Abstract: in the framework of Lagrangian approach to hydrodynamics we suggest a special stochastic perturbation of the flow of perfect incompressible fluid on flat ndimensional torus T n and obtain the description of viscous incompressible fluid with viscous term in the form of some second order differential operator more general than Laplacian. <...> We show that transition to Euler description of such a fluid yields the solution of an analogue of Navier-Stokes equation without external force. <...> Key words and phrases: group of diffeomorphisms; flat torus; stochastic perturbation; perfect incompressible fluid; Reynolds equation; Navier-Stokes equation. <...> INTRODUCTION In this paper we present a development of idea, suggested in [1] (see also [2]), of the use of special stochastic perturbations of flows of perfect fluids to obtain stochastic flows whose expectation describes the motion of viscous fluids. <...> This approach is based on machinery of mean derivatives (see [3], [4], [5] and on geometry of groups of Sobolev diffeomorphisms (see [6]). <...> The flow of perfect fluid is considered as a curve in the group of diffeomorphisms and its stochastic perturbation satisfies a special equation in terms of mean derivatives. <...> In [1] this idea is realized for classical viscous fluids for which Euler’s description is given by the Navier-Stokes equation. <...> Here we deal with the fluids for which in Euler’s description the Laplacian is replaced by a more general second order differential operator. <...> PRELIMINARIES (Ω,F,P), and such that ξ(t) is an L1-random variable for all t. The ”present” for ξ(t) is the least complete σ-subalgebra N We denote by Eξ t . <...> Consider a stochastic process ξ(t) in Rn, where t ∈ [0,T], given on a certain probability space ξ σ-subalgebra that includes preimages of the Borel set of Rn under the map ξ(t) : Ω→Rn for s t is called the ”future”σ-algebra and is denoted by F Ω → Rn. <...> The least complete σ-subalgebra that includes preimages of the Borel set of Rn under the map ξ(t) : Ω → Rn for s t is called the ”past”σ-algebra and is denoted by P t of F that includes preimages of the Borel set of Rn under the map ξ(t) : ξ t . <...> МАТЕМАТИКА. 2013. № 1 t the conditional expectation with the respect to Nt . <...> FLUIDS BY THE METHODS <...>