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

Dotti, Margherita; Schlander, Rasmus Korslund; Buchhave, Preben; Velte, Clara Marika

doi:10.1007/s00348-020-03041-2

Cited by 7 publications

(12 citation statements)

References 33 publications

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“…We have illustrated these results in two ways that we shall publish separately. In one study 1 , we measured the development of the velocity power spectrum using a hot-wire anemometer in the laminar core of a large free jet in air into which we injected, by several different methods, a single large mode upstream. By measuring the power spectrum at several downstream locations, we could follow the time development of the spectrum and the appearance of the first higher harmonics generated by the nonlinear term in Navier-Stokes equation.…”

Section: Experiments and Numerical Simulationsmentioning

confidence: 99%

“…Knowing the velocity as a function of downstream position, we can calculate the convection time and thereby find the time history for the triad interactions. This will be described in detail in a forthcoming publication 1 .…”

Section: Experiments and Numerical Simulationsmentioning

confidence: 99%

“…In [1] we have investigated this phenomenon by laboratory experiments where a single Fourier mode is injected into a turbulent flow. In [2] we describe a computer program based on a one-dimensional projection of Navier-Stokes equation, used for illustrating the nonlinear processes.…”

Section: Introductionmentioning

confidence: 99%

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Dynamic triad interactions and evolving turbulence spectra

Buchhave,

Velte

2019

Preprint

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We investigate the effect of a four-dimensional Fourier transform on the formulation of Navier-Stokes equation in Fourier space and the way the energy is transferred between Fourier components (the so-called triad interactions). We consider the effect of a finite, digitally sampled velocity record on the triad interactions and find that Fourier components may interact within a broadened frequency window as compared to the usual integrals over infinite ranges. We also see how finite velocity records have a significant effect on the efficiency of the different triad interactions and thereby on the shape and development of velocity power spectra. These results explain the occurrence and time development of the so-called Richardson cascade and also why deviations from the classical Richardson cascade may occur. Finally, we quote results from companion papers that deal with laboratory and computer measurements of the time development of velocity power spectra in a turbulent jet flow into which a single Fourier mode is injected.

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Section: Experiments and Numerical Simulationsmentioning

confidence: 99%

Section: Experiments and Numerical Simulationsmentioning

confidence: 99%

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Dynamic triad interactions and evolving turbulence spectra

Buchhave,

Velte

2019

Preprint

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“…It is basically a one-cell Direct Numerical Simulation tool, with which we have been able to predict the downstream development even of high intensity turbulent flows. The simulations have been validated by several experiments [27]. The only input into these simulations is the Navier-Stokes Equation.…”

Section: The Navier-stokes Machine and New Theory Developmentsmentioning

confidence: 99%

Dynamic Triad Interactions and Non-equilibrium Turbulence

Velte

Buchhave²

2021

Springer Proceedings in Physics

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The classical K41 theory, based on the ideas of Kolmogorov, Richardson and Batchelor, has in recent years with accumulating evidence become subject to increased scrutiny. We elaborate on the idea that the deficiencies of the theory originate in the fundamental assumption of universal equilibrium, which in turn is the result of the basic assumption of locality of nonlinear interactions. These very fundamental assumptions are argued to have no anchoring in the governing Navier-Stokes equation. The possibility for other kinds of solutions are discussed from a historical perspective. K41 is also identified to represent an equilibrium solution that cannot predict non-equilibrium turbulence. Why the need for new perspectives on the established theory?The theoretical framework developed by Kolmogorov (including the contributing ideas of Richardson and Batchelor, often collectively referred to as the 'K41' theory [1, 2, 3]), has comprised the cornerstone of our understanding of turbulence for more than half a century. It has up until recently not been so frequently acknowledged that Kolmogorov's ideas were initially heavily questioned. In fact, it took two decades before K41 was convincingly supported by experiments; first in a turbulent round jet by Gibson [4] and secondly (and more widely acknowledged) by Grant, Stewart and Moilliet [5]. Once these empirical studies supporting K41 finally appeared, the theory has been amply supported by further experiments and simulations in some flows, while other theories have been more successful in predicting non-K41 types of flows (c.f.

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“…However, not many such experiments are to be found in the literature. An earlier study by our group describes measurements of vortex shedding behind a single rectangular rod inserted across a low turbulence uniform flow and behind oscillating airfoils in a highly turbulent flow, [4]. By spectral analysis, it was possible to follow the development of the oscillating modes introduced in the flow.…”

Section: Introductionmentioning

confidence: 99%

Triad interactions investigated by dual vortex shedding

Buchhave¹,

Ren

Velte

2023

Preprint

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The study of the exchange of momentum and energy between wave components of the turbulent velocity field, the so-called triad interactions, offers a unique way of visualizing and describing turbulence. Most often, this study has been carried out by Direct Numerical Simulations or by power spectral measurements. Due to the complexity of the problem and the great range of velocity scales in high Reynolds number developed turbulence, direct measurements of the interaction between the individual wave components have been rare. In the present work, we therefore present measurements and related computer simulations of triad interactions between controlled wave components injected into an approximately laminar and uniform flow from an open wind tunnel by vortex shedding from two rods suspended into the flow. This well-defined vortex shedding approximates well a two-dimensional flow, which makes the analysis of the triadic interactions considerably less complex to analyze than in a fully developed spatially three-dimensional flow. With the information obtained from the simulations, we are hereby able to isolate and display the individual triad interactions taking place as the flow develops downstream as well as the strengths of these interactions. The experiments provide the time constants governing the development of higher order frequency components. The combination of these experiments and simulations provide unique insight into the inner workings of turbulence and shows how the nonlinear term in the Navier-Stokes equation on average forces the energy towards higher frequencies, which is the reason for the so-called energy cascade.

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

Cited by 7 publications

References 33 publications

Dynamic triad interactions and evolving turbulence spectra

Dynamic triad interactions and evolving turbulence spectra

Dynamic Triad Interactions and Non-equilibrium Turbulence

Triad interactions investigated by dual vortex shedding

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