A unifying scaling theory for vortex dynamics in two-dimensional turbulence
نویسندگان
چکیده
D. G. Dritschel, R. K. Scott, C. Macaskill, G. A. Gottwald and C. V. Tran School of Mathematics and Statistics, University of St Andrews, St Andrews KY16 9SS, UK e-mail: [email protected], [email protected], [email protected] School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia e-mail: [email protected], [email protected] 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, significantly steeper than the classical Batchelor-Kraichnan scaling. High-resolution numerical simulations corroborate the model.
منابع مشابه
Unifying scaling theory for vortex dynamics in two-dimensional turbulence.
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 vort...
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