Strategy for spatial simulation of co‐rotating vortices

The present numerical study is motivated by the challenge to simulate the three-dimensional spatial dynamics of a co-rotating vortex system, through the development of an elliptic instability (C. R. Phys. 2005; 6(4–5):431–450) using a high-order solver of the compressible Navier–Stokes equations. This phenomenon was studied previously only by temporal simulations. The interest of spatial simulation is first to analyse the effect of the axial velocity on the merging process, which are neglected with the temporal approach, and to study interaction with jet flows. The numerical problem is the choice of boundary conditions (BCs): for the inflow and outflow conditions as well as for the lateral BCs to represent a fluid at rest. Special attention will be paid to the latter because the difficulties come from the non-zero circulation of the vortex system considered. The classic BCs of Poinsot and Lele (J. Comput. Phys. 1992; 101: 104–129) based on the characteristics wave approach have been modified to be more adapted to the physics considered here. This new BC is based on the assumption of an irrotational flow close to the borders (in order to determine the magnitude of the waves), as the vorticity field is concentrated on the computational domain centre where the vortex system is initially placed. After a validation of these improved BCs and of all numerical tools used such as selective artificial dissipation, two spatial simulations of the vortex breakdown phenomenon have allowed validating our solver for a three-dimensional case by comparison with the results of Ruith et al. (J. Fluid Mech. 2003; 486:331–378). Thus, the merging process of equal co-rotating vortices through the development of elliptic instability with axial velocity were simulated. Three vortex flow configurations were considered with different vortex systems and velocity peaks ratio (azimuthal and axial velocities). A numerical tool has been elaborated and validated for the simulation of spatial instability development in vortex flows. The first results show this ability, and the influence of the axial velocity on the dynamics of the instabilities. However, spatial simulations are limited by the computational resources (linked to the resolution and axial domain length to capture the merging process) and restricted to academic vortex flow configuration. Copyright © 2008 John Wiley & Sons, Ltd.