Skip to main content
SpringerLink
Log in

Characterising the energy cascade using the zero-crossings of the longitudinal velocity fluctuations

  • Research Article
  • Published:
Experiments in Fluids Aims and scope Submit manuscript

Abstract

It is well known that the zero-crossings of the longitudinal velocity fluctuations can be used to estimate the Taylor length scale of turbulence via the Rice theorem. Furthermore, it has recently been shown that they can also be used to compute the turbulence integral length scale. We show how these two findings can be combined to study single-point statistics in turbulent flows. As these parameters are shaped by particular averaged properties of the turbulence cascade, they can be used to deduce some aspects of it. This approach is advantageous, as it makes possible the characterisation of turbulent flows in extremely challenging situations, i.e., statistically unsteady flows or conditions when adequate instrument calibration cannot be maintained. Using experimental data for a wide range of Taylor-scale-based Reynolds numbers from different flows (passive- and active-grid-generated turbulence and planar turbulent wakes), we show how, by solely using the zero-crossings of the longitudinal velocity fluctuations, some aspects of the energy cascade can be studied. Furthermore, using Voronoï tessellations, we study zero-crossing clustering properties. In particular, we discuss how its clusters and voids are related to the separation of scales in turbulent flows.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Availability of data and materials

Data will be made available upon reasonable request to the corresponding author.

Code availability

Not applicable.

References

  • Akinlabi EO, Wacławczyk M, Mellado JP, Malinowski SP (2019) Estimating turbulence kinetic energy dissipation rates in the numerically simulated stratocumulus cloud-top mixing layer: Evaluation of different methods. J Atmos Sci 76(5):1471–1488

    Article  Google Scholar 

  • Bos WJ, Rubinstein R (2017) Dissipation in unsteady turbulence. Phys Rev Fluids 2(2):022601

    Article  Google Scholar 

  • Ferenc J-S, Néda Z (2007) On the size distribution of poisson voronoi cells. Phys A Stat Mech Appl 385(2):518–526

    Article  Google Scholar 

  • Ferran A, Angriman S, Mininni PD, Obligado M (2022) Characterising single and two-phase homogeneous isotropic turbulence with stagnation points. Dynamics 2(2):63–72

    Article  Google Scholar 

  • Goto S, Vassilicos J (2016) Unsteady turbulence cascades. Phys Rev E 94(5):053108

    Article  Google Scholar 

  • Huang KY, Katul GG, Hultmark M (2021) Velocity and temperature dissimilarity in the surface layer uncovered by the telegraph approximation. Bound-Layer Meteorol 180(3):385–405

    Article  Google Scholar 

  • Liepmann H, Robinson M (1953) Counting methods and equipment for mean-value measurements in turbulence research

  • Mazellier N, Vassilicos J (2008) The turbulence dissipation constant is not universal because of its universal dependence on large-scale flow topology. Phys Fluids 20(1):015101

    Article  MATH  Google Scholar 

  • McFadden J (1958) The axis-crossing intervals of random functions-ii. IRE Trans Inf Theory 4(1):14–24

    Article  MathSciNet  MATH  Google Scholar 

  • Meldi M, Vassilicos JC (2021) Analysis of lundgren’s matched asymptotic expansion approach to the kármán-howarth equation using the eddy damped quasinormal markovian turbulence closure. Phys Rev Fluids 6(6):064602

    Article  Google Scholar 

  • Monchaux R, Bourgoin M, Cartellier A (2010) Preferential concentration of heavy particles: a Voronoï analysis. Phys Fluids 10(1063/1):3489987

    Google Scholar 

  • Mora DO, Obligado M (2020) Estimating the integral length scale on turbulent flows from the zero crossings of the longitudinal velocity fluctuation. Exp Fluids 61(9):1–10. https://doi.org/10.1007/s00348-020-03033-2

    Article  Google Scholar 

  • Mora DO, Pladellorens E, Riera Turró P, Lagauzere M, Obligado M (2019) Energy cascades in active-grid-generated turbulent flows. Phys Rev Fluids 4:104601. https://doi.org/10.1103/PhysRevFluids.4.104601

    Article  Google Scholar 

  • Mora DO, Cartellier A, Obligado M (2019) Experimental estimation of turbulence modification by inertial particles at moderate \({\text {re}}_{\lambda }\). Phys Rev Fluids 4:074309. https://doi.org/10.1103/PhysRevFluids.4.074309

    Article  Google Scholar 

  • Mora D, Bourgoin M, Mininni PD, Obligado M (2021) Clustering of vector nulls in homogeneous isotropic turbulence. Phys Rev Fluids 6(2):024609

    Article  Google Scholar 

  • Obligado M, Vassilicos J (2019) The non-equilibrium part of the inertial range in decaying homogeneous turbulence. Europhys Lett 127(6):64004

    Article  Google Scholar 

  • Puga AJ, LaRue JC (2017) Normalized dissipation rate in a moderate taylor reynolds number flow. J Fluid Mech 818:184–204

    Article  MathSciNet  MATH  Google Scholar 

  • Rice SO (1945) Mathematical analysis of random noise. Bell Syst Tech J 24(1):46–156

    Article  MathSciNet  MATH  Google Scholar 

  • Sinhuber M, Bodenschatz E, Bewley GP (2015) Decay of turbulence at high reynolds numbers. Phys Rev Lett 114:034501. https://doi.org/10.1103/PhysRevLett.114.034501

    Article  Google Scholar 

  • Smith J, Hopcraft K, Jakeman E (2008) Fluctuations in the zeros of differentiable gaussian processes. Phys Rev E 77(3):031112

    Article  MathSciNet  Google Scholar 

  • Sreenivasan K, Bershadskii A (2006) Clustering properties in turbulent signals. J Stat Phys 125(5–6):1141–1153

    Article  MATH  Google Scholar 

  • Sreenivasan K, Prabhu A, Narasimha R (1983) Zero-crossings in turbulent signals. J Fluid Mech 137:251–272

    Article  Google Scholar 

  • Steiros K (2022) Balanced nonstationary turbulence. Phys Rev E 105(3):035109

    Article  MathSciNet  Google Scholar 

  • Taylor GI (1935) Statistical theory of turbulence. Proc R Soc Lond Ser A Math Phys Sci 151(873):444–454. https://doi.org/10.1098/rspa.1935.0159

    Article  Google Scholar 

  • Valente PC, Vassilicos JC (2012) Universal dissipation scaling for nonequilibrium turbulence. Phys Rev Lett 108(21):214503

    Article  Google Scholar 

  • Vassilicos JC (2015) Dissipation in turbulent flows. Annu Rev Fluid Mech 47:95–114

    Article  MathSciNet  Google Scholar 

  • Zheng Y, Nagata K, Watanabe T (2021) Turbulent characteristics and energy transfer in the far field of active-grid turbulence. Phys Fluids 33(11):115119

    Article  Google Scholar 

Download references

Acknowledgements

Our work has been partially supported by the LabEx Tec21 (Investissements d’Avenir - Grant Agreement \(\#\) ANR-11-LABX-0030), and by the ANR project ANR-15-IDEX-02. The experiments in the passive grid were made during the Lille Turbulence Program (LTP). We thank Kostas Steiros, Christophe Cuvier and Pierre Bragança for their help planning and performing the experiments in Lille’s wind tunnel.

Funding

LabEx Tec21 (Investissements d’Avenir - Grant Agreement \(\#\) ANR-11-LABX-0030); ANR project ANR-15-IDEX-02.

Author information

Authors and Affiliations

  1. Université Grenoble Alpes, CNRS, Grenoble-INP, LEGI, F-38000, Grenoble, France

    Amélie Ferran & Martin Obligado

  2. Department of Mechanical Engineering, University of Washington, Seattle, USA

    Amélie Ferran & Alberto Aliseda

Authors
  1. Amélie Ferran
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alberto Aliseda
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Martin Obligado
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

MO and AF collected and curated the data. All authors reviewed and wrote the manuscript.

Corresponding author

Correspondence to Martin Obligado.

Ethics declarations

Conflict of interest

The authors have no conflict nor competing interests.

Ethical approval

Not applicable.

Consent to participate

Not applicable.

Consent for publication

Not applicable.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ferran, A., Aliseda, A. & Obligado, M. Characterising the energy cascade using the zero-crossings of the longitudinal velocity fluctuations. Exp Fluids 64, 176 (2023). https://doi.org/10.1007/s00348-023-03722-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00348-023-03722-8

Search

Navigation