A numerical investigation of impulsively generated vortical structures in deep and shallow fluid layers

Abstract

The evolution and formation of large-scale turbulent coherent structures induced by an impulsive jet between non-deformable stress-free layers are investigated via direct numerical simulation at a jet Reynolds number of 1250. The ratio of the initial size of the vortex to the domain depth is varied to study the influence of the bounding surface confinement. A non-conservative body force is applied to the governing equations to represent the momentum source. During the forcing period, the coherent structure appears in the form of a leading vortex ring together with a trailing jet, and breaks down to turbulence due to an instability very similar to the Widnall instability before interacting with the free surface. The input parameters (the momentum flux J, the forcing period Δtf, and the domain depth h) can be grouped together as the confinement number C = J1/2Δtf/h2 to parameterise the intensity and strength of the eddy signature at the free surface. Increasing the confinement number corresponds to reducing the ratio of the domain depth to the initial size of the vortex, which leads to a linear increase in the maximum amplitude of the surface signature in terms of the surface eddy strength. A dipole forms for values of C greater than about unity, even though the eddy signature appears at the free surface for all the confinement numbers considered.