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Multiparticle dispersion in homogeneous isotropic turbulence

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Results are presented for tetrad dispersion in homogeneous isotropic turbulence by means of a
simple 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