DERIVATION AND EVALUATION OF SUBGRID SCALE KINETIC ENERGY EQUATION

Abstract

We derive a subgrid scale (SGS) kinetic energy equation of an urban canopy model by employing the concept used in the immersed boundary method. The spatial averaging operation used in the derivation is equivalent to the conventional filtering operation used in large-eddy simulations (LES). The derived SGS kinetic energy equation has a term concerning the drag force of buildings (external-force term), in addition to the terms of conventional SGS kinetic energy equation. Furthermore, by using the results of a LES of the flow around a regular array of cubical blocks with a grid resolution sufficient to resolve the blocks, we investigate the budget for the time-mean SGS kinetic energy equation. As a result, we confirm that local equilibrium between production term and dissipation term of SGS kinetic energy is not satisfied in the canopy of the cubical blocks; contributions to the gain or loss of SGS kinetic energy from the external-force and dispersion terms are also prominent. The external-force term contributes to the gain of SGS kinetic energy in the most part of the canopy.