Small-scale universality in the spectral structure of transitional pipe flows

Abstract

Turbulent flows are not only everywhere, but every turbulent flow is the same at small scales. The extraordinary simplification engendered by this “small-scale universality” is a hallmark of turbulence theory. However, on the basis of the restrictive assumptions invoked by A. N. Kolmogorov to demonstrate this universality, it is widely thought that only idealized turbulent flows conform to this framework. Using experiments and simulations that span a wide range of Reynolds number, we show that small-scale universality governs the spectral structure of a class of flows with no apparent ties to the idealized flows: transitional pipe flows. Our results not only extend the universality of Kolmogorov’s framework beyond expectation but also establish an unexpected link between transitional pipe flows and Kolmogorovian turbulence.

Turbulent Superstructures in Inert Jets and Diffusion Jet Flames

“…All this indicates that the puff has a complicated internal spatial structure, in accordance with the data reported in the Ref. [25]. Apparently, the topology of such superstructures requires high-speed PIV tomographic research methods.…”

“…This means that, in the time scale, the instantaneous flow velocity looks like intermittent regions of laminar and turbulent motion. Note that critical Reynolds numbers (Recr) in pipes are often derived from friction factors or heat transfer coefficients [24,25]. The Recr values depend on velocity distribution and the amplitude of inlet flow perturbations [20] and can be as high as 250,000 [26].…”

The turbulent flow in a slug: a re-examination

“…Although scarce, some recent works have also studied the same diagnostic profiles as WC (Shan et al 1999;Priymak & Miyazaki 2004) and echoed the same conclusion. In addition, recent studies using other diagnostics have furnished further support for this conclusion: the friction in slug flow (that is, the unitless pressure drop per unit length of slugs) is found to obey the Blasius law, a signature macroscopic diagnostic of fully turbulent flow (Cerbus et al 2018); and the energy spectra in slug flow is found to conform to Kolmogorov's small-scale universality, a signature microscopic diagnostic of fully turbulent flow (Cerbus et al 2017). (For transitional flow with slugs, the slug flow We plot a grey scale intensity map (where darker shares correspond to higher intensity) of the kinetic energy of off-axis fluctuations in an x-y (axial-wall-normal) plane through the pipe centreline; the white regions are devoid of fluctuations and correspond to laminar flow.…”

“…2018); and the energy spectra in slug flow is found to conform to Kolmogorov’s small-scale universality, a signature microscopic diagnostic of fully turbulent flow (Cerbus et al. 2017). (For transitional flow with slugs, the slug flow and the surrounding laminar flow share the same , but the friction in slug flow obeys the Blasius law whereas the friction in laminar flow obeys the Hagen–Poiseuille law (Cerbus et al.…”

Qian Jian (1939–2018) and his contribution to small-scale turbulence studies

“…The term 'small scales of turbulence' also appeared in the title of a paper by Kim and Antonia (1993). The term 'small-scale universality' appeared the titles of papers of Schumacher, Scheel, Krasnov, Donzis, Yakhot and Srinivasan (2014) and Cerbus, Liu, Gioia and Chakraborty (2020).…”