An analysis of significant flow scale of key flow for vortex generation in terms of local flow geometry in isotropic homogeneous turbulence

The key flow for vortex generation in terms of the invariant local topology derived from the velocity gradient tensor is analysed with decomposing the flow scale in an isotropic homogeneous turbulence in a low Reynolds number. Swirlity that specifies the unidirectionality and intensity of the azimuthal flow in the local topology monitors the flow transition into a vortex. Then the specific coordinate system is defined associated with the predicted swirl plane, and the all velocity gradient tensor components are expressed as invariant quantities relating to the flow topology.

The statistical analysis of the time derivatives of the swirlity and tensor components shows that the key flow for the vortex generation is an invariant shear flow in the predicted swirl plane which direction is specified by the eigenvectors of the velocity gradient tensor. In the vortex generation, both vortical and non-vortical flows exist in the several decomposed flow scales. However, the intermediate flow scale exists to produce a predominant key flow component.