Analyzing energy cascade of filtered vortices using a novel turbulence database framework*

The Karman-Howarth-Monin-Hill (KHMH) equation is a generalization of the Karman-Howarth equation and is valid for non-homogeneous, non-isotropic flow conditions. It is here applied to spatial subsets of DNS data from homogeneous isotropic turbulence at R_λ=1,300 to explore possible correlations between the rate of energy cascade and features of large-scale motions (such as filtered vorticity). The cascade rate is identified and computed from DNS using a spherical surface integration in length-scale space on the triple velocity difference term of the KHMH equation. On global average, this term is related to the mean rate of dissipation by a factor of -4/5 as in the classic formulation of the 4/5th law. Locally, we find anticorrelations between the cascade rate and the filtered vorticity magnitude at the same length scale, confirming that locally the cascade rate is reduced when large-scale rotation is strong. To explore connections with the filtering approach used in the LES literature, we compare the KHMH cascade rate with the subfilter-scale dissipation rate. Qualitative similarity and positive correlation are observed, but the two quantities differ in detail, and are therefore not equivalent.  The high-resolution isotropic DNS data are accessible via novel cyberinfrastructure tools built upon the data housed in the Johns Hopkins Turbulence Database (JHTDB). This new suite of database access tools is based on python notebooks and provides fast and stable operation on the existing turbulence data sets while enabling user-programmable, server-side computations.