Vortex profiles in grid turbulence observed by PIV

Grid turbulence is often thought to be a prototype of isotropic and homogeneous turbulence of Kolmogorov style. There is no some single vortex dominating the flow, rather there is lot of vortices distributed along the Richardson cascade. These vortices are searched in experimentally obtained velocity data by using the individual vortex searching algorithm developed at the University of West Bohemia in Pilsen. For the purpose of vortex profile study, only the pre-fit is used, because the full fitting already uses some vortex model and thus it would be not suitable for exploring the vortex profile. The pre-fit is based on the patches of divergence-free Q invariant of velocity gradient tensor; it does not explicitly use the vortex model. The preliminary research suggests that the velocity decreases faster than 1/r, which is the dependence of all standard vortex models in far-field. The standard vortex models are developed for single vortex dominating the flow such as Rankine vortex or Oseen vortex and they do not need to apply for this case, because the turbulent flow is constructed of many different-size interacting vortices without some single dominating one. Here we introduce a new vortex model with velocity decay faster than 1/r, explicitly u(r)=(Γ/2πR) · (r/R) / (1+(r/2R)2)2. Its applicability to, at least some, experimental data is shown in the case grid turbulence.