Abstract
An important process at the heart of many fluid phenomena in the physical andengineering sciences is the advection and diffusion of a passive scalar. One of thecanonical idealizations of this process is the problem first broached by Zeldovich(1937), in which the scalar is advected inside a closed container by an incompressiblefluid with an arbitrary velocity field. There is no source or sink of the scalar withinthe fluid, and its concentration is maintained in some fixed pattern on parts of theboundary, whilst other areas of the boundary are impermeable.The mathematical formulation of Zeldovich’s problem is the advection–diffusionequation for the scalar field,
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