Subgrid scale motion

Subgrid scale motion The scale of motion smaller than the grid size. 

The filtered quantity / is resolved in the numerical simulation whereas / = / — / is the subgrid scale part due to the unresolved flow motion. For variable density p, a mass-weighted Favre filtering is introduced so that ... 

The above equations describe the large-scale motion. Lij represents the interactions among the large scales. The effect of small scales appears through the residual stress tensors (i.e., Cij and Rij). In particular, Cij represents the interactions between the large and small scales, and Rij reflects the interactions between subgrid scales. The tensors Lij, Cij and Rij are known as the Leonard stress, cross-term stress and the residual Reynolds stress, respectively. 

Recently, Pozorski and Apte [39] performed a systematic study of the direct effect of subgrid scale velocity on particle motion for particle-laden forced isotropic turbulence using a stochastic model based on filtered particle tracking (FPT). The FPT approach statistically reconstructs the imresolved carrier-phase velocity along particle trajectories. A reasonable assumption for LES is to consider the residual turbulent motion as locally homogeneous and isotropic. Then, the fluid velocity... 

The task of subgrid-scale parameterization differs greatly depending on how realistically one wishes to forecast the atmospheric motions of various scales (see Table I). For a low horizorrtal resolution model (grid increment of about 300 to 500 km), the itse of a simple... 

In LESs (see, e.g., Crowe et al, 1996 Van den Akker, 2006), most of the turbulent motions of the flow field of the carrier phase are resolved. A particle being tracked in an LES flow field feels all the associated velocity fluctuations. Now, just the subgrid scale (SGS) fluctuations are not resolved while they still may have an effect on the particle motions modeling their effect is usually done by means of a Gaussian stochastic procedure (Derksen et al, 2008), on the basis of the idea that these SGS velocity fluctuations (in the absence of particles) are more or less isotropic. It may be anticipated, however, that the resolved velocity fluctuations are much stronger than the SGS fluctuations. When, in addition, the particle relaxation time is larger than the time step applied in the LES, Derksen (2003) argued that particle motion is hardly influenced by the SGS velocities. 

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