On the self-similarity of line segments in decaying homogeneous isotropic turbulence

Abstract

The self-similarity of a passive scalar in homogeneous isotropic decaying turbulence is investigated by the method of line segments (M. Gauding et al., Physics of Fluids 27.9 (2015): 095102). The analysis is based on a highly resolved direct numerical simulation of decaying turbulence. The method of line segments is used to perform a decomposition of the scalar field into smaller sub-units based on the extremal points of the scalar along a straight line. These sub-units (the so-called line segments) are parameterized by their length and the difference ∆φ of the scalar field between the ending points. Line segments can be understood as thin local convective-diffusive structures in which diffusive processes are enhanced by compressive strain. From DNS, it is shown that the marginal distribution function of the length assumes complete self-similarity when re-scaled by the mean length m . The joint statistics of ∆φ and , from which the local gradient g = ∆φ/ can be defined, play an important role in understanding the turbulence mixing and flow structure. Large values of g occur at a small but finite length scale. Statistics of g are characterized by rare but strong deviations that exceed the standard deviation by more than one order of magnitude. It is shown that these events break complete self-similarity of line segments, which confirms the standard paradigm of turbulence that intense events (which are known as internal intermittency) are not self-similar.

New scaling laws of passive scalar with a constant mean gradient in decaying isotropic turbulence

“…Though it has been shown that statistical symmetries play a key role for the understanding of moment scalings in wall-bounded shear flows (see e.g. Oberlack et al 2015), we found no clear indication for its involvement for the temporal evolution of statistical quantities in the present flow when comparing to the DNS data of Gauding et al (2019). Still, as different initial conditions may have an influence via the statistical symmetries (see e.g.…”

“…5.1. Details of the direct numerical simulations We compare the derived theoretical solutions (4.12)-(4.15) and (4.24)-(4.27) based on the symmetry analysis against the highly resolved DNS results of decaying homogeneous isotropic turbulence, performed by Gauding et al (2015Gauding et al ( , 2017Gauding et al ( , 2019. While more details can be found in these references, we only briefly describe the details of their DNS code, which solved the incompressible Navier-Stokes equations (2.22) in a triply periodic cubic box with size 2π by a pseudo-spectral method.…”

“…To ensure an appropriate resolution of all scales, Gauding et al (2017Gauding et al ( , 2019 have used a grid resolution of 4096 3 points in their DNS. Additionally, a resolution condition of k max η > 1 has been maintained for all cases to accurately compute the high-order statistics.…”

“…Their similarity analysis predicts that the scaling functions are expected to be related to the temperature variance and a characteristic length scale such as λ θ . Gauding et al (2015), Gauding, Danaila & Varea (2017) and Gauding et al (2019) also studied the self-similarity of a passive scalar in decaying homogeneous isotropic turbulence by the method of line segments. They found that, by using the classical Kolmogorov length scale, η k , although the similarity of the normalized scalar correlation function is very poor, the self-preservation of the normalized derivative correlation function is satisfactory using this length scale.…”

“…As a consequence of the current analytical work, we propose new scaling laws for both the passive scalar and velocity moments. The results of direct numerical simulations (DNS) conducted by Gauding et al (2015Gauding et al ( , 2017Gauding et al ( , 2019 are used to compare the new scaling laws.…”