Decay of scalar turbulence revisited
Abstract
The most efficient mixing of a scalar, passively advected by a random flow, occurs if the flow is spatially smooth. However, any realistic turbulent, or simply chaotic, flow cannot be smooth at all scales. We demonstrate that at long times the rate of scalar decay is dominated by regions (in real space or in inverse space) where mixing is not as efficient as in an ideal smooth flow. We examine two situations. The first is a spatially homogeneous stationary turbulent flow with both viscous and inertial scales present. It is shown that at large times scalar fluctuations decay algebraically in time at all spatial scales (particularly in a the viscous range, where the velocity is smooth). The second example explains chaotic stationary flow in a disk/pipe. The boundary region of the flow controls the long-time decay, which is algebraic at some transient (asymptotically large, if diffusion is weak) times, but becomes exponential, with the decay rate dependent on the scalar diffusion coefficient, at longer times.Keywords
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