Slow modes in passive scalar turbulent advection

This communication describes the computation of slow modes in a generic shell model of passive turbulent advection. It is argued that the propagator for the correlation functions possesses a ladder of slow modes associated with each zero mode. These slow modes decay algebraically fast, as opposed to exponential. Using the explicit form of the propagator of the 2-point structure function, we show that the slow modes structure for the generic case is analogous to the case of a Gaussian correlated advecting field, for which the differential structure of the operator allows a direct computation of these modes. Numerical computations of the slow modes are performed and compare very well to our results.