The advection of a passive substance by a turbulent flow is important in many natural and engineering settings. The concentration of such a substance can exhibit complex dynamic behaviour that shows many phenomenological parallels with the behaviour of the turbulent velocity field. Yet the statistical properties of this so-called 'passive scalar' turbulence are decoupled from those of the underlying velocity field. Passive scalar turbulence has recently yielded to mathematical analysis, and such progress may ultimately lead to a better understanding of the still intractable problem of fluid turbulence itself.
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