Space-local turbulence

Turbulent flow is a complex multi-scale phenomenon, but its small-scales exhibit universal statistics (K41 universality) almost regardless of its macroscopic configuration. The small-scale universality is associated with scale locality; the nonlinear interaction in Fourier space is dominated by modes with similar scales.

This scale locality in turbulence has received considerable attention. Another feature of turbulence is its space nonlocality. Indeed, to determine the velocity at a point in space, information on the full vorticity field at every point in space is needed.

In the present investigation, we consider how the dynamics of turbulence are altered if not the information of the complete field is taken into account to evolve the vorticity; we employ only the vorticity in a finite subspace around a point to evaluate the so-called 'space-local velocity'.

We contrast observations of post-process analysis of Navier-Stokes turbulence to a simulation of a decimated system where only space-local interactions are retained. The results suggest that spatially nonlocal interaction plays an important role in the first step of the energy cascade.