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On the Lamb vector divergence in Navier–Stokes flows

Published online by Cambridge University Press:  08 August 2008

CURTIS W. HAMMAN ,
JOSEPH C. KLEWICKI  and
ROBERT M. KIRBY
CURTIS W. HAMMAN
Affiliation:
Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, UT 84112, USA
JOSEPH C. KLEWICKI
Affiliation:
Department of Mechanical Engineering, University of New Hampshire, Durham, NH 03824, USA
ROBERT M. KIRBY
Affiliation:
Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, UT 84112, USA School of Computing, University of Utah, Salt Lake City, UT 84112, USA
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Abstract

The mathematical and physical properties of the Lamb vector divergence are explored. Toward this aim, the instantaneous and mean dynamics of the Lamb vector divergence are examined in several analytic and turbulent flow examples relative to its capacity to identify and characterize spatially localized motions having a distinct capacity to effect a time rate of change of momentum. In this context, the transport equation for the Lamb vector divergence is developed and shown to accurately describe the dynamical mechanisms by which adjacent high- and low-momentum fluid parcels interact to effect a time rate of change of momentum and generate forces such as drag. From this, a transport-equation-based framework is developed that captures the self-sustaining spatiotemporal interactions between coherent motions, e.g. ejections and sweeps in turbulent wall flows, as predicted by the binary source–sink distribution of the Lamb vector divergence. New insight into coherent motion development and evolution is found through the analysis of the Lamb vector divergence.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 610 , 10 September 2008 , pp. 261 - 284
Copyright
Copyright © Cambridge University Press 2008

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References

REFERENCES

Adrian, R. J. & Moin, P. 1988 Stochastic estimation of organized turbulent structure: Homogeneous shear flow. J. Fluid Mech. 190, 531–559.CrossRefGoogle Scholar
Alim, A. 2007 A physical comprehensive definition of a vortex based on the Lamb vector. Algerian J. Appl. Fluid Mech. 1, 1–5.Google Scholar
Aubry, N., Holmes, P., Lumley, J. L. & Stone, E. 1988 The dynamics of coherent structures in the wall region of a turbulent boundary layer. J. Fluid Mech. 192, 115–173.CrossRefGoogle Scholar
Bakewell, H. P. & Lumley, J. L. 1967 Viscous sublayer and adjacent wall region in turbulent pipe flow. Phys. Fluids 10, 1880–1889.CrossRefGoogle Scholar
Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.Google Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
Berkooz, G., Holmes, P. & Lumley, J. L. 1991 Intermittent dynamics in simple models of the turbulent wall layer. J. Fluid Mech. 230, 75–95.CrossRefGoogle Scholar
Berkooz, G., Holmes, P. & Lumley, J. L. 1993 The proper orthogonal decomposition in the analysis of turbulent flows. Annu. Rev. Fluid Mech. 25, 539–575.CrossRefGoogle Scholar
Blackburn, H. M., Govardhan, R. & Williamson, C. H. K. 2001 A complementary numerical and physical investigation of vortex-induced vibration. J. Fluids Struct. 15, 481–488.CrossRefGoogle Scholar
Brasseur, J. G. & Lin, W. 2005 Kinematics and dynamics of small-scale vorticity and strain-rate structures in the transition from isotropic to shear turbulence. Fluid Dyn. Res. 36, 357–384.CrossRefGoogle Scholar
Chakraborty, P., Balachandar, S. & Adrian, R. J. 2005 On the relationships between local vortex identification schemes. J. Fluid Mech. 535, 189–214.CrossRefGoogle Scholar
Chambers, D. H., Adrian, R. J., Stewart, D. S. & Sung, H. J. 1988 Karhunen–Loève expansion of Burgers' model of turbulence. Phys. Fluids 31, 2573–2582.CrossRefGoogle Scholar
Choi, H., Moin, P. & Kim, J. 1993 Direct numerical simulation of turbulent flow over riblets. J. Fluid Mech. 255, 503–539.CrossRefGoogle Scholar
Crawford, C. H., Marmanis, H. & Karniadakis, G. E. 1998 The Lamb vector and its divergence in turbulent drag reduction. In Proc. Intl Symposium on Seawater Drag Reduction, pp. 99–107.Google Scholar
Dombre, T., Frisch, U., Greene, J. M., Henon, M., Mehr, A. & Soward, A. M. 1986 Chaotic streamlines in the ABC flows. J. Fluid Mech. 167, 353–391.CrossRefGoogle Scholar
Ferrante, A. & Elghobashi, S. 2004 On the physical mechanisms of drag reduction in a spatially developing turbulent boundary layer laden with microbubbles. J. Fluid Mech. 503, 345–355.CrossRefGoogle Scholar
Hinze, J. O. 1975 Turbulence. McGraw-Hill.Google Scholar
Howe, M. S. 1975 Contributions to the theory of aerodynamic sound, with application to excess jet noise and the theory of the flute. J. Fluid Mech. 71, 625–673.CrossRefGoogle Scholar
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69–94.CrossRefGoogle Scholar
Klewicki, J. C. 1989 Velocity–vorticity correlations related to the gradients of the Reynolds stresses in parallel turbulent wall flows. Phys. Fluids A 1, 1285–1288.CrossRefGoogle Scholar
Klewicki, J. C., Fife, P., Wei, T. & McMurtry, P. A. 2007 A physical model of the turbulent boundary layer consonant with mean momentum balance structure. Phil. Trans. R. Soc. Lond. 365, 823–839.Google ScholarPubMed
Klewicki, J. C. 1998 Connecting vortex regeneration with near-wall stress transport. In AIAA Paper 1998-2963.CrossRefGoogle Scholar
Kollmann, W. 2006 Critical points and manifolds of the Lamb vector field in swirling jets. Comput. Fluids 35, 746–754.CrossRefGoogle Scholar
Küchemann, D. 1965 Report on the IUTAM symposium on concentrated vortex motions in fluids. J. Fluid Mech. 21, 1–20.CrossRefGoogle Scholar
Lighthill, M. J. 1952 On sound generated aerodynamically. Part I. Proc. R. Soc. Lond. A 211, 564–587.Google Scholar
Lumley, J. L. 1967 The structure of inhomogeneous turbulent flows. In Atmospheric Turbulence and Radio Wave Propagation (ed. Yaglom, A. M. & Tatarsky, V. I.), pp. 166–178. Nauka, Moscow.Google Scholar
Marcu, B., Meiburg, E. & Newton, P. K. 1994 Dynamics of heavy particles in a Burgers vortex. Phys. Fluids 7, 400–410.CrossRefGoogle Scholar
Marmanis, H. 1998 Analogy between the Navier–Stokes equations and Maxwell's equations: Application to turbulence. Phys. Fluids 10, 1428–1437.CrossRefGoogle Scholar
Moffatt, H. K. & Tsinober, A. 1992 Helicity in laminar and turbulent flow. Annu. Rev. Fluid Mech. 24, 281–312.CrossRefGoogle Scholar
Moffatt, H. K. 1985 Magnetostatic equilibria and analogous Euler flows of arbitrarily complex topology. Part 1. Fundamentals. J. Fluid Mech. 159, 359–378.CrossRefGoogle Scholar
Moffatt, H. K. 1986 a Magnetostatic equilibria and analogous Euler flows of arbitrarily complex topology. Part 2. Stability considerations. J. Fluid Mech. 166, 359–378.CrossRefGoogle Scholar
Moffatt, H. K. 1986 b On the existence of localized rotational disturbances which propagate without change of structure in an inviscid fluid. J. Fluid Mech. 173, 289–302.CrossRefGoogle Scholar
Monin, A. & Yaglom, A. 1977 Statistical Fluid Mechanics. MIT Press.Google Scholar
Moser, R. D., Kim, J. & Mansour, N. N. 1999 Direct numerical simulation of turbulent channel flow up to Reτ=590. Phys. Fluids 11, 943–945.CrossRefGoogle Scholar
Offen, G. R. & Kline, S. J. 1975 A proposed model of the bursting process in turbulent boundary layers. J. Fluid Mech. 70, 209–228.CrossRefGoogle Scholar
Protas, B. & Wesfreid, J. E. 2001 Drag force in the open-loop control of the cylinder wake in the laminar regime. Phys. Fluids 14, 810–826.CrossRefGoogle Scholar
Robinson, S. K. 1991 Coherent motions in turbulent boundary layers. Annu. Rev. Fluid Mech. 23, 601–639.CrossRefGoogle Scholar
Rousseaux, G., Seifer, S., Steinberg, V. & Wiebel, A. 2007 On the Lamb vector and the hydrodynamic charge. Exps. Fluids 42, 291–299.CrossRefGoogle Scholar
Shiels, D. & Leonard, A. 2001 Investigation of a drag reduction on a circular cylinder in rotary oscillation. J. Fluid Mech. 431, 297–322.CrossRefGoogle Scholar
Sposito, G. 1997 On steady flows with Lamb surfaces. Intl J. Engng Sci. 35, 197–209.CrossRefGoogle Scholar
Taylor, G. I. 1935 Statistical theory of turbulence. Proc. R. Soc. Lond. 151, 421–444.Google Scholar
Truesdell, C. 1951 A form of Green's transformation. Am. J. Maths 73, 43–47.CrossRefGoogle Scholar
Truesdell, C. 1954 The Kinematics of Vorticity. Indiana University Press.Google Scholar
Tsinober, A. 1990 On one property of Lamb vector in isotropic turbulent flow. Phys. Fluids 2, 484–486.CrossRefGoogle Scholar
Tsinober, A. 1998 Is concentrated vorticity that important? Eur. J. Mech. B 17, 421–449.CrossRefGoogle Scholar
Tsinober, A. & Levich, E. 1983 On the helical nature of three dimensional coherent structures in turbulent flows. Phys. Rev. Lett. A 99, 321–323.CrossRefGoogle Scholar
Wei, T., Fife, P., Klewicki, J. & McMurtry, P. 2005 Properties of the mean momentum balance in turbulent boundary layer, pipe and channel flows. J. Fluid Mech. 522, 303–327.CrossRefGoogle Scholar
Wu, J.-Z., Ma, H.-Y. & Zhou, M.-D. 2006 Vorticity and Vortex Dynamics. Springer.CrossRefGoogle Scholar
Xu, J., Maxey, M. R. & Karniadakis, G. E. 2002 Numerical simulation of turbulent drag reduction using micro-bubbles. J. Fluid Mech. 468, 271–281.CrossRefGoogle Scholar
Yang, Y. T., Zhang, R. K., An, Y. R. & Wu, J. Z. 2007 Steady vortex force theory and slender-wing flow diagnosis. Acta Mechanica Sinica 23, 609–619.CrossRefGoogle Scholar