Abstract
We study the von Kármán–Howarth (KH) equation by group theoretical methods. This scalar partial differential equation involves two dependent variables (closure problem) and, it has been derived from the Navier–Stokes equations. The equivalence Lie algebra L has been found to be infinite-dimensional and, it is spanned by the four operators. The subalgebra of L is spanned by the three operators. Furthermore, ideal comprises one operator. Optimal systems of one-, two- and three-dimensional subalgebras have been obtained. Normalizers for the one- and two-dimensional subalgebras have been calculated. Finally we have obtained the submodels of the KH equation corresponding to optimal system of one- and two-dimensional subalgebras. This merely suggests alternative solutions to the closure problem of isotropic turbulence.
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