INSTABILITIES IN 2-DIMENSIONAL SPATIALLY PERIODIC FLOWS .3. INVISCID TRIANGULAR LATTICE

The instability of a two-dimensional triangular array of vortices with respect to inviscid perturbations is investigated. A numerical treatment in the framework of Floquet theory provides critical parameters for instability onset and the spatial structure of unstable oscillatory modes which are in agreement with experiments of Sommeria et al [Mechanics of Fluids and Transport Processes (Kluwer Academic, Dordrecht, The Netherlands, 1989), Vol. 10] in electromagnetically driven flows of a liquid metal layer. A point vortex model allows one to relate the dynamics of infinitesimal displacements of vortices to the concept of waves in a lattice of linearly coupled oscillators.