Small-scale structure of the Taylor–Green vortex

The dynamics of both the inviscid and viscous Taylor–Green (TG) three-dimensional vortex flows are investigated. This flow is perhaps the simplest system in which one can study the generation of small scales by three-dimensional vortex stretching and the resulting turbulence. The problem is studied by both direct spectral numerical solution of the Navier–Stokes equations (with up to 256 3 modes) and by power-series analysis in time. The inviscid dynamics are strongly influenced by symmetries which confine the flow to an impermeable box with stress-free boundaries. There is an early stage during which the flow is strongly anisotropic with well-organized (laminar) small-scale excitation in the form of vortex sheets located near the walls of this box. The flow is smooth but has complex-space singularities within a distance (t) of real (physical) space which give rise to an exponential tail in the energy spectrum. It is found that (t) decreases exponentially in time to the limit of our resolution. Indirect evidence is presented that more violent vortex stretching takes place at later times, possibly leading to a real singularity ( (t) = 0) at a finite time. These direct integration results are consistent with new temporal power-series results that extend the Morf, Orszag th energy dissipation has considerable spatial intermittency; its spectrum has a k −1+μ inertial range with the codimension μ ≈ 0. 3−0. 7. Skewness and flatness results are also presented.