By Mikhail Ya Marov, Aleksander V. Kolesnichenko
This ebook makes a speciality of the improvement of continuum types of common turbulent
media. It offers a theoretical method of the suggestions of alternative difficulties
related to the formation, constitution and evolution of astrophysical and
geophysical gadgets. A stochastic modeling process is utilized in the mathematical
treatment of those difficulties, which displays self-organization tactics in open
dissipative platforms. The authors additionally think about examples of ordering for numerous
objects in house all through their evolutionary techniques.
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Extra info for Turbulence And Self Organization: Modeling Astrophysical Objects
We will note at once that no universal mechanism of the transition to turbulent chaos in hydrodynamic flows of various types has been found as yet. We recall here very briefly the four known mechanisms of the transition from a laminar flow to a turbulent one when the Reynolds number reaches its critical value Recr . This question is presented in greater detail in Sections 30-32 of the third revised edition of “Fluid Mechanics” by Landau and Lifshitz (1988), to which we refer the interested reader.
M. Belotserkovskii (1994): “Thus, the hypothesis that turbulence is completely 22 1 Turbulent Chaos and Self-Organization in Cosmic Natural Media described by the Navier-Stokes equations is mathematically unjustified, because there is no general theorem guaranteeing the global existence of solutions to the Navier-Stokes equations as a problem with initial conditions. It is quite probable (though there are no such examples as yet) that these solutions can become singular, so that the equations cease to be valid and new physical principles outside the scope of classical hydrodynamics are apparently needed to construct a complete theory”.
It is also assumed in Kolmogorov’s theory that the vortices continuously fill the entire region G on each scale (at each cascade step). We now turn to an important relation concerning the viscosity-conditioned lower threshold À the Kolmogorov dissipation scale. 5) In Kolmogorov’s theory, the inertial range therefore encompasses the range of scales that grows with increasing Reynolds number as Re3=4 . If a developed turbulent flow is numerically simulated on a uniform grid, then the minimum number of grid points in a cube with a side equal to the main scale length L must be N / Re9=4 .