Kolmogorov’s hypotheses and global energy spectrum of turbulence

Liao, Zi-Ju; Su, Weidong

doi:10.1063/1.4916964

Cited by 8 publications

(6 citation statements)

References 33 publications

(37 reference statements)

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“…Consequently, the interaction between harmonics wavenumbers remains more efficient, leading to conservation of the same multiplicity of frequencies and to make the initial structure visible far downstream in the jet. This result lends strong support to the ideas of turbulence dependency upon initial conditions [18] and provides stark contrast to the classically hypothesized universal scaling of all high Reynolds number turbulence flows at the small and intermediate scales. The time for absorption of the peaks in Figure 6 can be found from the integration of the downstream decaying velocity over the downstream distance (see Table 1).…”

Section: Experiments 2 -Oscillating Airfoil Measurements Using Hot-wi...supporting

confidence: 73%

“…Other outstanding questions concern the persistence [14] of the initial conditions into the developed turbulence and the precise form of the final decay of the turbulent fluctuations [15]. Moreover, the fact that many papers report deviations from the -5/3 slope in the logarithmic plot of turbulence velocity power spectra [13,[16][17][18] and that significant differences occur between measurements and model calculations in flows of significant stagnation, separation and transient processes (i.e. where the flows can potentially be pushed out of the assumed equilibrium) highlight the limitations of the Kolmogorov theory.…”

Section: Introductionmentioning

confidence: 99%

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Experimental investigation of the turbulent cascade development by injection of single large-scale Fourier modes

Dotti

Schlander

Buchhave³

et al. 2020

Exp Fluids

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The current work presents an experimental investigation of interactions between flow scales. Injecting a single Fourier mode into a round jet flow made it possible to isolate and analyze the generation process of the high spectral components along the downstream flow development and to measure when they eventually are absorbed into the fully developed turbulence. Furthermore, an interesting dynamic evolution of the measured power spectra has been observed that confirms the cascaded delays reported by Josserand et al. 2017. Lately, these cascade delays have also been derived directly from a one-dimensional interpretation of Navier-Stokes equations described in a companion paper. The results in the current work provide vital information about the time scales in the triad interaction process.

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Section: Experiments 2 -Oscillating Airfoil Measurements Using Hot-wi...supporting

confidence: 73%

Section: Introductionmentioning

confidence: 99%

Experimental investigation of the turbulent cascade development by injection of single large-scale Fourier modes

Dotti

Schlander

Buchhave³

et al. 2020

Exp Fluids

View full text Add to dashboard Cite

show abstract

“…1. It can be shown that it is always possible to transform from one to the other (Mininni & Montgomery 2006;Mininni, Montgomery & Turner 2007;Liao & Su 2015). CK function can be seen as generalization to spherical geometry of Fourier modes.…”

Section: Magnetic Field Power Spectrum and Ck Functionsmentioning

confidence: 99%

Polarization properties of turbulent synchrotron bubbles: an approach based on Chandrasekhar–Kendall functions

Bucciantini

2017

Monthly Notices of the Royal Astronomical Society

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Synchrotron emitting bubbles arise when the outflow from a compact relativistic engine, either a Black Hole or a Neutron Star, impacts on the environment. The emission properties of synchrotron radiation are widely used to infer the dynamical properties of these bubbles, and from them the injection conditions of the engine. Radio polarization offers an important tool to investigate the level and spectrum of turbulence, the magnetic field configuration, and possibly the degree of mixing. Here we introduce a formalism based on Chandrasekhar-Kendall functions that allows us to properly take into account the geometry of the bubble, going beyond standard analysis based on periodic cartesian domains. We investigate how different turbulent spectra, magnetic helicity and particle distribution function, impact on global properties that are easily accessible to observations, even at low resolution, and we provide fitting formulae to relate observed quantities to the underlying magnetic field structure.

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“…given Reynolds number, all turbulent states are indistinguishable at inertial and viscous lengthscales, and that small-scale universality (Kolmogórov;1941;Liao and Su;Schumacher et al; holds regardless of state, in accord with the phenomenological theory.…”

Section: Accepted Manuscriptmentioning

confidence: 66%

Spectral link and macroscopic non-universality in turbulent plane Couette flow

Zhang¹

2019

Fluid Dyn. Res.

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In fully developed turbulent plane Couette flow the classical experimental data of frictional factor f vs. Reynolds number Re display well-known disparities which have long remained unexplained. These disparities are accompanied by previously unnoticed disparities in the wakes, and only in the wakes, of the attendant meanvelocity profiles (MVPs). To help explain these experimental data, we apply the model of the "spectral link" for MVPs to turbulent plane Couette flows. The model links the dissipative range, the inertial range, and the energetic range of the standard phenomenological model of the spectrum of turbulent kinetic energy to, respectively, the buffer layer, the log layer, and the wake of the MVPs. By assessing the empirical data using the spectral model, we argue for the existence, in plane Couette flow, of multiple states of turbulence which differ from one another only at the largest lengthscales in the flow, corresponding to the energetic range, where the spectrum is subject to finite-domain effects. Thus, the multiplicity of turbulent states is entirely consistent with small-scale universality, and the experimental data on plane Couette flow pose no challenge to the phenomenological theory of turbulence. Our findings might apply more broadly to a general class of flows engendered by moving boundaries.

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Kolmogorov’s hypotheses and global energy spectrum of turbulence

Cited by 8 publications

References 33 publications

Experimental investigation of the turbulent cascade development by injection of single large-scale Fourier modes

Experimental investigation of the turbulent cascade development by injection of single large-scale Fourier modes

Polarization properties of turbulent synchrotron bubbles: an approach based on Chandrasekhar–Kendall functions

Spectral link and macroscopic non-universality in turbulent plane Couette flow

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