Measuring noninertial physics of turbulence: quasiscaling analysis

Quasiscaling exponent zeta(n)(M;D) is introduced by the ratio of turbulence velocity structure functions S(n) (r(D))/S(n)(r(M)) = (r(D)/r(M))(zeta(n)(M;D)) at scales r(M) and r(D) to measure the viscous and large-scale effects. Two inertial phenomenologies, respectively, that by She and Leveque [Phys. Rev. Lett. 72, 336 (1994)] and that by Meneveau and Sreenivason [Phys. Rev. Lett. 59, 1424 (1987)], are extended for quasiscaling as case studies. Both extended models fit well to the measurements and quantify the noninertial behaviors from different physical aspects, i.e., logarithmic-nonhomogeneous Poissonian and non-conservative binomial cascade, through the scale-dependent behaviors of the model parameters extracted from experimental data; and the physical meanings of the extended self-similarity properties for them are exposed.