Kinematics of Small Scale Motions in Homogeneous Isotropic Turbulence

Abstract

Using direct numerical simulation and ‘kinematic simulation’ (henceforth KS) of velocity fields, measurement, flow visualisation and novel kinematic analysis, the following aspects of small scale motions in turbulence were investigated: (i) Random advection and distortion of small scale motions by larger scale motions; (ii) the Lagrangian spectrum at high frequency of particles moving in small scale eddies and the effects of the time dependence of the eddies; (iii) the relative velocities Δu and the separation distance l between pairs of particles, to find the decorrelation time scales of Δu and the relation between the mean square separation ${\bar l^2}$ and the conditional displacements of single particles; (iv) how the forms of these motions can be inferred from the asymptotic forms of Fourier series and spectra; (v) the specific implications for Eulerian and Lagrangian spectra of the small scales being mostly associated with elongated regions of spiralling motions in which there are different orders of discontinuous derivatives of velocity normal to streamline surfaces. These studies suggest that small scale motion in isotropic turbulence has a characteristic spiralling structure, which is generally consistent with statistics, such as fractals, spectra and probability distributions.