Abstract
Hinze’s conceptual model for turbulence near a wall is modelled by a linear constitutive equation and closure hypothesis on an intrinsic rotational degree of freedom. Integration of the model equations yield the universal logarithmic profile for velocity in the transition layer. Verhulst-type non-linear growth of transition layer vorticity is normalized and discretized to an iteration along the real axis of the complex Mandelbrot algorithm with \( {Z_{{n + 1}}} = {Z_{n}}^{2} +\frac{1}{4} \) . This locates vorticity iteration in the transition layer precisely on the domain boundary between a zero-vorticity attractor for the free stream, and an infinite- vorticity attractor for the wall.
Hinze’s horseshoe vortices are modelled as kink-free constructions of scaling circle arcs analogous to Mandelbrot’s line-based “teragon” constructions for Koch- and Peanocurves. Circular initial vortex rings in a superfluid are deformed into differentiable fractal curves growing inward and/or outward without self-intersections. General formulas for three types of admissible circle deformations are given, and their scale factors, growth rates and fractal dimensions are tabulated. Conservation of angular momentum accelerates circulating light nuclei in a discharge plasma above nuclear reaction velocities in twelve stages of the strongest fractal stretching process.
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Dijkhuis, G.C. (1994). Verhulst Dynamics and Fractal Stretching of Transition Layer Vorticity. In: Kikuchi, H. (eds) Dusty and Dirty Plasmas, Noise, and Chaos in Space and in the Laboratory. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-1829-7_14
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DOI: https://doi.org/10.1007/978-1-4615-1829-7_14
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