Lagrangian kinematics of turbulent vortex stretching

By employing a vortex-tube model of filamentary coherent structures in incompressible Navier–Stokes turbulence, we investigate the Lagrangian kinematics of turbulent vortex stretching at very high Reynolds numbers. The computed flow fields present a sizable Kolmogorov inertial range and are induced by a chaotic tangle of strongly stretched and folded filamentary vortical structures. After a transient of the order of the large-eddy turnover time, the finite-time Lyapunov exponents approach a statistical steady state, where the intermediate Lyapunov exponent is much smaller than the largest one and positive. Within our resolution limits, the probability density functions (PDFs) of first and third Lyapunov exponents present long tails. The folding process is typically gradual, and very sharp folding angles are rare, although possible due to their long-tailed PDF. The thick tail of the accumulated strain PDF hints at the existence of extreme deformation events that could lead to flow singularities. The PDFs of normalized instantaneous stretching rates of vorticity exhibit long tails and, at high strain rates, enter a quasi-plateau regime. In this regime, turbulent stretching shows no internal bias toward any particular strain rate—it treats all dynamically allowed values equally, effectively maximizing entropy under the constraints imposed by the coherent filament topology. The results reveal deviations in the alignment between vorticity and strain-rate eigenvectors compared to those observed for material line elements. These differences stem from the inherently nonlinear nature of vortex dynamics and their capacity for self-stretching, and they are closely linked to the emergence of the maximal-entropy regime.