A simple phenomenological model for a passive scalar subject to a mean gradient and undergoing random advection plus molecular mixing yields an exponential distribution as a consequence of general analytic properties of the steady-state solution. The result persists in the presence of a coherent mean flow. Experimental realizations of our model are proposed.

• Received 17 January 1991

DOI:https://doi.org/10.1103/PhysRevLett.66.2984