Can the dynamic eddy-viscosity class of subgrid-scale models capture inertial-range properties of Burgers turbulence?

References

• Geurts , B. J. 2003 . Elements of Direct and Large-Eddy Simulation , Philadelphia : Edwards .
   Google Scholar
• Meneveau , C. and Katz , J. 2000 . Scale-invariance and turbulence models for large-eddy simulation . Ann. Rev. Fluid Mech. , 32 : 1 – 32 .
   Web of Science ®Google Scholar
• Pope , S. B. 2000 . Turbulent Flows , Cambridge, UK : Cambridge University Press .
   Google Scholar
• Sagaut , P. 2002 . Large Eddy Simulation for Incompressible Flows , Berlin : Springer .
   Google Scholar
• Germano , M. , Piomelli , U. , Moin , P. and Cabot , W. H. 1991 . A dynamic subgrid-scale eddy viscosity model . Phys. Fluids , 3 : 1760 – 1765 .
   Web of Science ®Google Scholar
• Lilly , D. K. 1992 . A proposed modification of the Germano subgrid-scale closure method . Phys. Fluids A , 4 : 633 – 635 .
   Web of Science ®Google Scholar
• Pope , S. B. 2004 . Ten questions concerning the large-eddy simulation of turbulent flows . New J. Phys. , 6 : 35
   Web of Science ®Google Scholar
• Burgers , J. M. 1974 . The Nonlinear Diffusion Equation , Dordrecht : Reidel .
   Google Scholar
• Love , M. D. 1980 . Subgrid modelling studies with Burgers' equation . J. Fluid Mech. , 100 : 87
   Web of Science ®Google Scholar
• Scotti , A. and Meneveau , C. 1997 . Fractal model for coarse-grained nonlinear partial differential equations . Phys. Rev. Lett. , 78 : 867
   Web of Science ®Google Scholar
• Scotti , A. and Meneveau , C. 1999 . A fractal model for large eddy simulation of turbulent flow . Physica D , 127 : 198
   Web of Science ®Google Scholar
• Das , A. and Moser , D. 2002 . Optimal large-eddy simulation of forced Burgers equation . Phys. Fluids , 14 : 4344 – 4351 .
   Web of Science ®Google Scholar
• Stefano , G. D. and Vasilyev , O. V. 2002 . Sharp cutoff versus smooth filtering in large eddy simulation . Phys. Fluids , 14 : 362 – 369 .
   Web of Science ®Google Scholar
• Chambers , D. H. , Adrian , R. J. , Moin , P. , Stewart , D. S. and Sung , H. J. 1988 . Karhunen–Loéve expansion of Burgers' model of turbulence . Phys. Fluids , 31 : 2573 – 2582 .
   Web of Science ®Google Scholar
• Choi , H. , Temam , R. , Moin , P. and Kim , J. 1993 . Feedback control for unsteady flow and its application to the stochastic Burgers equation . J. Fluid Mech. , 253 : 509 – 543 .
   Web of Science ®Google Scholar
• Yakhot , V. and She , Z.-S. 1988 . Long-time, large-scale properties of the random-force-driven Burgers equation . Phys. Rev. Lett. , 60 : 1840 – 1843 .
   PubMed Web of Science ®Google Scholar
• Medina , E. , Hwa , T. , Kardar , M. and Zhang , Y.-C. 1989 . Burgers equation with correlated noise: renormalization-group analysis and applications to directed polymers and interface growth . Phys. Rev. A , 39 : 3053 – 3075 .
   PubMed Web of Science ®Google Scholar
• She , Z.-S. , Aurell , E. and Frisch , U. 1992 . The inviscid Burgers equation with initial data of Brownian type . Comm. Math. Phys. , 148 : 623 – 641 .
   Web of Science ®Google Scholar
• Sinai , Y. G. 1992 . Statistics of shocks in solutions of inviscid Burgers equation . Comm. Math. Phys. , 148 : 601 – 621 .
   Web of Science ®Google Scholar
• Bertini , L. , Cancrini , N. and Jona-Lasinio , G. 1994 . The stochastic Burgers equation . Comm. Math. Phys. , 165 : 211 – 232 .
   Web of Science ®Google Scholar
• Chekhlov , A. and Yakhot , V. 1995 . Kolmogorov turbulence in a random-force-driven Burgers equation . Phys. Rev. E , 51 : R2739 – R2742 .
   PubMed Web of Science ®Google Scholar
• Chekhlov , A. and Yakhot , V. 1995 . Kolmogorov turbulence in a random-force-driven Burgers equation: Anomalous scaling and probability density functions . Phys. Rev. E , 52 : 5681 – 5684 .
   PubMed Web of Science ®Google Scholar
• Polyakov , A. M. 1995 . Turbulence without pressure . Phys. Rev. E , 52 : 6183 – 6188 .
   PubMed Web of Science ®Google Scholar
• Yakhot , V. and Chekhlov , A. 1996 . Algebraic tails of probability density functions in the random-force-driven Burgers turbulence . Phys. Rev. Lett. , 77 : 3118
   PubMed Web of Science ®Google Scholar
• Hayot , F. and Jayaprakash , C. 1996 . Multifractality in the stochastic Burgers equation . Phys. Rev. E , 54 : 4681 – 4684 .
   PubMed Web of Science ®Google Scholar
• Hayot , F. and Jayaprakash , C. 1997 . Structure functions in the stochastic Burgers equation . Phys. Rev. E , 56 : 227 – 230 .
   Web of Science ®Google Scholar
• Hayot , F. and Jayaprakash , C. 1997 . From scaling to multiscaling in the stochastic Burgers equation . Phys. Rev. E , 56 : 4259 – 4262 .
   Web of Science ®Google Scholar
• Bouchaud , J.-P. and Mézard , M. 1996 . Velocity fluctuations in forced Burgers turbulence . Phys. Rev. E , 54 : 5116 – 5121 .
   PubMed Web of Science ®Google Scholar
• Boldyrev , S. A. 1997 . Velocity-difference probability density functions for Burgers turbulence . Phys. Rev. E , 55 : 6907 – 6910 .
   Web of Science ®Google Scholar
• Kraichnan , R. H. 1999 . Note on forced Burgers turbulence . Phys. Fluids , 11 : 3738 – 3742 .
   Web of Science ®Google Scholar
• Anderson , W. C. , Basu , S. and Letchford , C. W. 2007 . Comparison of dynamic subgrid-scale models for simulations of neutrally buoyant shear-driven atmospheric boundary layer flows . Environ. Fluid Mech. , 7 : 195 – 215 .
   Web of Science ®Google Scholar
• Bohr , T. , Jensen , M. H. , Paladin , G. and Vulpiani , A. 1998 . Dynamical Systems Approach to Turbulence , Cambridge, UK : Cambridge University Press .
   Google Scholar
• Frisch , U. 1995 . Turbulence: The Legacy of A. N. Kolmogorov , Cambridge, UK : Cambridge University Press .
   Google Scholar
• Smagorinsky , J. S. 1963 . General Circulation Experiments with the Primitive Equations . Mon. Wea. Rev. , 91 : 99 – 164 .
   Google Scholar
• Wong , V. C. and Lilly , D. K. 1994 . A comparison of two dynamic subgrid closure methods for turbulent thermal convection . Phys. Fluids , 6 : 1016 – 1023 .
   Web of Science ®Google Scholar
• Lilly , D. K. 1967 . The representation of small-scale turbulence in numerical simulation experiments , Yorktown Heights, NY : Scientific Computing Symposium on Environmental Sciences .
   Google Scholar
• Meneveau , C. 1991 . Analysis of turbulence in the orthonormal wavelet representation . J. Fluid Mech. , 232 : 469 – 520 .
   Web of Science ®Google Scholar
• Meneveau , C. 1994 . Statistics of turbulence subgrid-scale stresses: Necessary conditions and experimental results . Phys. Fluids , 6 : 815 – 833 .
   Web of Science ®Google Scholar
• Delour , J. , Muzy , J. F. and Arnéodo , A. 2001 . Intermittency of 1D velocity spatial profiles in turbulence: A magnitude cumulant analysis . Eur. Phys. J. B , 23 : 243 – 248 .
   Web of Science ®Google Scholar
• Malécot , Y. , Auriault , C. , Kahalerras , H. , Gagne , Y. , Chanal , O. , Chabaud , B. and Castaing , B. 2000 . A statistical estimator of turbulence intermittency in physical and numerical experiments . Eur. Phys. J. B. , 16 : 549
   Web of Science ®Google Scholar
• Basu , S. , Foufoula-Georgiou , E. , Lashermes , B. and Arnéodo , A. 2007 . Estimating intermittency exponent in neutrally stratified atmospheric surface layer flows: A robust framework based on magnitude cumulant and surrogate analyses . Phys. Fluids , 19 : 115102
   Web of Science ®Google Scholar
• He , G.-W. , Rubinstein , R. and Wang , L.-P. 2002 . Effects of subgrid-scale modeling on time correlations in large eddy simulation . Phys. Fluids , 14 : 2186 – 2193 .
   Web of Science ®Google Scholar
• Kaneda , Y. 1993 . Lagrangian and Eulerian time correlations in turbulence . Phys. Fluids , 5 : 2835
   Web of Science ®Google Scholar