport schemes on general overset grids. The main feature of the approach is its reduced complexity, which simplifies the use of higher-order schemes and higher dimensions on general grids and in particular for overset grids. The method also does not degrade substantially the order of the overall scheme despite the extra constraints of monotonicity and conservation. The approach is applied to achieve mass conservation with semi-Lagrangian schemes and its performance is analyzed using simple one-dimensional overlapping grids and a two-dimensional spherical Yin-Yang grid. The Yin-Yang grid is a special overset grid for the sphere and it is of a special interest in the atmospheric modeling community, as it is one of the grids that may resolve the scaling issue of existing longitude-latitude-grid based atmospheric models on massively parallel machines.