Evolution of isolated turbulent trailing vortices

Abstract

In this work, the temporal evolution of a low swirl-number turbulent Batchelor vortex is studied using pseudo-spectral direct numerical simulations. The solution of the governing equations in the vorticity-velocity form allows for accurate application of boundary conditions. The physics of the evolution is investigated with an emphasis on the mechanisms that influence the transport of axial and angular momentum. Excitation of normal mode instabilities gives rise to coherent large scale helical structures inside the vortical core. The radial growth of these helical structures and the action of axial shear and differential rotation results in the creation of a polarized vortex layer. This vortex layer evolves into a series of hairpin-shaped structures that subsequently breakdown into elongated fine scale vortices. Ultimately, the radially outward propagation of these structures results in the relaxation of the flow towards a stable high-swirl configuration. Two conserved quantities, based on the deviation from the laminar solution, are derived and these prove to be useful in characterizing the polarized vortex layer and enhancing 1 the understanding of the transport process. The generation and evolution of the Reynolds stresses is also addressed.2

Boundary conditions and vortex wandering

“…Weaker, distributed peaks in the Reynolds stresses are apparent at around η ∼ 1 for t 2. These, with the strong cross-correlations between the different velocity components at different radii, are consistent with the 'hairpin' structures identified by Duraisamy & Lele (2008) and tangential velocity components indicate that the dominant secondary structures in the core flow are not aligned with the primary vortex. Taken together with the overall increase in turbulent kinetic energy for t/T 2.5, this provides further evidence that the main mechanism of turbulent production during this stage of vortex development is the formation and organization of these secondary structures within the core.…”

“…This formulation has been used extensively for fundamental numerical studies of turbulent vortex flows; for additional details, the reader is referred to Pradeep & Hussain (2004), Goto (2008) and Duraisamy & Lele (2008).…”

“…As expected, the available DNS data agreed reasonably well with the present results for the case of the periodic boundary conditions; the magnitudes were similar, with very low gradients near the vortex centre and through into the core region. The solutions begin to differ for η 0.5, though this is likely due to differences in the both the domain size and the initial and boundary conditions: Qin (1998) used only 15 × 15 points in the cross-flow plane, and implemented some inviscid modelling near the boundaries as well (see also Duraisamy & Lele 2008). Since solutions express boundary condition sensitivity at this t/T , some disagreement at larger η between models is expected.…”

A factor involved in efficient breakdown of supersonic streamwise vortices

“…When D is small, no large scale structures form within the vortex core, in contrast to many previous studies of Batchelor vortices. 15,[31][32][33] To explain this discrepancy, we adopt the helicity density description of streamwise vortices. Swirling vortices such as streamwise vortices can be described using helicity density.…”

Applications of Eddy Resolving Methods

“…Reasonable agreement is found with the measured radial distributions of circulation. Duraisamy and Lele (2008) perform pseudo-spectral DNS. The governing equations are solved in the velocityvorticity form.…”