The Camassa-Holm equations and turbulence

Physica D: Nonlinear Phenomena

Volumn 133, Issue 1-4, 1999, Pages 49-65

  Chen, S ^a   Foias, C ^a,b   Holm, D D ^a   Olson, E ^a,b   Titi, E S ^c,d   Wynne, S ^c,d  

^a CENTER FOR NONLINEAR STUDIES   (United States)

^b INDIANA UNIVERSITY   (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

^d LOS ALAMOS NATIONAL LABORATORY   (United States)

Author keywords

Camassa Holm equations; Turbulent channel and pipe flows

Indexed keywords

EID: 0039964945     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(99)00098-6     Document Type: Article

References (20)

1. M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions, 9th ed., Dover, New York (1964).
2. Barenblatt G.I., Chorin A.J. Scaling laws and vanishing viscosity limits in turbulence theory. SIAM Rev. 40(2):1998;265.
3. Barenblatt G.I., Chorin A.J., Prostokishin V.M. Scaling laws for fully developed turbulent flow in pipes. Appl. Mech. Rev. 50:1997;413.
4. S. Chen, D.D. Holm, L.G. Margolin, R. Zhang, The 3D DNS of the Camassa-Holm Equations as an LES Model for Turbulence, in preparation.
5. Chen S., Foias C., Holm D.D., Olson E., Titi E.S., Wynne S. The Camassa-Holm equations as a closure model for turbulent channel and pipe flow. Phys. Rev. Lett. 81:1998;5338.
6. S. Chen, C. Foias, D.D. Holm, E. Olson, E.S. Titi, S. Wynne, A connection between the Camassa-Holm equations and turbulent flows in channels and pipes, Phys. Fluids, in press.
7. Constantin P., Foias C., Temam R. On the dimension of the attractor in two-dimensional turbulence. Physica D. 30:1988;284-296.
8. Dean R.B. Reynolds number dependence of skin friction and other bulk flow variables in two-dimensional rectangular duct flow. Trans. ASME I; J. Fluids Eng. 100:1978;215.
9. Dunn J.E., Fosdick R.L. Thermodynamics, stability, and boundedness of fluids of complexity 2 and fluids of second grade. Arch. Rat. Mech. Anal. 56:1974;191-252.
10. Dunn J.E., Rajagopal K.R. Fluids of differential type: critical reviews and thermodynamic analysis. Int. J. Eng. Sci. 33:1995;689-729.
11. Foias C. What do the Navier-Stokes equations tell us about turbulence? Contemporary Math. 208:1997;151-179.
12. C. Foias, D.D. Holm, E.S. Titi, The Three Dimensional Viscous Camassa-Holm Equations, and Their Relation to the Navier-Stokes Equations and Turbulence Theory, in preparation.
13. Holm D.D., Marsden J.E., Ratiu T.S. The Euler-Poincaŕe equations and semidirect products with applications to continuum theories. Adv. Math. 137:1998;1-81.
14. J.N. Hunt, Incompressible Fluid Dynamics, Wiley, New York, 1964, p. 127.
15. Kim J., Moin P., Moser R. Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177:1987;133-166.
16. 0=395 .
17. J.L. Lumley, H. Tennekes, A First Course in Turbulence, MIT Press, Cambridge, MA, 1972.
18. Panton R.L. A Reynolds stress function for wall layers. J. Fluids Eng. 119:1997;325-329.
19. Wei T., Willmarth W.W. Reynolds-number effects on the structure of a turbulent channel flow. J. Fluid Mech. 204:1989;57-95.
20. M.V. Zagarola, Mean-flow scaling of turbulent pipe flow, PhD Thesis, Princeton University Press, Princeton, NJ, 1996.