Dynamic triad interactions and evolving turbulence spectra

Buchhave, Preben; Velte, Clara M.

doi:10.48550/arxiv.1906.04756

Cited by 6 publications

(20 citation statements)

References 16 publications

(20 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As is also explained more in detail in P. Buchhave and C.M. Velte 2019 [19], the 2 nd order nature of the non-linear term imposes a phase match condition on the wave vector of the velocities: 𝒌𝒌 = 𝒌𝒌 1 + 𝒌𝒌 2 . This means that the energy transfer between flow structures can happen only by the interaction of two wave vector terms to form a third one, the socalled triad interactions.…”

Section: Navier-stokes Equationsmentioning

confidence: 97%

See 1 more Smart Citation

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

Dotti

Schlander

Buchhave³

et al. 2020

Exp Fluids

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Navier-stokes Equationsmentioning

confidence: 97%

“…where the flows can potentially be pushed out of the assumed equilibrium) highlight the limitations of the Kolmogorov theory. For this reason, the authors believe that the turbulence energy transfer investigation should refer directly to the governing Navier-Stokes equations [19].…”

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

Self Cite

View full text Add to dashboard Cite

show abstract

“…We see four different frequencies generated from the original k 1 and k 2 : The double frequency of each components and the sum and difference frequencies with the sum-frequency having the greatest coefficient, especially for k 1 ∼ = k 2 . Energy will therefore on average tend towards higher values since local interactions have a higher interaction efficiency (as described in [8]).…”

Section: Single Short Pulsementioning

confidence: 99%

“…In the specific simulation result in Figure 18, these odd harmonics are in fact suppressed down to the statistical noise level of the spectrum. This effect is attributed to the influence of the spatial windowing caused by the finite size of the flow region, an effect that is described in detail in [8].…”

Section: Single Fourier Mode Injectionmentioning

confidence: 99%

“…Later in the present paper, we compare these experimental results to computations with the Navier-Stokes Machine program using the initial measured record as input to the algorithm. In another paper, we consider the effect of performing a fourdimensional Fourier transform on the flow velocity recognizing the fact that the velocity fluctuations are in reality a stochastic function of four independent variables, three spatial variables and time [8].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Understanding developing turbulence by a study of the nonlinear energy transfer in the Navier-Stokes equation

Buchhave¹,

Velte²

2020

Preprint

Self Cite

View full text Add to dashboard Cite

In the present work, we investigate a numerical one-dimensional solver to the Navier-Stokes equation that retains all terms, including both pressure and dissipation. Solutions to simple examples that illustrate the actions of the nonlinear term are presented and discussed. The calculations take the full 4D flow as its starting point and continuously projects the forces acting on the fluid at a fixed Eulerian point onto the direction of the instantaneous velocity. Pressure is included through modeling. Adhering to the requirement that time must in general be considered an independent variable, the time development of the time records and power spectra of the velocity fluctuations are studied. It is found that the actions of the nonlinear term in the Navier-Stokes equation manifests itself by generating sharp pulses in the time traces, where the sharpness is bounded by the finite viscosity. In the spectral domain, the sharp gradients in the pulses generate energy contributions at high frequencies that yields a −2 slope across the inertial range. The −2 (or −6/3) slope is explained through a simple example and the classically expected −5/3 slope in the inertial range can be recovered from the pressure fluctuations from the full flow field that can be considered a noise contribution at the Financial support from the Poul Due Jensen Foundation (Grundfos Foundation) for this research is gratefully acknowledged. Grant number 2018-039.

show abstract

Dynamic Triad Interactions and Non-equilibrium Turbulence

Velte

Buchhave²

2021

Springer Proceedings in Physics

View full text Add to dashboard Cite

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.

show abstract

Dynamic triad interactions and evolving turbulence spectra

Cited by 6 publications

References 16 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

Understanding developing turbulence by a study of the nonlinear energy transfer in the Navier-Stokes equation

Dynamic Triad Interactions and Non-equilibrium Turbulence

Contact Info

Product

Resources

About