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On the spectrum of a stretched spiral vortex. (English) Zbl 0832.76036
A model of turbulent flow consisting of stretched spiral vortices (originally suggested by Lundgren) is used to make predictions about properties of homogeneous turbulence. For example, the dependence of the Kolmogorov constant and skewness coefficient on Reynolds number is estimated, and energy dissipation and squared vorticity spectra are obtained. To extend the previous Pullin-Saffman model, an additional requirement is introduced, namely that the vortex structures are approximately space filling, together with a new assumption that there exists a finite upper cutoff which limits the growth of the core. The extended model is shown to be self-consistent through agreement in skewness calculations using two independent methods, the first being essentially kinematic and the second based on the dynamical Kármán- Howarth equation. Also, the model suggests that the energy and enstrophy spectra are composed of two components arising from the asymmetric spiral and axisymmetric core parts of spiral vortex. A special realization of the Lundgren spiral vortex is considered, consisting of a thin shear layer in the process of roll-up, and undergoing stretching in the direction of vortex lines.

MSC:
76F10 Shear flows and turbulence
76F99 Turbulence
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