The effect of forcing on the spatial structure and spectra of chaotically advected passive scalars

Zoltan Neufeld; Peter H. Haynes; Guillemette Picard

doi:10.1063/1.1289504

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arXiv · chao-dyn/9912015

The effect of forcing on the spatial structure and spectra of chaotically advected passive scalars

Zoltan Neufeld·Peter H. Haynes·Guillemette Picard

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Abstract

The stationary distribution of passive tracers chaotically advected by a two-dimensional large-scale flow is investigated. The tracer field is force by resetting the value of the tracer in certain localised regions. This problem is mathematically equivalent to advection in open flows and results in a fractal tracer structure. The spectral exponent of the tracer field is different from that for a passive tracer with the usual additive forcing (the so called Batchelor spectrum) and is related to the fractal dimension of the set of points that have never visited the forcing regions. We illustrate this behaviour by considering a time-periodic flow whose effect is equivalent to a simple two-dimensional area-preserving map. We also show that similar structure in the tracer field is found when the flow is aperiodic in time.

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Zoltan Neufeld, Peter H. Haynes, Guillemette Picard. 1999-12-09. The effect of forcing on the spatial structure and spectra of chaotically advected passive scalars. https://doi.org/10.1063/1.1289504

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