Velocity correlation considered as a ‘scale average’ in a hierarchical particle model of turbulence: Part II. The role of viscosity

Abstract

In Part I of this paper (Summers and Roberts, J. Turbul, 10(2) (2009)), a particle model of homogeneous turbulence was introduced – a model which is based on a self-similarity in the kinematics inherent to a scale hierarchy of interacting particles. The hierarchy in question was taken to be infinitely ‘deep’: this has the implication that no allowance is made for a lower bound to the hierarchy at the viscous length scale characterizing the fluid – this scale is O(), where ν is kinematic viscosity. We now introduce such a lower bound into the hierarchy and demonstrate the effect of this on the statistics of the fluctuation field. We show that imposing a viscous lower bound to the scale hierarchy introduces a ‘zero’ into the energy spectrum the location of which depends on the maximum eddy size in the ensemble.

Keywords:

• velocity correlation
• particle model
• homogeneous turbulence
• viscosity