Quasi-two-dimensional hydrodynamics and problems of two-dimensional turbulence

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Abstract
The principal problems of quasi-two-dimensional (Q2-D) hydrodynamics are discussed. Accounting for Q2-D flow vertical structure is shown to eliminate ‘‘genetic’’ defects of the formal 2-D idealization of 3-D Navier–Stokes equations and allows under certain conditions to formulate corrected 2-D motion equations which adequately describe real hydrodynamic processes. The applicability of the approach is directly verified in laboratory experiments. Special attention is paid to the problem of 2-D turbulence. Its simulation on the basis of ordinary 2-D equations is unjustified because of the absence of the external Kolmogorov dissipation scale and reverse spectral energy flux. An alternative approach allows one to introduce the natural external scale of 2-D turbulence which depends only on physical properties of the system under consideration and to formulate the conditions under which the large scale vortex dynamics is expected to be universal at large Reynolds number, i.e., to be independent on the size and form of integration domain and lateral boundary conditions.