GAKUTO International Series Mathematical Sciences and Applications, Vol.32(2010) Current Advances in Nonlinear Analysis and Related Topics, pp.419–427 GAKKOTOSHO TOKYO JAPAN MIXING IN THE VICINITY OF THE VORTEX Kamil Kwiatkowski Institute of Geophysics, Faculty of Physics, University of Warsaw Pasteura 7, 02-093 Warsaw, Poland E-mail: kamil@igf.fuw.edu.pl and Konrad Bajer Institute of Geophysics, Faculty of Physics, University of Warsaw Pasteura 7, 02-093 Warsaw, Poland E-mail: kbajer@fuw.edu.pl Abstract. The mixing process near a vortex is studied in the paper. We find and describe the case where analytical solution of the advection-diffusion of passive scalar exists. It allows us to investigate the solution for different on vortex strength and to test numerical simulations. Numerical calculations will extend this study to the mixing of reactive scalars, where analytical methods fail. AMS Subject Classification 76R50, 76M55, 76B47, 74S30, 76V05 c ⃝Gakk¯otosho 2010, GAKK ¯ OTOSHO CO.,LTD