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2003 | 1 | 2 | 258-267
Article title

On the lyman problem

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EN
Abstracts
EN
This paper attempts to answer Lyman's question (1990) on the non-uniqueness in defining the 3D measure of the boundary vorticity-creation rate. Firstly, a straightforward analysis of the vorticity equation introduces a definition of a general vorticity flux-density tensor and its ‘effective’ part. The approach is strictly based on classical field theory and is independent of the constitutive structure of continuous medium. Secondly, the fundamental question posed by Lyman dealing with the ambiguity of the 3D measure of the boundary vorticity-creation rate for incompressible flow is discussed. It is shown that the original 3D measure (for an incompressible Newtonian fluid defined by Panton 1984), which is reminiscent of an analogy to Fourier's law, is in its character ‘effective’ and plays a crucial role in the prognostic vorticity transport equation. The alternative 3D measure proposed by Lyman includes, on the other hand, a ‘non-effective’ part, which plays a role in the local determination of the ‘effective’ measure as well as in a certain diagnostic integral boundary condition.
Publisher
Journal
Year
Volume
1
Issue
2
Pages
258-267
Physical description
Dates
published
1 - 6 - 2003
online
1 - 6 - 2003
References
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  • [5] F.A. Lyman: “Vorticity production at a solid boundary”, Appl. Mech. Rev., Vol. 43, (1990), pp. 157–158, In: L.M. Trefethen, R.L. Panton: “Some unanswered questions in fluid mechanics”, Appl. Mech. Rev., Vol. 43, (1990), pp. 153–170.
  • [6] R.L. Panton: “Incompressible Flow”, Wiley-Interscience, New York, 1984.
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  • [8] A. Honkan, Y. Andreopoulos: “Vorticity, strain-rate and dissipation characteristics in the near-wall region of turbulent boundary layers”, J. Fluid Mech., Vol. 350, (1997), pp. 29–96. http://dx.doi.org/10.1017/S0022112097006770[Crossref]
  • [9] C. Truesdell, R.A. Toupin: “The Classical Field Theories”, In: S. Flügge, Ed.: Encyclopedia of Physics, Vol. III/1, Principles of Classical Mechanics and Field Theory, Springer-Verlag, Berlin, 1960.
  • [10] E.W. Billington, A. Tate: “The Physics of Deformation and Flow”, McGraw-Hill, New York, 1981.
  • [11] V. Kolář, D.A. Lyn, W. Rodi: “Ensemble-averaged measurements in the turbulent near wake of two side-by-side square cylinders”, J. Fluid Mech., Vol. 346, (1997), pp. 201–237. http://dx.doi.org/10.1017/S0022112097006307[Crossref]
  • [12] P.M. Gresho: “Incompressible fluid dynamics: some fundamental formulation issues”, Annu. Rev. Fluid Mech., Vol. 23, (1991), pp. 413–453. http://dx.doi.org/10.1146/annurev.fl.23.010191.002213[Crossref]
  • [13] M. Larchevêque: “Pressure field, vorticity field, and coherent structures in two-dimensional incompressible flows”, Theor. Comput. Fluid Dyn., Vol. 5, (1993), pp. 215–222. http://dx.doi.org/10.1007/BF00271659[Crossref]
Document Type
Publication order reference
YADDA identifier
bwmeta1.element.-psjd-doi-10_2478_BF02476296
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