Helicity in the formation of turbulence

Physics of Fluids

Volumn 19, Issue 2, 2007, Pages

  Holm, D D ^a   Kerr, R M ^b  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

^b UNIVERSITY OF WARWICK   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; EULER EQUATIONS; FLOW VISUALIZATION; NAVIER STOKES EQUATIONS; VORTEX FLOW; VORTICITY;

EULER DYNAMICS; HELICITY;

TURBULENCE;

COMPUTER SIMULATION; EULER EQUATIONS; FLOW VISUALIZATION; NAVIER STOKES EQUATIONS; TURBULENCE; VORTEX FLOW; VORTICITY;

EID: 33847675788     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2375077     Document Type: Article

References (29)

1. In order to celebrate mathematics in the new millennium, the Clay Mathematics Institute of Cambridge, Massachusetts has named seven "prize" problems. The official Navier-Stokes problem asks for proof of one of four statements, all related to either existence and smoothness of the Navier- Stokes equations, or their breakdown in three dimensions. For further information, see The Millennium Prize Problems, edited by J. Carlson (Clay Mathematics Institute, Providence, RI 2005); URL: www.claymath.org/millennium/
2. J. T. Beale, T. Kato, and A. Majda, "Remarks on the breakdown of smooth solutions of the 3-D Euler equations," Commun. Math. Phys. 94, 61 (1984).
3. M. E. Brachet, D. I. Meiron, S. A. Orszag, B. G. Nickel, R. H. Morf, and U. Frisch, "Small-scale structure of the Taylor-Green vortex," J. Fluid Mech. 130, 411 (1983).
4. M. E. Brachet, M. Meneguzzi, A. Vincent, H. Politano, and P. L. Sulem, "Numerical evidence of smooth self-similar dynamics and possibility subsequent collapse for three-dimensional ideal flows," Phys. Fluids A 4, 2845 (1992).
5. R. M. Kerr, "Evidence for a singularity of the three-dimensional, incompressible Euler equations," Phys. Fluids A 5, 1725 (1993).
6. R. Grauer, C. Marliani, and K. Germaschewski, "Adaptive mesh refinement for singular solutions of the incompressible Euler equations," Phys. Rev. Lett. 80, 4177 (1998).
7. A. Brandenburg and R. M. Kerr, "Helicity in hydro and MHD reconnection," in Quantized Vortex Dynamics and Superfluid Turbulence, edited by C. F. Barenghi, R. S. Donnelly, and J. Vinen (Cambridge University Press, Cambridge, UK, 2001).
8. E. D. Siggia, "Numerical study of small scale intermittency in threedimensional turbulence," J. Fluid Mech. 107, 375 (1981).
9. R. M. Kerr, "Higher order derivative correlations and the alignment small-scale structures in isotropic numerical turbulence," J. Fluid Mech. 153, 31 (1985).
10. A. Vincent and M. Meneguzzi, "The spatial structure and statistical properties of homogeneous turbulence," J. Fluid Mech. 225, 1 (1991).
11. G. Compte-Bellot and S. Corrsin, "Simple Eulerian time correlation of full- and narrow-band velocity signals in grid-generated, 'isotropic' turbulence," J. Fluid Mech. 48, 273 (1971).
12. J. R. Herring and R. M. Kerr, "Comparison of direct numerical simulation with prediction of two-point closures," J. Fluid Mech. 118, 205 (1982).
13. J. R. Herring and R. M. Kerr, "Development of enstrophy and spectra in numerical turbulence," Phys. Fluids A 5, 2792 (1993).
14. D. D. Holm and R. M. Kerr, "Transient vortex events in the initial value problem for turbulence," Phys. Rev. Lett. 88, 244501 (2002).
15. L. G. Margolin, P. K. Smolarkiewicz, and A. A. Wyszogradzki, "Implicit turbulence modeling for high Reynolds number flows," J. Fluids Eng. 124, 862 (2002).
16. D. Drikakis, "Advances in turbulent flow computations using highresolution methods," Prog. Aerosp. Sci. 39, 405 (2003).
17. Unfortunately, the size of the peak, H(k=6.5) at t=0.7 in our earlier work (Ref. 14), was an artifact of an FFT hardware error when analysis of a Cray-YMP calculation was done on a Cray-J9. The strong peak disappears after t ≈ 0.55.
18. R. M. Kerr, "Velocity and scaling of collapsing Euler vortices," Phys. Fluids 17, 075103 (2005).
19. L. Biferale and R. M. Kerr, "On the role of inviscid invariants in shell models of turbulence," Phys. Rev. E 52, 6113 (1995).
20. W. Polifke and L. Shtilman, "The dynamics of helical decaying turbulence," Phys. Fluids A 1, 2025 (1989).
21. A similar effect was found in a simulation of forced isotropic turbulence in energy transfer spectra. R. M. Kerr, "Velocity, scalar and transfer spectra in numerical turbulence," J. Fluid Mech. 211, 309 (1990).
22. Z.-S. She, E. Jackson, and S. A. Orszag, "Intermittent vortex structures in homogeneous isotropic turbulence," Nature (London) 344, 226 (1990).
23. A. Pumir and E. D. Siggia, "Vortex dynamics and the existence of solutions of the Navier-Stokes equations," Phys. Fluids 30, 1606 (1987).
24. S. Kida and M. Takaoka, "Vortex reconnection," Annu. Rev. Fluid Mech. 26, 169 (1994).
25. R. M. Kerr and F. Hussain, "Simulation of vortex reconnection," Physica D 37, 474 (1989).
26. L. Biferale, "Shell models of energy cascade in turbulence," Annu. Rev. Fluid Mech. 35, 441 (2003).
27. L. Kadanoff, D. Lohse, and J. Wang, "Scaling and dissipation in the shell GOY model," Phys. Fluids 7, 617 (1995).
28. H. K. Moffatt, "Magnetostatic equilibria and analogous Euler flows of arbitrarily complex topology. Part 1, fundamentals," J. Fluid Mech. 159, 359 (1985).
29. F. Waleffe, "Inertial transfers in the helical decomposition," Phys. Fluids A 5, 677 (1993).