Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2003-05-28
Nonlinear Sciences
Chaotic Dynamics
10 LaTex pages, 1 PS figure. Changes: comments added below previous (3.10); Previous (3.16) has been corrected; Minor changes
Scientific paper
10.1017/S0022112003006505
The issue of the parameterization of small scale (``subgrid'') turbulence is addressed in the context of passive scalar transport. We focus on the Kraichnan advection model which lends itself to the analytical investigation of the closure problem. We derive systematically the dynamical equations which rule the evolution of the coarse-grained scalar field. At the lowest-order approximation in $l/r$, $l$ being the characteristic scale of the filter defining the coarse-grained scalar field and $r$ the inertial range separation, we recover the classical eddy-diffusivity parameterization of small scales. At the next-leading order a dynamical closure is obtained. The latter outperforms the classical model and is therefore a natural candidate for subgrid modelling of scalar transport in generic turbulent flows.
Afonso Marco Martins
Celani Antonio
Festa R.
Mazzino Andrea
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