Coherent Vortices and Subharmonic Interactions in the Two-Dimensional Navier-Stokes Equations

Abstract

2D Navier-Stokes solutions are generated for a periodic shear layer with a fundamental (m=0) and a single subharmonic (m>0) disturbance. For m=2, 3, and 4 we find clusters with m+1 vortices without the formation of vortex pairs. This implies enhanced spreading in a spatially growing mixing layer. However, when m=5 we find a different dynamical clustering due to nondirect energy transfer from the fundamental to the subharmonic. Additionally, if we force the layer with a wavelength smaller than the fundamental we find a new mechanism called "collective interaction."