A Mathematical Analysis of Scale Similarity (Communications in Computational Physics, 2018)
Scale similarity is found in many natural phenomena in the universe, fromfluid dynamics to astrophysics. In large eddy simulations of turbulent flows, somesub-grid scale (SGS) models are based on scale similarity. The earliest scale similaritySGS model was developed by Bardina et al., which produced SGS stresses with goodcorrelation to the true stresses. In the present study, we perform a mathematical analysisof scale similarity. The analysis has revealed that the ratio of the resolved stressto the SGS stress is $γ^2$ , where $γ$ is the ratio of the second filter width to the first filterwidth, under the assumption of small filter width. The implications of this analysis arediscussed in the context of large eddy simulation.