Vortex-in-cell method for a spatially growing uniformly sheared flow

A mixed Lagrangian-Eulerian approach based on the vortex-in-cell method and the velocity-vorticity formulation is developed to solve the three-dimensional, incompressible, inviscid spatially growing uniformly sheared flow. The Lagrangian vortex filaments are initially subjected to a 3D random perturbation in order to simulate an initial fluctuating velocity field with nearly isotropic conditions. Contours plots for the two orientation angles of the vortex filaments and the fluctuating vorticity vectors indicate the presence of preferred angles relative to the mean flow direction as the flow develops. A comparison with previously reported numerical simulation suggests that the prediction corresponds to the phase of early development where the non-dimensional time τ<2. The downstream evolution of the component energy ratios K11 , K22 and K33 are qualitatively in agreement with previous numerical simulations and experiments. (author)