Subgrid modeling in two-dimensional turbulent flow using the principle of maximum entropy

We consider the problem of parameterization of subgrid processes in the context of two-dimensional incompressible
fluid flow on a doubly periodic domain. In this idealized context we address the question how the small scales
of a high-resolution reference simulation can be parameterized in a low-resolution model aimed at reproducing
the reference simulation. The basis of the parameterization that we propose is a probability density function of
the small, unresolved, scales that has maximum information entropy, constrained by normalization and averaged
budgets of energy and enstrophy.
Due to the generality of the constraints, the parameterization that results is completely fixed in terms of
the parameters of the reference model. The advantage is that the parameterization needs not to be tuned and
automatically adjusts itself to any change in the parameters of the reference model. To assess its merits in
practice, it has been tested with regard to short-term performance in reproducing vorticity fields and with regard
to long-term performance in reproducing the statistics of energy and enstrophy. In both respects the proposed
parameterization outperforms conventional parameterizations such as eddy viscosity.