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Updated: Jun 29, 2026

Preparation of Free-Surface Hyperbolic Water Vortices
Published on: July 28, 2023
Unifying scaling theory for vortex dynamics in two-dimensional turbulence
D G Dritschel1, R K Scott, C Macaskill
1School of Mathematics and Statistics, University of St. Andrews, St. Andrews KY16 9SS, United Kingdom. dgd@mcs.st-and.ac.uk
Abstract:
We present a scaling theory for unforced inviscid two-dimensional turbulence. Our model unifies existing spatial and temporal scaling theories. The theory is based on a self-similar distribution of vortices of different sizes A. Our model uniquely determines the spatial and temporal scaling of the associated vortex number density which allows the determination of the energy spectra and the vortex distributions. We find that the vortex number density scales as n(A,t)-t(-2/3)/A, which implies an energy spectrum E-k(-5), significantly steeper than the classical Batchelor-Kraichnan scaling. High-resolution numerical simulations corroborate the model.
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