Towards the Visualization of the Turbulence Cascade

Abstract

A turbulent flow is composed of swirling eddies of many sizes. Energy, which is added to the flow at the larger scales, is transferred down through consecutively smaller eddies until the scale is small enough that viscous forces dominate, at which point the energy is dissipated. The mechanism by which energy is transferred down the scales of eddies is generally described as eddy break-up, but the process of eddies breaking into smaller eddies has never been directly observed. The objective of this research is to identify and visualize eddies and their breakage into smaller eddies in numerically simulated isotropic turbulence flows. A corre- lation vector is defined at each point in space, based upon the dot product of velocity over spatial distance. This function shows eddies as the result of correlation over the entire field for each point, in contrast to ear- lier eddy identification techniques which focus only on local properties of the flow, such as kinetic energy magnitude. The resultant correlation field shows blobs of high correlation, which can be interpreted as the kernel of a coherent structure in the flow. These kernels can be seen splitting into smaller kernels over time — an indication of the turbulent energy cascade at work. Making use of the Biot-Savart law, the veloc- ity field associated with a coherent blob of correlation is generated from the associated vorticity field. The reconstructed velocity field is vortex-like in structure, and appears to break into two separate vortices as the kernel separates into two distinct kernels, yielding a visualization of turbulent eddy dynamics in real space — the first step towards the visualization of the turbulent energy cascade.