IL NUOVO CIMENTO Novembre-Dicembre 1999 VOL. 22 C, N. 6 Numerical study of the evolution of vortices in a linearly stratified fluid (*)(**) M. BECKERS ( 1 ), R. VERZICCO ( 2 ), H. J. H. CLERCX ( 1 ) and G. J. F. VAN HEIJST ( 1 ) ( 1 ) J. M. Burgers Centre for Fluid Dynamics, Eindhoven University of Technology Department of Physics - P. O. Box 513, 5600 MB Eindhoven, The Netherlands ( 2 ) Università di Roma “La Sapienza", Dipartimento di Meccanica e Aeronautica via Eudossiana 18, 00184, Roma, Italy (ricevuto il 18 Novembre 1998; approvato il 6 Maggio 1999) Summary. — This paper presents a numerical study in which the evolution of vortices in a stratified fluid is compared to the evolution of two-dimensional vortices. The influence of the Reynolds number and the Froude number are investigated, for the evolution of axisymmetric vortices, for their azimuthal instability and for the subsequent formation of tripoles. It is found that due to radial diffusion axisymmetric vortices with various initial vorticity profiles all evolve towards the same profile. This evolution reduces the growth of azimuthal instabilities which may lead to the formation of a tripole. For vortices in a stratified fluid the effect of the ambient stratification on the evolution of the vortices is investigated. It is found that a process of vortex stretching, which becomes more pronounced for increasing Froude numbers, leads to a weaker tripole formation. PACS 92.10.Ei – Coriolis effects. PACS 47.32.Cc – Vortex dynamics. PACS 47.55.Hd – Stratified flows. PACS 47.11 – Computational methods in fluid dynamics. PACS 01.30.Cc – Conference proceedings. 1. – Introduction Flows in a linearly density-stratified fluid show large resemblance with two-dimen- sional (2D) flows due to the presence of buoyancy forces, which strongly suppress vertical motions. Such 2D flows are characterized by the process of self-organization, i.e. small-scale turbulent structures evolve towards large-scale vortices (see, e.g., [1]). Experiments on the evolution of turbulence in stratified fluids, in which the initial flow was forced by horizontal injection of a jet or by towing a rake through the fluid, have also revealed the formation of coherent vortex structures. In the first case dipolar (*) Paper presented at the International Workshop on “Vortex Dynamics in Geophysical Flows”, Castro Marina (LE), Italy, 22-26 June 1998. (**) The authors of this paper have agreed to not receive the proofs for correction. G Società Italiana di Fisica 847