Hostname: page-component-7dd5485656-dk7s8 Total loading time: 0 Render date: 2025-10-29T17:49:26.267Z Has data issue: false hasContentIssue false
  • English
  • Français

Gabor mode enrichment in large eddy simulations of turbulent flow

Published online by Cambridge University Press:  21 September 2020

A. S. Ghate Open the ORCID record for A. S. Ghate [Opens in a new window]  and
S. K. Lele
A. S. Ghate
Affiliation:
Department of Aeronautics and Astronautics, Stanford University, Stanford, CA, USA
S. K. Lele*
Affiliation:
Department of Aeronautics and Astronautics, Stanford University, Stanford, CA, USA Department of Mechanical Engineering, Stanford University, Stanford, CA, USA
*
†Email address for correspondence: lele@stanford.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

A turbulence enrichment model for subfilter-scale motions in large eddy simulations (LES) is comprehensively evaluated in the context of a posteriori analysis. The paper further develops the Gabor mode enrichment model first introduced in Ghate & Lele (J. Fluid Mech., vol. 819, 2017, pp. 494–539) by analysing three key requisites of LES enrichment using solenoidal small-scale velocity fields: (a) consistent spectral extrapolation and improvement of resolved single- and two-point second-order correlations; (b) ability to accurately capture the flow physics responsible for temporal decorrelation at small scales; and (c) accurate representation of spatially localized and intermittent interscale energy transfer between scales resolved by the coarse-grid LES and subfilter scales. We argue that the spatially and spectrally localized Gabor wavepackets offer an optimal basis to represent small-scale turbulence within quasi-homogeneous regions, although the alignment of fine-scale vorticity with large-scale strain appears to be somewhat overemphasized. Consequently, we interpret the resulting subfilter scales as those induced by a set of spatially dispersed Burgers–Townsend vortices with orientations determined by the larger scale velocity gradients resolved by the coarse-grid LES. Enrichment of coarse-grid simulations of two high Reynolds number flow configurations, homogeneous isotropic turbulence and a rough-wall turbulent boundary layer show promising results.

JFM classification

Turbulent Flows: Turbulence modelling Turbulent Flows: Turbulence simulation Turbulent Flows: Homogeneous turbulence

Information

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 903 , 25 November 2020 , A13
Check for updates
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

del Álamo, J. C. & Jiménez, J. 2003 Spectra of the very large anisotropic scales in turbulent channels. Phys. Fluids 15 (6), L41–L44.CrossRefGoogle Scholar
Ashurst, W. T., Kerstein, A., Kerr, R. & Gibson, C. 1987 Alignment of vorticity and scalar gradient with strain rate in simulated Navier–Stokes turbulence. Phys. Fluids 30 (8), 2343–2353.CrossRefGoogle Scholar
Bae, H. J. 2018 Investigation of dynamic subgrid-scale and wall models for turbulent boundary layers. PhD Thesis, Stanford University.Google Scholar
Bae, H. J., Lozano-Duran, A., Bose, S. & Moin, P. 2018 Turbulence intensities in large-eddy simulation of wall-bounded flows. Phys. Rev. Fluids 3 (1), 014610.CrossRefGoogle ScholarPubMed
Balakumar, B. & Adrian, R. 2007 Large-and very-large-scale motions in channel and boundary-layer flows. Philos. T. Roy. Soc. A 365 (1852), 665–681.CrossRefGoogle ScholarPubMed
Bassenne, M., Esmaily, M., Livescu, D., Moin, P. & Urzay, J. 2019 A dynamic spectrally enriched subgrid-scale model for preferential concentration in particle-laden turbulence. Int. J. Multiphas. Flow 116, 270–280.CrossRefGoogle Scholar
Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.Google Scholar
Bose, S. T. & Park, G. I. 2018 Wall-modeled large-eddy simulation for complex turbulent flows. Annu. Rev. Fluid Mech. 50, 535–561.CrossRefGoogle ScholarPubMed
Bou-Zeid, E., Meneveau, C. & Parlange, M. 2005 A scale-dependent lagrangian dynamic model for large eddy simulation of complex turbulent flows. Phys. Fluids 17 (2), 025105.CrossRefGoogle Scholar
Brasseur, J. G. & Wei, T. 2010 Designing large-eddy simulation of the turbulent boundary layer to capture law-of-the-wall scaling. Phys. Fluids 22 (2), 021303.CrossRefGoogle Scholar
Cantwell, B. J. 1992 Exact solution of a restricted euler equation for the velocity gradient tensor. Phys. Fluids A-Fluid 4 (4), 782–793.CrossRefGoogle Scholar
Canuto, V. & Dubovikov, M. 1996 A dynamical model for turbulence. I. General formalism. Phys. Fluids 8 (2), 571–586.CrossRefGoogle Scholar
Carati, D., Ghosal, S. & Moin, P. 1995 On the representation of backscatter in dynamic localization models. Phys. Fluids 7 (3), 606–616.CrossRefGoogle Scholar
Deardorff, J. W. 1970 A three-dimensional numerical investigation of the idealized planetary boundary layer. Geophys. Astro. Fluid 1 (3–4), 377–410.Google Scholar
Debnath, L. & Shah, F. A. 2002 Wavelet Transforms and Their Applications. Springer.CrossRefGoogle Scholar
Doan, N. A. K., Swaminathan, N., Davidson, P. & Tanahashi, M. 2018 Scale locality of the energy cascade using real space quantities. Phys. Rev. Fluids 3 (8), 094601.CrossRefGoogle Scholar
Dubrulle, B., Laval, J.-P., Nazarenko, S. & Kevlahan, N.-R. 2001 A dynamic subfilter-scale model for plane parallel flows. Phys. Fluids 13 (7), 2045–2064.CrossRefGoogle Scholar
Dubrulle, B., Laval, J.-P., Sullivan, P. P. & Werne, J. 2002 A new dynamical subgrid model for the planetary surface layer. Part 1. The model and a priori tests. J. Atmos. Sci. 59 (4), 861–876.2.0.CO;2>CrossRefGoogle Scholar
Farge, M. & Schneider, K. 2001 Coherent vortex simulation (CVS), a semi-deterministic turbulence model using wavelets. Flow Turbul. Combust. 66 (4), 393–426.CrossRefGoogle Scholar
Flohr, P. & Vassilicos, J. 2000 A scalar subgrid model with flow structure for large-eddy simulations of scalar variances. J. Fluid Mech. 407, 315–349.CrossRefGoogle Scholar
Fung, J. C. H., Hunt, J. C., Malik, N. & Perkins, R. 1992 Kinematic simulation of homogeneous turbulence by unsteady random fourier modes. J. Fluid Mech. 236, 281–318.CrossRefGoogle Scholar
Ghate, A., Towne, A. & Lele, S. 2020 Broadband reconstruction of inhomogeneous turbulence using spectral proper orthogonal decomposition and Gabor modes. J. Fluid Mech. 888, R1.CrossRefGoogle Scholar
Ghate, A. S. 2018 Gabor mode enrichment in large eddy simulation of turbulent flows. PhD Thesis, Stanford University.Google Scholar
Ghate, A. S. & Lele, S. K. 2017 Subfilter-scale enrichment of planetary boundary layer large eddy simulation using discrete Fourier–Gabor modes. J. Fluid Mech. 819, 494–539.CrossRefGoogle Scholar
Goldstein, D. E. & Vasilyev, O. V. 2004 Stochastic coherent adaptive large eddy simulation method. Phys. Fluids 16 (7), 2497–2513.CrossRefGoogle Scholar
Greengard, L. & Lee, J.-Y. 2004 Accelerating the nonuniform fast fourier transform. SIAM Rev. 46 (3), 443–454.CrossRefGoogle Scholar
Hamlington, P. E., Schumacher, J. & Dahm, W. J. 2008 Direct assessment of vorticity alignment with local and nonlocal strain rates in turbulent flows. Phys. Fluids 20 (11), 111703.CrossRefGoogle Scholar
Hutchins, N. & Marusic, I. 2007 Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 1–28.CrossRefGoogle Scholar
Jiang, Q., Wang, S. & Sullivan, P. 2018 Large-eddy simulation study of log laws in a neutral Ekman boundary layer. J. Atmos. Sci. 75 (6), 1873–1889.CrossRefGoogle Scholar
Jiménez, J. 2012 Cascades in wall-bounded turbulence. Annu. Rev. Fluid Mech. 44, 27–45.CrossRefGoogle Scholar
Johnson, P. L. 2020 Energy transfer from large to small scales in turbulence by multiscale nonlinear strain and vorticity interactions. Phys. Rev. Lett. 124 (10), 104501.CrossRefGoogle ScholarPubMed
Kawai, S. & Asada, K. 2013 Wall-modeled large-eddy simulation of high Reynolds number flow around an airfoil near stall condition. Comput. Fluids 85, 105–113.CrossRefGoogle Scholar
Kawai, S. & Larsson, J. 2012 Wall-modeling in large eddy simulation: length scales, grid resolution, and accuracy. Phys. Fluids 24 (1), 015105.CrossRefGoogle Scholar
Kelly, M. C. 2018 From standard wind measurements to spectral characterization: turbulence length scale and distribution. Wind Energy Sci. 3 (2), 533–543.CrossRefGoogle Scholar
Kosović, B. 1997 Subgrid-scale modelling for the large-eddy simulation of high-Reynolds-number boundary layers. J. Fluid Mech. 336, 151–182.CrossRefGoogle Scholar
Kraichnan, R. H. 1970 Diffusion by a random velocity field. Phys. Fluids 13 (1), 22–31.CrossRefGoogle Scholar
Larsson, J., Kawai, S., Bodart, J. & Bermejo-Moreno, I. 2016 Large eddy simulation with modeled wall-stress: recent progress and future directions. Mech. Engng Rev. 3 (1), 15–00418.Google Scholar
Laval, J., Dubrulle, B. & Nazarenko, S. 2001 Nonlocality and intermittency in three-dimensional turbulence. Phys. Fluids 13 (7), 1995–2012.CrossRefGoogle Scholar
Laval, J.-P., Dubrulle, B. & Nazarenko, S. 2004 Fast numerical simulations of 2d turbulence using a dynamic model for subfilter motions. J. Comput. Phys. 196 (1), 184–207.CrossRefGoogle Scholar
Leonard, A. 1975 Energy cascade in large-eddy simulations of turbulent fluid flows. In Advances in Geophysics, vol. 18, pp. 237–248. Elsevier.Google Scholar
Lozano-Durán, A. & Jiménez, J. 2014 Effect of the computational domain on direct simulations of turbulent channels up to $Re_\tau = 4200$. Phys. Fluids 26 (1), 011702.CrossRefGoogle Scholar
Lumley, J. L. 1970 Stochastic Tools in Turbulence. Academic Press.Google Scholar
Lund, T. S. & Rogers, M. M. 1994 An improved measure of strain state probability in turbulent flows. Phys. Fluids 6 (5), 1838–1847.CrossRefGoogle Scholar
Mallat, S. 1999 A Wavelet Tour of Signal Processing. Elsevier.Google Scholar
Mann, J. 1994 The spatial structure of neutral atmospheric surface-layer turbulence. J. Fluid Mech. 273, 141–168.CrossRefGoogle Scholar
Mazzitelli, I. M., Toschi, F. & Lanotte, A. S. 2014 An accurate and efficient lagrangian sub-grid model. Phys. Fluids 26 (9), 095101.CrossRefGoogle Scholar
Meneveau, C. & Katz, J. 2000 Scale-invariance and turbulence models for large-eddy simulation. Annu. Rev. Fluid Mech. 32 (1), 1–32.CrossRefGoogle Scholar
Misra, A. & Pullin, D. I. 1997 A vortex-based subgrid stress model for large-eddy simulation. Phys. Fluids 9 (8), 2443–2454.CrossRefGoogle Scholar
Moeng, C.-H. 1984 A large-eddy-simulation model for the study of planetary boundary-layer turbulence. J. Atmos. Sci. 41 (13), 2052–2062.2.0.CO;2>CrossRefGoogle Scholar
Nazarenko, S., Kevlahan, N.-R. & Dubrulle, B. 1999 Wkb theory for rapid distortion of inhomogeneous turbulence. J. Fluid Mech. 390, 325–348.CrossRefGoogle Scholar
Nicoud, F., Toda, H., Cabrit, O., Bose, S. & Lee, J. 2011 Using singular values to build a subgrid-scale model for large eddy simulations. Phys. Fluids 23 (8), 085106.CrossRefGoogle Scholar
Piomelli, U. & Balaras, E. 2002 Wall-layer models for large-eddy simulations. Annu. Rev. Fluid Mech. 34 (1), 349–374.CrossRefGoogle Scholar
Porté-Agel, F., Meneveau, C. & Parlange, M. 2000 A scale-dependent dynamic model for large-eddy simulation: application to a neutral atmospheric boundary layer. J. Fluid Mech. 415, 261–284.CrossRefGoogle Scholar
Pullin, D. & Saffman, P. 1994 Reynolds stresses and one-dimensional spectra for a vortex model of homogeneous anisotropic turbulence. Phys. Fluids 6 (5), 1787–1796.CrossRefGoogle Scholar
Pullin, D. & Saffman, P. 1998 Vortex dynamics in turbulence. Annu. Rev. Fluid Mech. 30 (1), 31–51.CrossRefGoogle Scholar
Rozema, W., Bae, H. J., Moin, P. & Verstappen, R. 2015 Minimum-dissipation models for large-eddy simulation. Phys. Fluids 27 (8), 085107.CrossRefGoogle Scholar
Schneider, K. & Vasilyev, O. V. 2010 Wavelet methods in computational fluid dynamics. Annu. Rev. Fluid Mech. 42, 473–503.CrossRefGoogle Scholar
Schumann, U. 1975 Subgrid scale model for finite difference simulations of turbulent flows in plane channels and annuli. J. Comput. Phys. 18 (4), 376–404.CrossRefGoogle Scholar
She, Z.-S., Jackson, E. & Orszag, S. A. 1990 Intermittent vortex structures in homogeneous isotropic turbulence. Nature 344 (6263), 226.CrossRefGoogle Scholar
Smits, A. J., McKeon, B. J. & Marusic, I. 2011 High–Reynolds number wall turbulence. Annu. Rev. Fluid Mech. 43, 353–375.CrossRefGoogle Scholar
Spalart, P. R. 2015 Philosophies and fallacies in turbulence modeling. Prog. Aerosp. Sci. 74, 1–15.CrossRefGoogle Scholar
Spyropoulos, E. T. & Blaisdell, G. A. 1996 Evaluation of the dynamic model for simulations of compressible decaying isotropic turbulence. AIAA J. 34 (5), 990–998.CrossRefGoogle Scholar
Stevens, R. J., Wilczek, M. & Meneveau, C. 2014 Large-eddy simulation study of the logarithmic law for second-and higher-order moments in turbulent wall-bounded flow. J. Fluid Mech. 757, 888–907.CrossRefGoogle Scholar
Sullivan, P. P. & Patton, E. G. 2011 The effect of mesh resolution on convective boundary layer statistics and structures generated by large-eddy simulation. J. Atmos. Sci. 68 (10), 2395–2415.CrossRefGoogle Scholar
Tomkins, C. D. & Adrian, R. J. 2003 Spanwise structure and scale growth in turbulent boundary layers. J. Fluid Mech. 490, 37–74.CrossRefGoogle Scholar
Townsend, A. 1951 On the fine-scale structure of turbulence. P. Roy. Soc. Lond. A Mat. 208 (1095), 534–542.Google Scholar
Wyngaard, J. C. 2010 Turbulence in the Atmosphere. Cambridge University Press.CrossRefGoogle Scholar
Xiong, Z., Nagarajan, S. & Lele, S. K. 2004 Simple method for generating inflow turbulence. AIAA J. 42 (10), 2164–2166.CrossRefGoogle Scholar
Yang, X. I., Park, G. I. & Moin, P. 2017 Log-layer mismatch and modeling of the fluctuating wall stress in wall-modeled large-eddy simulations. Phys. Rev. Fluids 2 (10), 104601.CrossRefGoogle ScholarPubMed