2013/02/05 by Ran, Zheng
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Mathematical Physics (math-ph) #Statistical Mechanics (cond-mat.stat-mech)
paper · doi:10.48550/arxiv.1302.0919
We present developments of the Hamiltonian approach to problems of the freely decay of isotropic turbulence, and also consider specific applications of the modified Prelle-Singer procedure to isotropic turbulence. It demonstrates that a nonlinear second order ordinary differential equation is intimately related to the self-preserving solution of Karman-Howarth equation, admitting time-dependent first integrals and also proving the nonstandard Hamiltonian structure, as well as the Liouville sense of integrability.