arXiv:1002.3847v1 [physics.flu-dyn] 20 Feb 2010 FAST TRACK COMMUNICATION Symmetrization of advection-diffusion operators Tobias Sch¨ afer, Jesenko Vukadinovic, Andrew C. Poje Department of Mathematics College of Staten Island Victory Blvd 2800 1S-215 Staten Island, NY 10314 E-mail: tobias@math.csi.cuny.edu Abstract. We present a new method to transform an expanded class of non- selfadjoint advection-diffusion operators into self-adjoint operators. The transform is based on a combination of a point transform and Lie transform in conjunction with an asymptotic expansion in terms of the diffusivity. We illustrate the method in the context of simple shear flow where the expansion is exact and all transformation steps can be performed explicitly. PACS numbers: 47.10A-,02.30.Jr Submitted to: J. Phys. A: Math. Gen.