The energy spectrum of stochastic eddies with gamma distribution

Abstract

Çinlar velocity field which is based on eddies of rotational form is a promising subgrid velocity model for its use in large eddy simulation (LES). This has been confirmed by data analysis of high frequency radar observations. The energy spectrum plays a central role for representing the subgrid scales in filtered Navier-Stokes equations used in LES. We consider a truncated Gamma distribution for eddy sizes to replicate the subgrid scale energy spectrum analytically. Kolmogorov proposed a form of the spectrum that extends to the inertial scale. Lundgren vortex has a spectrum involving an exponential function and has been used in LES. Çinlar velocity spectrum which is based on the truncated Gamma distribution indicates a good match with the spectrum estimated from real data. The results of this study can be used for designing a method for representing the small scale structures in LES by modeling the subgrid stress.