Biomedical subjects

J C Vassilicos

Publications and source records attributed to J C Vassilicos.

9 recordsLinked to original sources

PubMed2003

Turbulent pair diffusion.

Kinematic simulations of turbulent pair diffusion in planar turbulence with a k(-5/3) energy spectrum reproduce the laboratory results of Jullien et al. [Phys. Rev. Lett. 82, 2872 (1999)]], in particular the stretched exponential form of the probability density function of pair separations and their correlation functions. The root mean square separation is found to be strongly dependent on initial conditions for very long stretches of time. This dependence is consistent with the topological picture where pairs initially close enough travel together for long stretches of time and separate violently when they meet straining regions around hyperbolic points. A new argument based on the divergence of accelerations is given to support this picture.

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PubMed2002

Mixing in vortical, chaotic and turbulent flows.

Mixing is discussed in relation to stirring as reflected in the geometry of advected interfaces, the behaviour of fluid-element pairs and their separation rates. Stirring is different in vortical, chaotic and turbulent flows because of qualitative differences in spatio-temporal flow structure, thus giving rise to different mixing laws. Important applications of the mixing and stirring properties discussed in this review are chlorine deactivation and ozone depletion in stratospheric mid-latitudes.

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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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PubMed2001

Scalings of scalar structure functions in a velocity field with coherent vortical structures.

In planar turbulence modeled as an isotropic and homogeneous collection of two-dimensional noninteracting compact vortices, the structure functions S(p)(r) of a statistically stationary passive scalar field have the following scaling behavior in the limit where the Péclet number Pe-->infinity: S(p)(r) approximately const+ln(r/L Pe(-1/3)) for L Pe(-1/3)<<r<<L, S(p)(r) approximately (r/L Pe(-1/3))(6(1-D)) for L Pe(-1/2)<<r<<L Pe(-1/3), where L is a large scale and D is the fractal codimension of the spiral scalar structures generated by the vortices (1/2 < or =D < 2/3). Note that L Pe(-1/2) is the scalar Taylor microscale that stems naturally from our analytical treatment of the advection-diffusion equation. The essential ingredients of our theory are the locality of interscale transfer and Lundgren's time average assumption. A phenomenological theory explicitly based only on these two ingredients reproduces our results and a generalization of this phenomenology to spatially smooth chaotic flows yields (k ln k)(-1) generalized power spectra for the advected scalar fields.

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PubMed2001

Quantum signature of superfluid turbulence.

Using a numerical simulation backed up by physical arguments, we predict that the pressure spectrum of superfluid turbulence has a k(-2) dependence on the wave number k, which represents a macroscopic quantum signature not to be found in the classical Kolmogorov theory of turbulence.

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PubMed2001

Kelvin waves cascade in superfluid turbulence.

We study numerically the interaction of four initial superfluid vortex rings in the absence of any dissipation or friction. We find evidence for a cascade of Kelvin waves generated by individual vortex reconnection events which transfers energy to higher and higher wave numbers k. After the vortex reconnections occur, the energy spectrum scales as k(-1) and the curvature spectrum becomes flat. These effects highlight the importance of Kelvin waves and reconnections in the transfer of energy within a turbulent vortex tangle.

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PubMed1999

Time-dependent geometry and energy distribution in a spiral vortex layer.

The purpose of this paper is to study how the geometry and the spatial distribution of energy fluctuations of different length scales in a spiral vortex layer are related to each other in a time-dependent way. The numerical solution of Krasny [J. Comput. Phys. 65, 292 (1986)], corresponding to the development of the Kelvin-Helmholtz instability, is analyzed in order to determine some geometrical features necessary for the analysis of Lundgren's unstrained spiral vortex. The energy distribution of the asymptotic solution of Lundgren characterized by a similar geometry is investigated analytically (1) in the wavelet radius-scale space, with a wavelet selective in the radial direction, and (2) in the wavelet azimuth-scale space, with a wavelet selective in the azimuthal direction. Energy in the wavelet radius-scale space is organized in "blobs" distributed in a way determined by the Kolmogorov capacity of the spiral D(K) in [1,2] (which determines the rate of accumulation of spiral turns). As time evolves these blobs move towards the small scale region of the wavelet radius-scale space, until their scale is of the order of the diffusive length scale square root[nut], where t is the time and nu is the kinematic viscosity. In contrast, energy in the wavelet azimuth-scale space is not localized, and is characterized by a shear-augmented viscous cutoff proportional to sqaure root[nut(3)]. An accelerated viscous dissipation of the enstrophy and energy of Lundgren's spiral vortex is found for D(K) > 1.75, but not for D(K) < or =1.75.

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