On the True nature of turbulence

Li, Y. Charles

doi:10.1007/bf02984759

Cited by 9 publications

(8 citation statements)

References 20 publications

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“…As discussed in details in [3] [4] [5], an effective description of turbulence means a solution to the problem of turbulence. An effective description of chaos is also very useful in applications of chaos theory.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

A Markov chain approximation of a segment description of chaos

Labovsky

Li²

2010

Dynamics of Partial Differential Equations

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Abstract. We test a Markov chain approximation to the segment description of chaos (and turbulence) on a tent map, the Minea system, the Hénon map, and the Lorenz system. For the tent map, we compute the probability transition matrix of the Markov chain on the segments for segment time length (iterations) T = 1, 2, 3, 100. The matrix has 1, 2, 4 tents corresponding to T = 1, 2, 3; and is almost uniform for T = 100. As T → +∞, our conjecture is that the matrix will approach a uniform matrix (i.e. every entry is the same). For the simple fixed point attractor in the Minea system, the Reynolds average performs excellently and better than the maximal probability Markov chain and segment linking. But for the strange attractors in the Hénon map, and the Lorenz system, the Reynolds average performs very poorly and worse than the maximal probability Markov chain and segment linking.

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Section: Conclusion and Discussionmentioning

confidence: 99%

A Markov chain approximation of a segment description of chaos

Labovsky

Li²

2010

Dynamics of Partial Differential Equations

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“…Their delicate experimental measurements on turbulence have led them to such a conclusion. A simple form of the Navier-Stokes equations, describing viscous incompressible fluids, can be written as [Li05,Li06] …”

Section: The Governing Equations Of Turbulencementioning

confidence: 99%

“…Of course, there exist non-Newtonian fluids like volcanic lava for which the viscous term is more complicated and can be nonlinear. According to the theoretical physicist's way, the viscous term was obtained from an expansion which has no reason to stop at its leading order term Re −1 u i,jj [Li05,Li06].…”

Section: The Governing Equations Of Turbulencementioning

confidence: 99%

“…The fact that fluid experimentalists quickly discovered shocks in compressible fluids and never found any finite time blow up in incompressible fluids, indicates that there might be no finite time blow up in Navier-Stokes equations (even Euler equations). On the other hand, the solutions of Navier-Stokes equations can definitely be turbulent (chaotic) [Li05,Li06].…”

Section: Global Well-posedness Of the Navier-stokes Equationsmentioning

confidence: 99%

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