Extraction of invariant manifolds and application to turbulence with a passive scalar.

The reduction of dimensionality of physical systems, especially in fluid dynamics, leads in many situations to nonlinear ordinary differential equations which have global invariant manifolds with algebraic expressions containing relevant physical information on the original system. We present a method to identify such manifolds, and we apply it to a reduced model for the Lagrangian evolution of field gradients in homogeneous and isotropic turbulence with a passive scalar.