Biomedical subjects

Alexandre J Chorin

Publications and source records attributed to Alexandre J Chorin.

5 recordsLinked to original sources

PubMed2006

On the existence and scaling of structure functions in turbulence according to the data.

We sample a velocity field that has an inertial spectrum and a skewness that matches experimental data. In particular, we compute a self-consistent correction to the Kolmogorov exponent and find that for our model it is zero. We find that the higher-order structure functions diverge for orders larger than a certain threshold, as theorized in some recent work. The significance of the results for the statistical theory of homogeneous turbulence is reviewed.

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PubMed2005

Viscosity-dependent inertial spectra of the Burgers and Korteweg-deVries-Burgers equations.

We show that the inertial range spectrum of the Burgers equation has a viscosity-dependent correction at any wave number when the viscosity is small but not zero. We also calculate the spectrum of the Korteweg-deVries-Burgers equation and show that it can be partially mapped onto the inertial spectrum of a Burgers equation with a suitable effective diffusion coefficient. These results are significant for the understanding of turbulence.

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PubMed2004

Dimensional reduction for a Bayesian filter.

An adaptive strategy is proposed for reducing the number of unknowns in the calculation of a proposal distribution in a sequential Monte Carlo implementation of a Bayesian filter for nonlinear dynamics. The idea is to solve only in directions in which the dynamics is expanding, found adaptively; this strategy is suggested by earlier work on optimal prediction. The construction should be of value in data assimilation, for example, in geophysical fluid dynamics.

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PubMed2004

A mathematical model for the scaling of turbulence.

We present a simple physical model of turbulent wall-bounded shear flows that reveals exactly the scaling properties we had previously obtained by similarity considerations. The significance of our results for the understanding of turbulence is pointed out.

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PubMed2003

Averaging and renormalization for the Korteveg-deVries-Burgers equation.

We consider traveling wave solutions of the Korteveg-deVries-Burgers equation and set up an analogy between the spatial averaging of these traveling waves and real-space renormalization for Hamiltonian systems. The result is an effective equation that reproduces means of the unaveraged, highly oscillatory, solution. The averaging enhances the apparent diffusion, creating an "eddy" (or renormalized) diffusion coefficient; the relation between the eddy diffusion coefficient and the original diffusion coefficient is found numerically to be one of incomplete similarity, setting up an instance of Barenblatt's renormalization group. The results suggest a relation between self-similar solutions of differential equations on one hand and renormalization groups and optimal prediction algorithms on the other. An analogy with hydrodynamics is pointed out.

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