The Problem of Closure Conditions for the Vlasov Turbulence

In turbulence-theory, the equations for the dynamics of statistical quantities usually form an infinite system. The coupled momentum equations are the best known example. Such relations can also be derived for the n-point-distribution functions which describe the stochastic state of a tur­ bulent medium at every instant. This will be shown for the case of Vlasov turbulence. In order to obtatin a solution, it is a common procedure, to terminate such infinite systems of equations by closure-conditions. Often this is considered as an approximation. In the case of Vlasov-turbulence it can be shown that a wide variety of closure conditions, all of which are exactly admissible, exists.