title: Exact relations between the moments of dissipation and longitudinal velocity derivatives in turbulent flows.
abstract: Following an approach by Siggia, we present coefficients C(n) relating the moments of the dissipation of kinetic energy 〈ɛ〉 and the longitudinal velocity gradient 〈∂u(1)/∂x(1)〉 under the assumption of isotropy and continuity. Particularly, we find that the moment 〈ɛ(n)〉 of order n is completely determined by 〈(∂u(1)/∂x(1))(2n)〉 and an order- (and viscosity-) dependent coefficient for all n under the assumption of (local) isotropy. This implies that all theories which specify 〈ɛ(n)〉 also implicitly determine 〈(∂u(1)/∂x(1))(2n)〉 and vice versa. As a corollary to the direct connection between the moments of the dissipation and the longitudinal velocity gradient, the even standardized moments of order 2n of ∂u(1)/∂x(1) (flatness, hyperflatness, and so on) are directly related to the ratio of the moments 〈ɛ(n)〉/〈ɛ〉(n). We compare the theoretical values of the coefficients C(n) up to n=6 with homogeneous isotropic DNS data ranging from Re(λ)=88 to Re(λ)=529.
authors.affiliation: Institut für Technische Verbrennung, RWTH Aachen University, Germany.
authors.forename: Jonas
authors.initials: J
authors.lastname: Boschung