Abstract
Scalar diffusion in one-dimensional Burgers' flow is considered. When the Prandtl number is unity, the diffusion equation with convective term is reduced to a simple diffusion equation by a generalized Cole-Hopf transformation. An exact solution of an initial value problem is obtained in a closed form. When the Prandtl number is arbitrary, a similar analytical treatment is possible for limited classes of Burgers' flow (expansion wave and single shock). The statistics of scalar field are discussed briefly.
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