  We propose a new model of turbulence for use in large-eddy simulations (LES).
The turbulent force, represented here by the turbulent Lamb vector, is divided
in two contributions. The contribution including only subfilter fields is
deterministically modeled through a classical eddy-viscosity. The other
contribution including both filtered and subfilter scales is dynamically
computed as solution of a generalized (stochastic) Langevin equation. This
equation is derived using Rapid Distortion Theory (RDT) applied to the
subfilter scales. The general friction operator therefore includes both
advection and stretching by the resolved scale. The stochastic noise is derived
as the sum of a contribution from the energy cascade and a contribution from
the pressure. The LES model is thus made of an equation for the resolved scale,
including the turbulent force, and a generalized Langevin equation integrated
on a twice-finer grid. The model is validated by comparison to DNS and is
tested against classical LES models for isotropic homogeneous turbulence, based
on eddy viscosity. We show that even in this situation, where no walls are
present, our inclusion of backscatter through the Langevin equation results in
a better description of the flow.
