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.