Solution of functional equations and reduction of dimension in the local energy transfer theory of incompressible, three-dimensional turbulence - art. no. 026308

It is shown that the set of integrodifferential and algebraic functional eq uations of the local energy transfer theory may be considerably reduced in dimension for the case of isotropic turbulence. This is achieved without re stricting the solution space. The basis for this is a complete analytical s olution to the functional equations Q(k;t,t') = H(k;t,t')Q(k;t',t') and H(k ;t,s)H(k;s,t') = H(k;t,t'). The solution is proved to depend only on a sing le function phi (k;t) solely determining Q and H. Hence the dimension of bo th the dependent and the independent variables is reduced by one. From the latter, the corresponding two integodifferential equations are lowered to a single integrodifferential equation for phi (k;t), extended by an integral side condition on the k dependence of phi (k;t). In the limit nu --> 0, a partial solution to the reduced set of equations is presented in the Append ix.