Scaling hypothesis leading to extended self-similarity in turbulence

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.

Sign-symmetry of temperature structure functions

New scalar structure functions with different sign-symmetry properties are defined. These structure functions possess different scaling exponents even when their order is the same. Their scaling properties are investigated for second and third orders, using data from high-Reynolds-number atmospheric boundary layer. It is only when structure functions with disparate sign-symmetry properties are compared can the extended self-similarity detect two different scaling ranges that may exist, as in the example of convective turbulence.

Intermittency and exponent field dynamics in developed turbulence

Spatiotemporal dynamics of intermittency in association with coarse-grained energy-dissipation rate fluctuations is discussed. This is done first by phenomenologically constructing the probability density for exponent field fluctuations that is introduced to characterize the energy-dissipation rate field, and then by proposing the Langevin dynamics derived with the projection-operator method on the basis of the Navier-Stokes equation. With a Gaussian approximation for exponent fluctuations, spatiotemporal correlation functions for coarse-grained energy-dissipation rate fluctuations are explicitly obtained.

Extended self-similarity and hierarchical structure in turbulence

We show that a generalization of the She-Leveque hierarchical structure [Z.S. She and E. Leveque, Phys. Rev. Lett. 72, 336 (1994)] together with a constant maximum magnitude of the velocity difference give rise to the extended self-similarity (ESS) [R. Benzi et al., Phy. Rev. E 48, R29 (1993)]. Our analysis thus suggests that the ESS measured in turbulent flows is an indication of the most intense structures being shocklike. Analyses of velocity measurements in a turbulent pipe flow support our conjecture.

Scaling hypothesis leading to generalized extended self-similarity in turbulence

A scaling hypothesis leading to generalized extended self-similarity (GESS) for velocity structure functions, valid for intermediate scales in isotropic, homogeneous turbulence, is proposed. By introducing an effective scale ŕ, monotonically depending on the physical scale r, with the use of the large deviation theory, the asymptotic forms of the probability densities for the velocity differences u(r) and for the coarse-grained energy-dissipation rate fluctuations epsilon(r), compatible with this GESS, are proposed. The probability density for epsilon(r) is shown to have the form P(r)(epsilon) approximately equal to epsilon(-1)(ŕ/L)(S(ŕ)[z(ŕ)](epsilon))) with z(ŕ)(epsilon)=ln(epsilon/epsilon(L))/ln(L/ŕ), where L and epsilon(L) are the stirring scale and the coarse-grained energy-dissipation rate over the scale L. The concave function S(ŕ)(z), the spectrum, plays the central role of the present approach. Comparing the results with numerical and experimental data, we explicitly obtain the fluctuation spectra S(ŕ)(z).

Self-similar fluctuation and large deviation statistics in the shell model of turbulence

Both static and dynamic multiscalings of fluctuations of energy flux and energy dissipation rate in the Gledzer-Ohkitani-Yamada (GOY) shell model of turbulence are numerically investigated. We compute the large deviation rate function of energy flux not only in the inertial range (IR) but also around the crossover between the inertial range and the dissipation range (DR). The rate function in IR exists to be concave, which assures the applicability of the Legendre transformation with the anomalous scaling exponents that have been investigated so far, and turns out to be independent of the Reynolds number. On the contrary, near the crossover scale, an intermediate dissipation range (IMDR) scaling is observed with the rate function in IMDR, which is accounted with the argument on dissipation scale fluctuation dominated by the energy flux fluctuation in the inertial range. Furthermore, to study the difference between IR intermittency and DR intermittency, we compute finite time-averaged quantities of energy flux and energy dissipation rate and investigate their multiscaling behavior. The difference observed in terms of their dynamic multiscaling is discussed.