Curvature of vortex tubes and sheets in turbulence
Seminar Room 1, Newton Institute
Weak structures of vorticity are studied as they evolve essentially passively as a result of the induced velocity field of the large-scale turbulence. Such objects are possibly an important component of the inertial and dissipation ranges of turbulence.
Earlier work [1} along these lines concentrated on the effects of accumulated strain, apropos of Lagrangian chaos, on localized packets of vorticity. In particular it was shown that time-averaging the self-energy spectrum of such a structure leads to a fractional power law for the energy spectrum.
In this paper we consider the effects of strain on the geometry of vortex tubes and sheets and concentrate on regions of high curvature, as an extension of other recent work . In the case of a vortex tube, we find that a region of high curvature on the tube is likely to develop around a point where the vorticity vector is orthogonal to the principal axis of maximum strain. For vortex sheets, a region of high curvature is likely to occur where the above-mentioned principal axis is normal to the sheet. The strain tensor in question is that corresponding to the future deformation of a material element. We explore the notion that such high-curvature structures play a role in establishing the energy spectrum in inertial-range turbulence.
1. A. Leonard 2002," Interaction of localized packets of vorticity with turbulence" in Proc. IUTAM Symp. on Tubes, Sheets, and Singularities in Fluid Dynamics (Kluwer) 201-210.
2. A. Leonard 2008, "The universal structure of high curvature regions of material lines in chaotic flows", submitted.