Homogeneous isotropic turbulence in four spatial dimensions

TL;DR

This study performs direct numerical simulations of four-dimensional homogeneous isotropic turbulence, revealing increased forward energy transfer, extended inertial range, and higher dissipation and skewness compared to lower dimensions.

Contribution

First detailed numerical analysis of turbulence in four spatial dimensions, highlighting differences from 2D and 3D turbulence.

Findings

Energy fluctuations decrease from 3D to 4D

Extended inertial range observed in 4D turbulence

Increased dissipation rate and skewness in 4D

Abstract

Direct Numerical Simulation is performed of the forced Navier-Stokes equation in four spatial dimensions. Well equilibrated, long time runs at sufficient resolution were obtained to reliably measure spectral quantities, the velocity derivative skewness and the dimensionless dissipation rate. Comparisons to corresponding two and three dimensional results are made. Energy fluctuations are measured and show a clear reduction moving from three to four dimensions. The dynamics appear to show simplifications in four dimensions with a picture of increased forward energy transfer resulting in an extended inertial range with smaller Kolmogorov scale. This enhanced forwards transfer is linked to our finding of increased dissipative anomaly and velocity derivative skewness.