Filtering of the Navier-Stokes equatios in the context of time-dependent flows

摘要

The concepts of filtering and decomposition as applied to the analysis and modelling of turbulent flows are reviewed, staring from the seminal work of Reynolds. The problems arising fromthe use of finite spatial or time filters are discussed, and the recent approach based on the concepts of scale-similarity and multi-level filtering are presented. Finally, the possible extension of these ideas to finite tiem filtering is considered, with a view to developing turbulence mdoels for time-dependent flows; a simple tow-dimensional direct simulation of a tubulent free convective flow is used as an example.