Abstract
We show that the decay of a passive scalar θ advected by a random incompressible flow with zero correlation time in the Batchelor limit can be mapped exactly to a certain quantum-mechanical system with a finite number of degrees of freedom. The Schrödinger equation is derived and its solution is analyzed for the case where, at the beginning, the scalar has Gaussian statistics with correlation function of the form Any equal-time correlation function of the scalar can be expressed via the solution to the Schrödinger equation in a closed algebraic form. We find that the scalar is intermittent during its decay and the average of (assuming zero mean value of θ) falls as at large where is a parameter of the flow, for and for independent of α.
- Received 30 June 1998
DOI:https://doi.org/10.1103/PhysRevE.59.R3811
©1999 American Physical Society