Abstract
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.
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Kolár, V. On the lyman problem. centr.eur.j.phys. 1, 258–267 (2003). https://doi.org/10.2478/BF02476296
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DOI: https://doi.org/10.2478/BF02476296