Experiments on free decay of quasi-two-dimensional turbulent flows.

Decaying quasi-two-dimensional turbulence in a thin-layer flow is explored in laboratory experiments. We report the presence of power-law interval in the enstrophy decay law, in agreement with earlier experiments by Cardoso et al. [Phys. Rev. E 49, 454 (1994)] and Hansen et al. [Phys. Rev. E 58, 7261 (1998)]. The decay exponent proves sensitive to the way in which the energy decay is compensated. For the range of initial microscale Reynolds numbers between 35 and 95, the decay exponent is close to -0.4 for the ratio of enstrophy to energy, and to -0.75 for the enstrophy multiplied with a compensating factor of exp(-2lambda(t)), where lambda is the bottom-drag coefficient and t the decay time. The vorticity behavior does not comply with the theory of Carnevale et al. [Phys. Rev. Lett. 66, 2735 (1991)]: robust vortices are not observed in the vorticity field and the vorticity kurtosis is less than the Gaussian value.

An advanced investigation of interaction of allocated quasi-two-dimensional vortices.

This work should be regarded as a natural development of the investigations by Dolzhanskii, Krymov and Manin [Sov. Phys. Usp. 33, 495-520 (1990); J. Fluid Mech. 241, 705-722 (1992); Russ. J. Comput. Model. 1, 107-118 (1993)] of quasi-two-dimensional (Q2D) flows in which the linear and weakly nonlinear stability theory based on the 2D hydrodynamic equations with the Rayleigh (Ekman) friction term imitating the influence of the bottom on the motion of upper fluid layers was corroborated with laboratory and observational data. The applicability of the Q2D approach to describe self-oscillating supercritical regimes was even more vague as Batchaev's experiments [Izv. AN SSSR Fiz. Atmos. Okeana 25, 434-439 (1989); Z. Prikl. Mech. Tech. Fiz., No. 4, 85-91 (1990)] on modeling the four vortex self-oscillations in a thin fluid layer by the magnetohydrodynamics method (the so called hydrodynamical clock [Obukhov, Dolzhanskii and Batchaev, Topological Fluid Mechanics, Proceedings of the IUTAM Symposium, Cambridge, 13-18 August 1989 (Cambridge University Press, Cambridge, 1989), pp. 304-314]) did not find an appropriate theoretical explanation. To remove earlier uncontrolled effects the supplementary detailed measurements of the experimental flow characteristics were implemented, including the spatial spectral composition of the external vorticity sources and free surface 2D velocity fields. Satisfactory agreement is found between experimentally measured flow characteristics and the results of numerical simulations. The frequency of self-oscillations was found to be greatly susceptible to the spectral composition of the external vorticity sources and fluid layer thickness, which should be taken into account in designing laboratory experiments to simulate the natural Q2D processes observed in the ocean and atmosphere. Applicability conditions of the Q2D approach and the influence of geometrical parameters of vortices on their nonlinear interplay are also discussed. (c) 1996 American Institute of Physics.

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

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.