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Multiparticle dispersion in homogeneous isotropic turbulence

Results are presented for tetrad dispersion in homogeneous isotropic turbulence by means of asimple Lagrangian stochastic model (LSM) and a separation-dependent eddy diffusivity model

(which is essentially an extension of Richardson's model for particle pair dispersion to tetrads).

The latter may be considered as a limiting case of the LSM and is referred to here as the

Richardson model. It will be shown that the tetrads' shape statistics computed from a direct numerical simulation

of turbulence agree very well with equivalent results from both the LSM and the Richardson model.

It will also be shown that the

degree of elongation of the tetrad in the inertial subrange of a turbulent-like

flow is controlled by the exponent, $m$, in an eddy diffusivity of the form $K(r) \propto r^m$ where

$r$ is the interparticle separation, becoming more elongated as $m$ increases in the range $0 \leqslant m < 2$.

The relationship between the shape statistics and the growth rates of the the mean square separation, the mean square

area and the mean square volume of the tetrads is discussed.

Author(s):

Benjamin Devenish

Meteorological Office

United Kingdom