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Number of degrees of freedom of two-dimensional turbulence
Chuong V Tran1, Luke Blackbourn
1School of Mathematics and Statistics, University of St. Andrews, St. Andrews KY16 9SS, United Kingdom.
Abstract:
We derive upper bounds for the number of degrees of freedom of two-dimensional Navier-Stokes turbulence freely decaying from a smooth initial vorticity field omega(x,y,0)=omega0. This number denoted by N is defined as the minimum dimension such that for n>or=N, arbitrary n-dimensional balls in phase space centered on the solution trajectory omega(x,y,t); for t>0, contract under the dynamics of the system linearized about omega(x,y,t). In other words, N is the minimum number of greatest Lyapunov exponents whose sum becomes negative. It is found that N
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