Remember Me
Or use your Academic/Social account:


Or use your Academic/Social account:


You have just completed your registration at OpenAire.

Before you can login to the site, you will need to activate your account. An e-mail will be sent to you with the proper instructions.


Please note that this site is currently undergoing Beta testing.
Any new content you create is not guaranteed to be present to the final version of the site upon release.

Thank you for your patience,
OpenAire Dev Team.

Close This Message


Verify Password:
Verify E-mail:
*All Fields Are Required.
Please Verify You Are Human:
fbtwitterlinkedinvimeoflicker grey 14rssslideshare1
Li, Y. (2010)
Publisher: American Institute of Physics
Languages: English
Types: Article

Classified by OpenAIRE into

arxiv: Physics::Fluid Dynamics, Condensed Matter::Superconductivity
In this paper we conduct an analysis of the geometrical and vortical statistics in the small scales of helical and nonhelical turbulences generated with direct numerical simulations. Using a filtering approach, the helicity flux from large scales to small scales is represented by the subgrid-scale (SGS) helicity dissipation. The SGS helicity dissipation is proportional to the product between the SGS stress tensor and the symmetric part of the filtered vorticity gradient, a tensor we refer to as the vorticity strain rate. We document the statistics of the vorticity strain rate, the vorticity gradient, and the dual vector corresponding to the antisymmetric part of the vorticity gradient. These results provide new insights into the local structures of the vorticity field. We also study the relations between these quantities and vorticity, SGS helicity dissipation, SGS stress tensor, and other quantities. We observe the following in both helical and nonhelical turbulences: (1) there is a high probability to find the dual vector aligned with the intermediate eigenvector of the vorticity strain rate tensor; (2) vorticity tends to make an angle of 45 with both the most contractive and the most extensive eigendirections of the vorticity strain rate tensor; (3) the vorticity strain rate shows a preferred alignment configuration with the SGS stress tensor; (4) in regions with strong straining of the vortex lines, there is a negative correlation between the third order invariant of the vorticity gradient tensor and SGS helicity dissipation fluctuations. The correlation is qualitatively explained in terms of the self-induced motions of local vortex structures, which tend to wind up the vortex lines and generate SGS helicity dissipation. In helical turbulence, we observe that the joint probability density function of the second and third tensor invariants of the vorticity gradient displays skewed distributions, with the direction of skewness depending on the sign of helicity input. We also observe that the intermediate eigenvalue of the vorticity strain rate tensor is more probable to take negative values. These interesting observations, reported for the first time, call for further studies into their dynamical origins and implications. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3336012]
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • [11] Q. Chen, S. Chen, and G. L. Eyink. The joint cascade of energy and helicity in threedimensional turbulence. Physics of Fluids, 15(2):361-374, 2003.
    • [12] R. M. Kerr. Histograms of helicity and strain in numerical turbulence. Phys. Rev. Lett., 59:783, 1987.
    • [13] T. Gomez, H. Politano, and A. Pouquet. Exact relationship for third-order structure functions in helical flows. Phys. Rev. E, 61(5):5321-5325, May 2000.
    • [14] S. Kurien, M. A. Taylor, and T. Matsumoto. Isotropic third-order statistics in turbulence with helicity: the 2/15-law. J. Fluid Mech., 515:87-97, 2004.
    • [15] P. D. Mininni, A. Alexakis, and A. Pouquet. Large-scale flow effects, energy transfer, and selfsimilarity on turbulence. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), 74(1):016303, 2006.
    • [16] W. Polifke and L. Shtilman. The dynamics of helical decaying turbulence. Phys. Fluids A, 1:2025, 1989.
    • [17] M. M. Rogers and P. Moin. Helicity fluctuations in incompressible turbulent flows. Phys. Fluids, 30:2662, 1987.
    • [18] J. M. Wallace, J.-L. Balint, and L. Ong. An experimental study of helicity density in turbulent flows. Phys. Fluids A, 4:2013, 1992.
    • [19] Q. Chen, S. Chen, G. L. Eyink, and D. D. Holm. Intermittency in the joint cascade of energy and helicity. Phys. Rev. Lett., 90:214503, 2003.
    • [20] Y. Choi, B. Kim, and C. Lee. Alignment of velocity and vorticity and the intermittent distribution of helicity in isotropic turbulence. Phys. Rev. E, 80(1):017301, 2009.
    • [21] H. K. Moffatt and A. Tsinober. Helicity in laminar and turbulent flow. Annu. Rev. Fluid Mech., 24:281, 1992.
    • [22] D. K. Lilly. The structure, energetics and propogation of rotating convective storms, Part II: Helicity and storm stablization. J. Atmos. Sci., 43:126, 1986.
    • [23] W.-S. Wu, D. K. Lilly, and R. M. Kerr. Helicity and thermal convection with shear. J. Atmos. Sci., 49:1800, 1992.
    • [24] P. D. Mininni and A. Pouquet. Helicity cascades in rotating turbulence. Phys. Rev. E, 79:026304, 2009.
    • [25] D. D. Holm and R. Kerr. Transient vortex events in the initial value problem for turbulence. Phys. Rev. Lett., 88:244501, 2002.
    • [26] D. D. Holm and R. M. Kerr. Helicity in the formation of turbulence. Phys. Fluids, 19:025101, 2007.
    • [27] D. Chae. Remarks on the helicity of the 3-d incompressible euler equations. Commun. Math. Phys., 240:501-507, 2003.
    • [28] C. Foias, L. Hoang, and B. Nicolaenko. On the helicity in 3d-periodic Navier-Stokes equations i: the non-statistical case. Proc. London Math. Soc., 94:53-90, 2007.
    • [29] C. Foias, L. Hoang, and B. Nicolaenko. On the helicity in 3d-periodic Navier-Stokes equations ii: the statistical case. Commun. Math. Phys., 290:679-717, 2009.
    • [30] L. C. Berselli and D. Cordoba. On the regularity of the solutions to the 3d Navier-Stokes equations: a remark on the role of the helicity. Comptes Rendus Mathematique, 347(11-12):613 - 618, 2009.
    • [31] G. L. Eyink. Multi-scale gradient expansion of the turbulent stress tensor. J. Fluid Mech., 549:159-190, 2006.
    • [32] C. Meneveau and J. Katz. Scale-invariance and turbulence models for large-eddy simulation. Annu. Rev. Fluid Mech., 32:1-32, 2000.
    • [33] B. Tao, J. Katz, and C. Meneveau. Statisticl geometry of subgrid-scale stresses determined from holographic particle image velocimetry measurements. J. Fluid Mech., 457:35-78, 2002.
    • [34] K. Horiuti. Roles of non-aligned eigenvectors of strain-rate and subgrid-scale stress tensors in turbulence generation. J. Fluid Mech., 491:65-100, 2003.
    • [35] Wm. T. Ashurst, A. R. Kerstein, R. M. Kerr, and C. H. Gibson. Alignment of vorticity and scalar gradient with strain rate in simulated Navier-Stokes turbulence. Phys. Fluids, 30:2343- 2353, 1987.
    • [36] A. Tsinober, E. Kit, and T. Dracos. Experimental investigation of the field of velocity-gradients in turbulent flows. J. Fluid Mech., 242:169-192, 1992.
    • [37] B. J. Cantwell. Exact solution of a restricted Euler equation for the velocity gradient tensor. Phys. Fluids A, 4:782-793, 1992.
    • [38] L. Shtilman, M. Spector, and A. Tsinober. On some kinematic versus dynamic properties of homogeneous turbulence. J. Fluid Mech., 247:65-77, 1993.
    • [39] A. Vincent and M. Meneguzzi. The dynamics of vortex tubes in homogeneous turbulence. J. Fluid Mech., 258:245-254, 1994.
    • [40] K. K. Nomura and G. K. Post. The structure and dynamics of vorticity and rate of strain in incompressible homogeneous turbulence. J. Fluid Mech., 377:65-97, 1998.
    • [41] A. Ooi, J. Martin, J. Soria, and M. S. Chong. A study of evolution and characteristics of the invariants of the velocity-gradient tensor in isotropic turbulence. J. Fluid Mech., 381:141-174, 1999.
    • [42] M. Guala, B. Lu¨thi, A. Liberzon, A. Tsinober, and W. Kinzelbach. On the evolution of material lines and vorticity in homogeneous turbulence. J. Fluid Mech., 533:339-359, 2005.
    • [43] B. Lu¨thi, A. Tsinober, and W. Kinzelbach. Lagrangian measurement of vorticity dynamics in turbulent flow. J. Fluid Mech., 528:87-118, 2005.
    • [44] G. Gulitski, M. Kholmyansky, W. Kinzelbach, B. Luethi, A. Tsinober, and S. Yorish. Velocity and temperature derivatives in high-Reynolds-number turbulent flows in the atmospheric surface layer. Part 3. Temperature and joint statistics of temperature and velocity derivatives. J. Fluid Mech., 589:103-123, OCT 25 2007.
    • [45] K. Ohkitani. Eigenvalue problems in three-dimensional Euler flows. Phys. Fluids A, 5:2570- 2572, 1993.
    • [46] P. Constantin. Geometric statistics in turbulence. SIAM Rev., 36:73-98, 1994.
    • [47] B. Galanti, J. D. Gibbon, and M. Heritage. Vorticity alignment results for the threedimensional Euler and Navier-Stokes equations. Nonlinearity, 10:1675-1694, 1997.
    • [48] S. Y. Chen, R. E. Ecke, G. L. Eyink, X. Wang, and Z. Xiao. Physical mechanism of the two-dimensioinal enstrophy cascade. Phys. Rev. Lett., 91:214501, 2003.
    • [49] P. Constantin and C. Fefferman. Direction of vorticity and the problem of global regularity of the navier-stokes equation. Indiana Univ. Math. J., 42:775-789, 1993.
    • [50] P. Constantin, I. Procaccia, and D. Segel. The creation and dynamics of vortex tubes in three-dimensional turbulence. Phys. Rev. E, 51:3207-3222, 1995.
    • [51] B. Galanti, I. Procaccia, and D. Segel. Dynamics of vortex lines in turbulent flows. Phys. Rev. E, 54:5122-5133, 1997.
    • [52] Y. Li, C. Meneveau, S. Chen, and G. L. Eyink. Subgrid-scale modeling of helicity and energy dissipation in helical turbulence. Phys. Rev. E, 74:026310, 2006.
    • [53] H. S. Kang and C. Meneveau. Effect of large-scale coherent structures on subgrid-scale stress and strain-rate eigenvector alignments in turbulent shear flow. Phys. Fluids, 17:055103, 2005.
    • [54] P. Vieillefosse. Local interaction between vorticity and shear in a perfect incompressible fluid. J. Phys., 43:837-842, 1982.
    • [55] A. E. Perry and M. S. Chong. A description of eddying motions and flow patterns using critical-point concepts. Annu. Rev. Fluid Mech., 19:125-155, 1987.
    • [56] J. Martin, C. Dopazo, and L. Valin˜o. Dynamics of velocity gradient invariants in turbulence: restricted Euler and linear diffusion models. Phys. Fluids, 10:2012-2025, 1998.
    • [57] F. van der Bos, B. Tao, C. Meneveau, and J. Katz. Effects of small-scale turbulent motions on the filtered velocity gradient tensor as deduced from holographic particle image velocimetry measurements. Phys. Fluids, 14:2456-2474, 2002.
    • [58] P. Vieillefosse. Internal motion of a small element of fluid in an inviscid flow. Physica A, 125:150-162, 1984.
  • No related research data.
  • Discovered through pilot similarity algorithms. Send us your feedback.

Share - Bookmark

Cite this article