Scaling laws and vanishing-viscosity limits for wall-bounded shear flows and for local structure in developed turbulence

Communications on Pure and Applied Mathematics

Volumn 50, Issue 4, 1997, Pages 381-398

  Barenblatt, G I ^b   Chorin, Alexandre J ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b STANFORD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031478945     PISSN: 00103640     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0312(199704)50:4<381::AID-CPA5>3.0.CO;2-6     Document Type: Article

References (39)

1. Barenblatt, G. I., Similarity, Self-Similarity and Intermediate Asymptotics, Consultants Bureau, New York-London, 1979.
2. Barenblatt, G. I., Scaling laws for fully developed turbulent shear flows, I. Basic hypotheses and analysis, J. Fluid Mech. 248, 1993, pp. 513-520.
3. Barenblatt, G. I., and Chorin, A. J., Small viscosity asymptotics for the inertial range of local structure and for the wall region of wall-bounded turbulence, Proc. Nat. Acad. Sciences USA 93, 1996, pp. 6749-6752.
4. Barenblalt, G. I., and Goldenfeld, N., Does fully developed turbulence exist? Reynolds number independence versus asymptotic covariance, Phys. Fluids 7, 1995, pp. 3078-3082.
5. Barenblatt, G. I., and Prostokishin, V. I., Scaling laws for fully developed turbulent shear flows, II. Processing of experimental data, J. Fluid Mech. 248, 1993, pp. 521-529.
6. Beale, J. T., Kato, T., and Majda, A., Remarks on the breakdown of smooth solutions for the 3D Euler equations, Connu. Math. Phys. 94, 1984, pp. 61-66.
7. Beale, J. T., and Majda, A., Rates of convergence for viscous splitting of the Navier-Stokes equations, Math. Comp. 37, 1981, pp. 243-259.
8. Chorin, A. J., Theories of turbulence, pp. 36-47 in: Turbulence Seminar (University of California, Berkeley Calif., 1976/1977), P. Bernard and T. Ratiu, eds., Lecture Notes in Mathematics No. 615, Springer-Verlag, Berlin, 1977.
9. Chorin, A. J., The evolution of a turbulent vortex, Comm. Math. Phys. 83, 1982, pp. 517-535.
10. Chorin, A. J., Vorticity and Turbulence, Applied Mathematical Sciences No. 103, Springer-Verlag, New York, 1994.
11. Chorin, A. J., Turbulence as a near-equilibrium process, pp. 235-249 in: Dynamical Systems and Probabilistic Methods in Partial Differential Equations (Berkeley, Calif., 1994), Lectures in Applied Mathematics No. 31, American Mathematical Society, Providence, R.I., 1996.
12. Chorin, A. J., Onsager's contribution to turbulence theory: Vortex dynamics and turbulence in ideal flow, in: L. Onsager, Collected Works with Commentary, P. Hemmer and others, eds., World Scientific, 1996.
13. Chorin, A. J., Partition functions and equilibirum measures for two-dimensional turbulence, Phys. Fluids 8, 1996, pp. 2656-2660.
14. Coles, D., The law of the wake in the turbulent boundary laver, J. Fluid Mech. 1, 1956, pp. 191-226.
15. Constantin, P., Note on loss of regularity for solutions of the 3D incompressible Euler and related equations, Comm. Math. Phys. 104, 1986, pp. 311-326.
16. Constantin, P., E, W., and Titi, E. S., Onsager's conjecture on the energy conservation for solutions of Euler's equation, Comm. Math. Phys. 165, 1994, pp. 207-209.
17. Constantin, P., and Wu, J., Inviscid limit for vortex patches, Nonlinearity 8, 1995, pp. 735-742.
18. Constantin, P., and Wu, J., The inviscid limit for non-smooth vorticity, Indiana Univ. Math. J. 45, 1996, pp. 67-81.
19. Frisch, U., Turbulence: The Legacy of A. N. Kolmogorov, Cambridge University Press, Cambridge, 1995.
20. Gad-el-Hak, M., and Bandyopadhyay, P. R., Reynolds number effects in wall-bounded turbulent flows, Appl. Mech. Rev. 47, 1994, pp. 307-366.
21. Goldenfeld, N., Lectures on Phase Transitions and the Renormalization Group, Addison-Wesley, Reading, Mass., 1992.
22. Grauer, R., and Sideris, T., Numerical computation of 3D incompressible ideal fluids with swirl, Phys. Rev. Lett. 67, 1991, pp. 3511-3514.
23. Kato, T., Remarks on zero viscosity limit for nonstationary Navier-Stokes flows with boundary, pp. 85-98 in: Seminar on Nonlinear Partial Differential Equations (Berkeley, Calif., 1983), S. S. Chern, ed., Mathematical Sciences Research Institute Publications No. 2, Springer-Verlag, New York-Berlin, 1984.
24. Kolmogorov, A. N., The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers, Dokl. Akad. Nauk USSR 30, 1941, pp. 299-302.
25. Lesieur, M., Turbulence in Fluids: Stochastic and Numerical Modelling, 2nd ed., Fluid Mechanics and Its Applications No. 1, Kluwer Academic, Dordrecht, Netherlands, 1990.
26. McComb, W. D., The Physics of Fluid Turbulence, Oxford Engineering Science Series No. 25, Oxford Science Publications, The Clarendon Press, Oxford University Press, Oxford-New York, 1991.
27. Minion, M., Two methods for the study of vortex patch evolution on locally refined grids, Doctoral Dissertation, University of California, Berkeley, 1994.
28. Monin, A. S., and Yaglom, A. M., Statistical Fluid Mechanics: Mechanics of Turbulence, vol. 1, MIT Press, Cambridge, Mass., 1971.
29. Nikuradze, J., Gesetzmaessigkeiten der turbulenten Stroemung in glatten Rohren, VDI Forschungheft 356, 1932.
30. Obukhov, A. M., Spectral energy distribution in turbulent flow, Dokl. Akad. Nauk USSR 32, 1941, pp. 22-24.
31. Onsager, L., Statistical hydrodynamics, Nuovo Cimento (9) 6, 1949, suppl. 2 (Convegno Internazionale di Meccanica Statistica), pp. 279-287.
32. Prandtl, L., Zur turbulenten Stroemung in Rohren und laengs Platten, Ergeb. Aerodyn. Versuch. 4, Goettingen, 1932.
33. Praskovsky, A., and Oncley, S., Measurements of the Kolmogorov constant and intermittency exponents at very high Reynolds number, Phys. Fluids A 7, 1994, pp. 2778-2784.
34. Schlichting, H., Boundary Layer Theory, 4th ed., McGraw-Hill, New York-Toronto-London, 1960.
35. Sreenivasan, K. R., On the universality of the Kolmogorov constant, Phys. Fluids A 7, 1995, pp. 2778-2784.
36. Tennekes, H., and Lumley, J. L., pp. 147, 263 in: A First Course in Turbulence, MIT Press, Cambridge, Mass., 1990.
37. Vishik, M. J., and Fursikov, A. V., Mathematical Problems of Statistical Hydromechanics, Kluwer Academic, Dordrecht, Netherlands, 1988.
38. von Kármán, T., Mechanische Aehnlichkeit und Turbulenz, Nach. Ges. Wiss. Goettingen Math-Phys. Klasse, 1932, pp. 58-76.
39. Zagarola, M. V., Smits, A. J., Orszag, S. A., and Yakhot, V., Experiments in high Reynolds number turbulent pipe flow, AIAA Paper 96-0654, Reno, Nev., 1996.