- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Fluids

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Inferring flow parameters and turbulent configuration with physics-informed data assimilation and spectral nudging

Patricio Clark Di Leoni1,*, Andrea Mazzino2,†, and Luca Biferale1,‡

  • 1Department of Physics and INFN, University of Rome Tor Vergata, Via della Ricerca Scientifica 1, 00133 Rome, Italy
  • 2Department of Civil, Chemical, and Environmental Engineering and INFN, University of Genova, Genova 16145, Italy

  • *patricio.clark@roma2.infn.it
  • †andrea.mazzino@unige.it
  • ‡luca.biferale@roma2.infn.it
PDF

Phys. Rev. Fluids 3, 104604 – Published 11 October, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.104604

Abstract

Inferring physical parameters of turbulent flows by assimilation of data measurements is an open challenge with key applications in meteorology, climate modeling, and astrophysics. Up to now, spectral nudging was applied for empirical data assimilation as a means to improve deterministic and statistical predictability in the presence of a restricted set of field measurements only. Here we explore under which conditions a nudging protocol can be used for two objectives: to unravel the value of the physical flow parameters and to reconstruct large-scale turbulent properties starting from a sparse set of information in space and in time. First, we apply nudging to quantitatively infer the unknown rotation rate and the shear mechanism for turbulent flows. Second, we show that a suitable spectral nudging is able to reconstruct the energy containing scales in rotating turbulence by using a blind setup, i.e., without any input about the external forcing mechanisms acting on the flow. Finally, we discuss the broad potentialities of nudging to other key applications for physics-informed data assimilation in environmental or applied flow configurations.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (44)

  1. I. F. Akyildiz, W. Su, Y. Sankarasubramaniam, and E. Cayirci, Wireless sensor networks: A survey, Comput. Netw. 38, 393 (2002).
  2. J. K. Hart and K. Martinez, Environmental sensor networks: A revolution in the earth system science? Earth-Sci. Rev. 78, 177 (2017).
  3. H. S. Fu, A. Vaivads, Y. V. Khotyaintsev, V. Olshevsky, M. André, J. B. Cao, S. Y. Huang, A. Retinó, and G. Lapenta, How to find magnetic nulls and reconstruct field topology with MMS data? J. Geophys. Res.: Space Phys. 120, 2015JA021082 (2015).
  4. P. Carpeggiani, M. Reduzzi, A. Comby, H. Ahmadi, S. Kühn, F. Calegari, M. Nisoli, F. Frassetto, L. Poletto, D. Hoff, J. Ullrich, C. D. Schröter, R. Moshammer, G. G. Paulus, and G. Sansone, Vectorial optical field reconstruction by attosecond spatial interferometry, Nat. Photon. 11, 383 (2017).
  5. J. Busch, D. Giese, L. Wissmann, and S. Kozerke, Reconstruction of divergence-free velocity fields from cine 3D phase-contrast flow measurements, Magn. Reson. Med. 69, 200 (2013).
  6. E. Kalnay, Atmospheric Modeling, Data Assimilation and Predictability (Cambridge University Press, Cambridge, 2003).
  7. J. L. Anderson and S. L. Anderson, A Monte Carlo implementation of the nonlinear filtering problem to produce ensemble assimilations and forecasts, Mon. Weather Rev. 127, 2741 (1999).
  8. J. L. Anderson, An ensemble adjustment Kalman filter for data assimilation, Mon. Weather Rev. 129, 2884 (2001).
  9. J. J. Ruiz, M. Pulido, and T. Miyoshi, Estimating model parameters with ensemble-based data assimilation: A review, J. Meteorol. Soc. Jpn. Ser. II 91, 79 (2013).
  10. M. C. Kennedy and A. O'Hagan, Bayesian calibration of computer models, J. R. Stat. Soc. Ser. B 63, 425 (2001).
  11. H. Xiao, J. L. Wu, J. X. Wang, R. Sun, and C. J. Roy, Quantifying and reducing model-form uncertainties in Reynolds-averaged Navier-Stokes simulations: A data-driven, physics-informed Bayesian approach, J. Comput. Phys. 324, 115 (2016).
  12. E. J. Parish and K. Duraisamy, A paradigm for data-driven predictive modeling using field inversion and machine learning, J. Comput. Phys. 305, 758 (2016).
  13. J. Ling, A. Kurzawski, and J. Templeton, Reynolds averaged turbulence modeling using deep neural networks with embedded invariance, J. Fluid Mech. 807, 155 (2016).
  14. M. Chertkov, L. Kroc, F. Krzakala, M. Vergassola, and L. Zdeborová, Inference in particle tracking experiments by passing messages between images, Proc. Natl. Acad. Sci. USA 107, 7663 (2010).
  15. S. L. Brunton, J. L. Proctor, and J. N. Kutz, Discovering governing equations from data by sparse identification of nonlinear dynamical systems, Proc. Natl. Acad. Sci. USA 113, 3932 (2016).
  16. S. H. Rudy, S. L. Brunton, J. L. Proctor, and J. N. Kutz, Data-driven discovery of partial differential equations, Sci. Adv. 3, e1602614 (2017).
  17. R. E. Thaler, Nobel lecture, From cashews to nudges: The evolution of behavioral economics, The Sveriges Riksbank Prize in Economic Sciences (2017), available at https://www.nobelprize.org/prizes/economics/2017/thaler/lecture/
  18. K. M. Waldron, J. Paegle, and J. D. Horel, Sensitivity of a spectrally filtered and nudged limited-area model to outer model options, Mon. Weather Rev. 124, 529 (1996).
  19. H. von Storch, H. Langenberg, and F. Feser, A spectral nudging technique for dynamical downscaling purposes, Mon. Weather Rev. 128, 3664 (2000).
  20. G. Miguez-Macho, G. L. Stenchikov, and A. Robock, Spectral nudging to eliminate the effects of domain position and geometry in regional climate model simulations, J. Geophys. Res. Atmos. 109, D13104 (2004).
  21. A. Farhat, E. Lunasin, and E. S. Titi, Abridged continuous data assimilation for the 2D Navier-Stokes equations utilizing measurements of only one component of the velocity field, J. Math. Fluid Mech. 18, 1 (2016).
  22. M. Gesho, E. Olson, and E. S. Titi, A computational study of a data assimilation algorithm for the two-dimensional Navier-Stokes equations, Commun. Comput. Phys. 19, 1094 (2016).
  23. D. A. F. Albanez, H. J. Nussenzveig Lopes, and E. S. Titi, Continuous data assimilation for the three-dimensional Navier-Stokes-α model, Asymptotic Anal. 97, 139 (2016).
  24. A. Farhat, H. Johnston, M. Jolly, and E. S. Titi, Assimilation of nearly turbulent Rayleigh-Bénard flow through vorticity or local circulation measurements: A computational study, J. Sci. Comput., doi:10.1007/s10915-018-0686-x.
  25. D. Pazó, J. M. López, R. Gallego, and M. A. Rodríguez, Synchronizing spatio-temporal chaos with imperfect models: A stochastic surface growth picture, Chaos 24, 043115 (2014).
  26. H. Omrani, P. Drobinski, and T. Dubos, Spectral nudging in regional climate modeling: How strongly should we nudge? Q. J. R. Meteorol. Soc. 138, 1808 (2012).
  27. C. C. Lalescu, C. Meneveau, and G. L. Eyink, Synchronization of Chaos in Fully Developed Turbulence, Phys. Rev. Lett. 110, 084102 (2013).
  28. L. M. Smith, J. R. Chasnov, and F. Waleffe, Crossover from Two- to Three-Dimensional Turbulence, Phys. Rev. Lett. 77, 2467 (1996).
  29. P. D. Mininni and A. Pouquet, Helicity cascades in rotating turbulence, Phys. Rev. E 79, 026304 (2009).
  30. P. D. Mininni, A. Alexakis, and A. Pouquet, Scale interactions and scaling laws in rotating flows at moderate Rossby numbers and large Reynolds numbers, Phys. Fluids 21, 015108 (2009).
  31. L. Biferale, S. Musacchio, and F. Toschi, Split energy-helicity cascades in three-dimensional homogeneous and isotropic turbulence, J. Fluid Mech. 730, 309 (2013).
  32. R. B. Scott and F. Wang, Direct evidence of an oceanic inverse kinetic energy cascade from satellite altimetry, J. Phys. Oceanogr. 35, 1650 (2005).
  33. R. Corrado, G. Lacorata, L. Palatella, R. Santoleri, and E. Zambianchi, General characteristics of relative dispersion in the ocean, Sci. Rep. 7, 46291 (2017).
  34. G. Lacorata, E. Aurell, B. Legras, and A. Vulpiani, Evidence for a k−5/3 spectrum from the EOLE Lagrangian balloons in the low stratosphere, J. Atmos. Sci. 61, 2936 (2004).
  35. 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).
  36. I. M. Navon, Practical and theoretical aspects of adjoint parameter estimation and identifiability in meteorology and oceanography, Dyn. Atmos. Oceans 27, 55 (1998).
  37. X. Zou, I. M. Navon, and F. X. Ledimet, An optimal nudging data assimilation scheme using parameter estimation, Q. J. R. Meteorol. Soc. 118, 1163 (1992).
  38. L. Yu and J. J. O'Brien, Variational estimation of the wind stress drag coefficient and the oceanic eddy viscosity profile, J. Phys. Oceanogr. 21, 709 (1991).
  39. C.-L. Lin, T. Chai, and J. Sun, Retrieval of flow structures in a convective boundary layer using an adjoint model: Identical twin experiments, J. Atmos. Sci. 58, 1767 (2001).
  40. M. C. Bove, P. Brotto, F. Cassola, E. Cuccia, D. Massabò, A. Mazzino, A. Piazzalunga, and P. Prati, An integrated PM2.5 source apportionment study: Positive matrix factorisation vs. the chemical transport model CAMx, Atmos. Environ. 94, 274 (2014).
  41. D. I. Cooper, W. E. Eichinger, R. E. Ecke, J. C. Y. Kao, J. M. Reisner, and L. L. Tellier, Initial investigations of microscale cellular convection in an equatorial marine atmospheric boundary layer revealed by lidar, Geophys. Res. Lett. 24, 45 (1997).
  42. V. Taillandier, A. Griffa, and A. Molcard, A variational approach for the reconstruction of regional scale Eulerian velocity fields from Lagrangian data, Ocean Model. 13, 1 (2006).
  43. V. Taillandier, A. Griffa, P.-M. Poulain, and K. Béranger, Assimilation of Argo float positions in the north western Mediterranean Sea and impact on ocean circulation simulations, Geophys. Res. Lett. 33, L11604 (2006).
  44. M. Berta, L. Bellomo, M. G. Magaldi, A. Griffa, A. Molcard, J. Marmain, M. Borghini, and V. Taillandier, Estimating Lagrangian transport blending drifters with HF radar data and models: Results from the TOSCA experiment in the Ligurian current (north western Mediterranean Sea), Prog. Oceanogr. 128, 15 (2014).

Outline

Information

Phys. Rev. Fluids 3, 104604– Published 11 October, 2018
  • Received 9 April 2018
Crossmark - Check for updates button

©2018 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation