AN ADVANCED INVESTIGATION OF INTERACTION OF ALLOCATED QUASI-2-DIMENSIONAL VORTICES

This work should be regarded as a natural development of the investiga tions by Dolzhanskii, Krymov and Manin [Sov. Phys. Usp. 33, 495-520 (1 990); J. Fluid Mech. 241, 705-722 (1992); Russ. J. Comput. Model. 1, 1 07-118 (1993)] of quasi-two-dimensional (Q2D) flows in which the linea r and weakly nonlinear stability theory based on the 2D hydrodynamic e quations with the Rayleigh (Ekman) friction term imitating the influen ce of the bottom on the motion of upper fluid layers was corroborated with laboratory and observational data. The applicability of the Q2D a pproach to describe self-oscillating supercritical regimes was even mo re vague as Batchaev's experiments [Izv. AN SSSR Fit. Atmos. Okeana 25 , 434-439 (1989); Z. Prikl. Mech. Tech. Fit., No. 4, 85-91 (1990)] on modeling the four vortex self-oscillations in a thin fluid layer by th e magnetohydrodynamics method (the so called hydrodynamical clock [Obu khov, Dolzhanskii and Batchaev, Topological Fluid Mechanics, Proceedin gs of the IUTAM Symposium, Cambridge, 13-18 August 1989 (Cambridge Uni versity Press, Cambridge, 1989), pp. 304-314]) did not find an appropr iate theoretical explanation. To remove earlier uncontrolled effects t he supplementary detailed measurements of the experimental flow charac teristics 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 frequen cy of self-oscillations was found to be greatly susceptible to the spe ctral composition of the external vorticity sources and fluid layer th ickness, which should be taken into account in designing laboratory ex periments to simulate the natural Q2D processes observed in the ocean and atmosphere. Applicability conditions of the Q2D approach and the i nfluence of geometrical parameters of vortices on their nonlinear inte rplay are also discussed. (C) 1996 American Institute of Physics.