A methodology to quantify the nonlinearity of the Reynolds stress tensor

References

• Boussinesq , M. 1987 . Essai sur la theorie des eaux courantes, , 3rd ed. , 46 Mem. pres. Acad. Sci. . Imprimerie Nationale, Paris XXIII
   Google Scholar
• Speziale , C. G. , Sarkar , S. and Gatski , T. B. 1991 . Modelling the pressure-strain correlation of turbulence: An invariant dynamical system approach . J. Fluid Mech. , 227 : 245 – 272 .
   Web of Science ®Google Scholar
• Lumley , J. L. 1970 . Toward a turbulent constitutive relation . J. Fluid Mech. , 41 : 413 – 434 .
   Web of Science ®Google Scholar
• Pope , S. 1975 . A more general effective-viscosity hypothesis . J. Fluid Mech. , 72 : 331 – 340 .
   Web of Science ®Google Scholar
• Speziale , C. G. 1987 . On non-linear k-l and k-ε models of turbulence . J. Fluid Mech. , 178 : 459 – 475 .
   Web of Science ®Google Scholar
• Gatski , T. B. and Jongen , T. 2000 . Nonlinear eddy viscosity and algebraic stress models for solving complex turbulent flows . Prog. Aerosp. Sci. , 36 : 655 – 682 .
   Web of Science ®Google Scholar
• Gatski , T. B. and Speziale , C. G. 1993 . On explicit algebraic stress models for complex turbulent flows . J. Fluid Mech. , 254 : 59 – 78 .
   Web of Science ®Google Scholar
• Girimaji , S. S. 1996 . Fully explicitly and self consistent algebraic Reynolds stress model . Theoret. Comput. Fluid Dyn. , 8 : 387 – 402 .
   Web of Science ®Google Scholar
• Wallin , S. and Johanson , A. V. 2000 . An explicit algebraic Reynolds stress model for incompressible and compressible turbulent flows . J. Fluid Mech , 403 : 89 – 132 .
   Web of Science ®Google Scholar
• Wallin , S. and Johanson , A. V. 2002 . Modelling streamlines curvature effects in explicit algebraic Reynolds stress turbulence model . Int. J. Heat Fluid Flow , 23 : 721 – 730 .
   Web of Science ®Google Scholar
• Jongen , T. and Gatski , T. 1998 . General explicit algebraic stress relations and best approximation for three-dimensional flows . Int. J. Eng. Sci. , 36 : 739 – 763 .
   Web of Science ®Google Scholar
• Mompean , G. , Gavrilakis , S. , Machiels , L. and Deville , M. 1996 . On predicting the turbulence-induced secondary flows using non-linear k −ε models . Phys. Fluids , 8 : 1856 – 1868 .
   Web of Science ®Google Scholar
• Naji , H. , Mompean , G. and El Yahyaoui , O. 2004 . Evaluation of explicit algebraic stress models using direct numerical simulations . J. Turbulence , 5 : 1 – 25 . 038
   Google Scholar
• Schmitt , F. G. 2007 . Direct test of nonlinear constitutive equation for simple turbulent shear flows using DNS data . Commun. Nonlinear Sci. Numer. Simul. , 12 : 1251 – 1264 .
   Web of Science ®Google Scholar
• Gavrilakis , S. 1992 . Numerical simulation of low-Reynolds-number turbulent flow through a straight square duct . J. Fluid Mech. , 244 : 101 – 116 .
   Web of Science ®Google Scholar
• Thais , L. , Tejada-Martínez , A. E. , Gatski , T. B. and Mompean , G. 2009 . Numerical simulations of turbulent viscoelastic drag reduction . Proceedings of the Second International Conference on Turbulence and Interaction . 31 May–5 June 2009 , Sainte Luce, Martinique, France.
   Google Scholar
• Kolmogorov , A. N. 1942 . Equations of turbulent motion of an incompressible fluid . Izvest. Acad. Sci., SSSR; Physics , 6 : 56 – 58 .
   Google Scholar
• Thompson , R. L. and Souza Mendes , P. R. 2005 . Persistence of straining and flow classification . Int. J. Eng. Sci , 43 ( 1-2 ) : 79 – 105 .
   Google Scholar
• Rumsey , C. L. , Gatski , T. B. and Morrison , J. H. 2000 . Turbulence model predictions of strongly curved flow in a U-duct . AIAA J. , 38 ( 8 ) : 1394 – 1402 .
   Google Scholar
• Mompean , G. , Thompson , R. L. and Souza Mendes , P. R. 2003 . A general transformation procedure for differential viscoelastic models . J. Non-Newtonian Fluid Mech. , 111 : 151 – 174 .
   Web of Science ®Google Scholar
• Thais , L. , Mompean , G. and Helin , L. 2005 . On the consequences of material frame-indifference in algebraic stress models . Theoret. Comp. Fluid Dyn. , 19 : 1 – 22 .
   Web of Science ®Google Scholar
• Gavrilakis , S. 1993 . Turbulent velocity structures derived from pod analyses C134 – C156 . Institut de Machines Hydrauliques et de Mécanique des Fluides, École Polytechnique Fédérale de Lausanne. Report T-93-30
   Google Scholar
• Lele , S. 1992 . Compact finite difference schemes with spectral-like resolution . J. Comp. Phys. , 103 ( 1 ) : 16 – 42 .
   Web of Science ®Google Scholar
• Moser , R. , Kim , J. and Mansour , N. 1999 . Direct numerical simulation of turbulent channel flow up to Re τ = 590 . Phys. Fluids , 11 ( 4 ) : 943 – 945 .
   Web of Science ®Google Scholar
• Hojas , F. H. and Jimenez , J. E. 2008 . Reynolds number effects on the Reynolds-stress budgets in turbulent channels . Phys. Fluids , 20 : 2182 – 2189 .
   Google Scholar
• Huser , A. and Biringen , S. 1993 . Direct numerical simulation of turbulent flow in a square duct . J. Fluid Mech. , 257 : 65 – 77 .
   Web of Science ®Google Scholar
• Mompean , G. 1998 . Numerical simulation of a turbulent flow near a righ-angled corner using the Speziale nonlinear model with RNG k−ε equations . Comput. Fluids , 27 : 847 – 859 .
   Web of Science ®Google Scholar
• Rajagopal , K. and Srinivasa , A. 2005 . On the nature of constraints for continua undergoing dissipative processes . Proc. R. Soc. Lond. A , 461 : 2785 – 2795 .
   Web of Science ®Google Scholar
• Thompson , R. L. 2008 . Some perspectives on the dynamic history of a material element . Int. J. Eng. Sci , 46 : 524 – 549 .
   Web of Science ®Google Scholar
• Huilgol , R. R. 1979 . Viscoelastic fluid theories based on the left Cauchy-Green tensor history . Rheol. Acta , 18 : 451 – 455 .
   Web of Science ®Google Scholar