Characterization of Dispersive Fluxes in Mesoscale Models Using LES of Flow over an Array of Cubes

Field studies have shown that local climate is strongly influenced by urban structures. This influences both energy consumption and the pedestrian comfort. It is thus useful to be able to simulate the urban environment to take these effects into account in building and urban design. But for computational reasons, conventional computational fluid dynamics (CFD) codes cannot be used directly on a grid fine enough to resolve all scales found in a city. For this, we use mesoscale models, variants of CFD codes in which the 3D conservation equations are solved on grids having a resolution of a few kilometers. At this resolution, the effects of subgrid scales need implicit representations. In other words, phenomena such as momentum and energy exchanges averaged over the mesoscale grid contribute necessary sources/sinks to the corresponding equations. Such spatial averaging results in additional terms called dispersive fluxes. Until now these fluxes have been ignored. To better understand these fluxes, we have conducted large eddy simulations (LESs) over an array of cubes for different inter-cube spacings. The study shows that these fluxes are as important as the turbulent fluxes and exhibit trends which are related to the eddy formations inside the canopies. 1. Introduction The large and continuous variety of scales present in the atmospheric flow over a city generates an intrinsic difficulty in the numerical treatment of the atmospheric conservation equations. From scaling considerations, the ratio between the smallest flow scale and the characteristic length scale is approximately proportional to ？？[1], where is the Reynolds number. This means that a 3D representation of the planetary boundary layer resolving all scales will require about grid cells. This number is far from being handled conveniently nowadays or in the near future by any computing device. Therefore, the transport phenomena over larger distances (in our case covering a city and its bounding context) must be handled by mesoscale atmospheric codes with spatial resolutions of a few kilometers either by subgrid urban parameterizations [2, 3] or by a coupling with a higher resoltion microscale model [4, 5]. In the former approach, the mesoscale codes cannot “see” buildings explicitly. Yet buildings and urban land use significantly impact the micro- and mesoscale flow, altering the wind, temperature, and turbulence fields and radiation exchanges [6, 7]. Since mesoscale numerical models do not have the spatial resolution to directly simulate the fluid dynamics and thermodynamics in and around urban