Three-dimensional turbulence vorticity: Numerical and experimental modeling

We show in this paper how a system of equations of motion, diffusion and continuity that present the effects of vorticity through a vorticity transfer length scale may be used to model 2D-3D vorticity behaviour. The local turbulent vorticity is separated from the large-scale flow following the Reynolds decomposition (Reynolds 1894, Taylor 1931)—∇ × v + ∇ × v —similar to the technique used for velocity. The system of equations extended through the terms ∇ × v and ∇ × v is solved numerically using a purely statistical local method that details the role of vorticity transport in the turbulence behaviour of the flow. Moreover, this numerical model that shows the temporal evolution of both fields, 3D velocity and 3D vorticity is used to investigate the propagation of turbulent perturbations that arise from the development of a vortex placed in the centre of the numerical domain. Even with a small mesh (60 × 60 × 120), the results show the propagation of vorticity-related waves both in the plane and in the vertical. The numerical results are compared with experiments performed in a stratified flow, where velocity and vorticity are measured with PIV as turbulence behind a grid decay, these experiments have been performed both in a rotating frame of reference and with no rotation and show features also detected in the numerical simulations when the assumption of a quasi– two-dimensional flow is used.