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Original Articles

A study of the Navier–Stokes-α model for two-dimensional turbulence

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Article: N30 | Published online: 09 Mar 2011

References

  • Cao , C. , Holm , D. and Titi , E. S. 2005 . On the Clark-å model of turbulence: global regularity and long-time dynamics . Journal of Turbulence , 6 ( 20 ) : 1 – 11 .
  • Cao , Y. , Lunasin , E. and Titi , E. S. 2006 . Global well-posedness of the three-dimensional viscous and inviscid simplified Bardina turbulence models . Communications in Mathematical Sciences , 4 ( 4 ) : 823 – 848 .
  • Chen , S. , Foias , C. , Holm , D. D. , Olson , E. , Titi , E. S. and Wynne , S. 1999 . The Camassa–Holm equations and turbulence . Physica D , 133 ( 1–4 ) : 49 – 65 .
  • Chen , S. , Foias , C. , Holm , D. D. , Olson , E. , Titi , E. S. and Wynne , S. 1999 . A connection between the Camassa–Holm equations and turbulent flows in channels and pipes . Physics of Fluids , 11 ( 8 ) : 2343 – 2353 .
  • Chen , S. , Foias , C. , Holm , D. D. , Olson , E. , Titi , E. S. and Wynne , S. 1998 . Camassa–Holm equations as a closure model for turbulent channel and pipe flow . Physical Review Letters , 81 ( 24 ) : 5338 – 5341 .
  • Chen , S. , Holm , D. D. , Margolin , L. G. and Zhang , R. 1999 . Direct numerical simulations of the Navier–Stokes alpha model . Physica D , 133 ( 1-4 ) : 66 – 83 .
  • Cheskidov , A. , Holm , D. D. , Olson , E. and Titi , E. S. 2005 . On a Leray-α model of turbulence . Philosophical Transactions of the Royal Society London, Series A , 461 : 629 – 649 .
  • Cioranescu , D. and Girault , V. 1996 . Solutions variationelles et classiques d'une famille de fluides de grade deux . Comptes Rendus de l'Academic des Sciences, Serie I , 322 : 1163 – 1168 .
  • Cioranescu , D. and Girault , V. 1996 . Weak and classical solutions of a family of second grade fluids . International Journal of Non-Linear Mechanics , 32 : 317 – 335 .
  • Clark , R. , Ferziger , J. and Reynolds , W. 1979 . Evaluation of subgrid scale models using an accurately simulated turbulent flow . Journal of Fluid Mechanics , 91 : 1 – 16 .
  • Constantin , P. and Foias , C. 1988 . Navier–Stokes Equations , Chicago , IL : University of Chicago Press .
  • Dunn , J. E. and Fosdick , R. L. 1974 . Thermodynamics, stability, and boundedness of fluids of complexity 2 and fluids of second grade . Archive for Rational Mechanics and Analysis , 56 : 191 – 252 .
  • Foias , C. 1997 . “ What do the Navier–Stokes equations tell us about turbulence? ” . In Harmonic Analysis and Nonlinear Differential Equations , Vol. 208 , 151 – 180 . Providence , RI : American Mathematical Society . Contemporary Mathematics
  • Foias , C. , Holm , D. D. and Titi , E. S. 2002 . The three dimensional viscous Camassa–Holm equations, and their relation to the Navier–Stokes equations and turbulence theory . Journal of Dynamics and Differential Equations , 14 : 1 – 35 .
  • Foias , C. , Holm , D. D. and Titi , E. S. 2001 . The Navier–Stokes–alpha model of fluid turbulence. Advances in nonlinear mathematics and science . Physica D , 152 ( 153 ) : 505 – 519 .
  • Foias , C. , Manley , O. , Rosa , R. and Temam , R. 2001 . Navier–Stokes Equations and Turbulence , Cambridge : Cambridge University Press .
  • Geurts , B. and Holm , D. 1999 . Fluctuation effect on 3d-Lagrangian mean and Eulerian mean fluid motion . Physical D , 133 : 215 – 269 .
  • Geurts , B. and Holm , D. 2003 . Regularization modeling for large eddy simulation . Physics of Fluids , 15 : L13 – L16 .
  • Holm , D. , Marsden and Ratiu , T. 1998 . Euler–Poincaré models of ideal fluids with nonlinear dispersion . Physical Review Letters , 80 : 4173 – 4176 .
  • Ilyin , A. , Lunasin , E. and Titi , E. S. 2006 . A modified-Leray-α subgrid scale model of turbulence . Nonlinearity , 19 : 879 – 897 .
  • Ilyin , A. and Titi , E. S. 2003 . Attractors for the two-dimensional Navier–Stokes-α model: an α-dependence study . Journal of Dynamics and Differential Equations , 14 ( 4 ) : 751 – 778 .
  • Kraichnan , R. H. 1967 . Inertial ranges in two-dimensional turbulence . Physics of Fluids , 10 : 1417 – 1423 .
  • Kraichnan , R. H. 1971 . Inertial-range transfer in two- and three dimensional turbulence . Physics of Fluids , 10 : 525 – 535 .
  • Layton , W. and Lewandowski , R. 2006 . On a well-posed turbulence model . Dicrete and Continuous Dynamic Systems B , 6 : 111 – 128 .
  • Mohseni , K. , Kosović , B. , Shkoller , S. and Marsden , J. 2003 . Numerical simulations of the Lagrangian averaged Navier–Stokes equations for homogeneous isotropic turbulence . Physics of Fluids , 15 ( 2 ) : 524 – 544 .
  • Nadiga , B. and Skoller . 2001 . Enhancement of the inverse-cascade of energy in the two-dimensional averaged Euler equations . Physics of Fluids , 13 : 1528 – 1531 .
  • Olson , E. and Titi , E. S. Viscosity versus vorticity stretching: global well-posedness for a family of Navier–Stokes–alpha–like models . Nonlinear Analysis A , 66 ( 11 ) 2427 – 2458 .
  • Temam , R. 2001 . Navier–Stokes Equations, Theory and Numerical Analysis. , 3rd edition , Amsterdam : North-Holland .

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