Biomedical subjects

A Wonhas

Publications and source records attributed to A Wonhas.

3 recordsLinked to original sources

PubMed2002

Mixing in fully chaotic flows.

Passive scalar mixing in fully chaotic flows is usually explained in terms of Lyapunov exponents, i.e., rates of particle pair separations. We present a unified review of this approach (which encapsulates also other nonchaotic flows) and investigate its limitations. During the final stage of mixing, when the scalar variance decays exponentially, Lyapunov exponents can fail to describe the mixing process. The failure occurs when another mixing mechanism, first introduced by Fereday et al. [Phys. Rev. E 65, 035301 (2002)], leads to a slower decay than the mechanism based on Lyapunov exponents. Here we show that this mechanism is governed by the large-scale nonuniformities of the flow which are different from the small scale stretching properties of the flow that are captured by the Lyapunov exponents. However, during the initial stage of mixing, i.e., the stage when most of the scalar variance decays, Lyapunov exponents describe well the mixing process. We develop our theory for the incompressible and diffusive baker map, a simple example of a chaotic flow. Nevertheless, our results should be applicable to all chaotic flows.

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PubMed2002

Diffusivity dependence of ozone depletion over the midnorthern latitudes.

The mixing and reaction properties of advected chemicals (and passive scalars) are determined by the fractal dimension D of the interface between the chemicals. We show that the scaling of the amount m of reacted chemicals with diffusivity kappa is m(0)-m(kappa) proportional, proportional to kappa(1-D/2) in the two-dimensional case. This relation is valid in a range of times and diffusivities where the diffusive length scales of the chemicals are within the range of scales where the chemical interface has a well-defined fractal dimension. We apply the relation to the problems of chlorine deactivation and ozone depletion over the midnorthern latitudes. We determine numerically the fractal dimension of an interface advected by stratospheric winds. This allows us, first, to explain the diffusivity dependence of chlorine deactivation and ozone depletion that was previously observed in numerical simulations (Tan et al., J. Geophys. Res., [Atmos.] 103, 1585 (1998)) and, second, to extrapolate the results of such simulations down to realistically low diffusivities.

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PubMed2002

Scalar variance decay in chaotic advection and Batchelor-regime turbulence.

The decay of the variance of a diffusive scalar in chaotic advection flow (or equivalently Batchelor-regime turbulence) is analyzed using a model in which the advection is represented by an inhomogeneous baker's map on the unit square. The variance decays exponentially at large times, with a rate that has a finite limit as the diffusivity kappa tends to zero and is determined by the action of the inhomogeneous map on the gravest Fourier modes in the scalar field. The decay rate predicted by recent theoretical work that follows scalar evolution in linear flow and then averages over all stretching histories is shown to be incorrect. The exponentially decaying scalar field is shown to have a spatial power spectrum of the form P(k) approximately k(-sigma) at wave numbers small enough for diffusion to be neglected, with sigma<1.

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