Abstract
Recent conjectures concerning the correlation between regions of high local helicity and low dissipation are examined from a rigorous theoretical standpoint based on the Navier-Stokes equations. It is proven that only the solenoidal part of the Lamb vector w × u (which is directly tied to the nonlocal convection and stretching of vortex lines) contributes to the energy cascade in turbulence. Consequently, it is shown that regions of low dissipation can be associated with either low or high helicity—a result which disproves earlier speculations concerning this direct connection between helicity and the energy cascade. Some brief examples are given along with a discussion of the consistency of these results with the most recent computations of helicity fluctuations in incompressible turbulent flows.
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© 1989 Springer-Verlag Berlin, Heidelberg
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Speziale, C.G. (1989). On Helicity Fluctuations and the Energy Cascade in Turbulence. In: Koh, S.L., Speziale, C.G. (eds) Recent Advances in Engineering Science. Lecture Notes in Engineering, vol 39. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83695-4_5
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DOI: https://doi.org/10.1007/978-3-642-83695-4_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-50721-5
Online ISBN: 978-3-642-83695-4
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