InterJournal Complex Systems, 606
Status: Submitted
Manuscript Number: [606]
Submission Date: 20912
Comment on manuscript revision number 37070
Comment on "Self-Organization in Navier-Stokes Turbulence" by Lewalle
Author(s): Anonymous

Subject(s): CX.25, CX.08

Category: General Audience Letter


This paper makes a fundamental advance in the mathematical modelling of turbulent flow. In spite of the fact that the incompressible Navier-Stokes equations for the hydrodynamic velocity and the pressure are differential equations, they are fundamentally nonlocal in character -- that is, they have a long-range Green's function. When the pressure is eliminated by means of the incompressibility condition, the remaining evolution equation for the velocity is integrodifferential in character. An alternative to the Poisson solve for the pressure is provided by the vorticity representation. The vorticity also evolves according to nonlocal evolution equations because, for example, it advects along the velocity field, which in turn arises from the vorticity according to the Biot-Savart law. Nevertheless, vortex representations of fluids have provided us with new and powerful methods of understanding and simulating fluids. The present paper provides an alternative representation, based on the "fluxion" (laplacian of velocity). The author derives equations of motion (involving the velocity) for this representation, and then performs a wavelet decomposition. He shows that the choice of a Gaussian wavelet casts the results in a particularly simple format. Though still inevitably nonlocal, these evolution equations are remarkable for their clear interpretation in terms of the multiscale decomposition of the turbulence, and for their immediate realization of a new and qualitatively different numerical method for fluid simulation. I recommend the paper for publication as a General Audience Letter, without reservation.

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