%0 Book Section %1 statphys23_0221 %A Lebed, I.V. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K classic development functions hydrodynamics loss pair stability statphys23 topic-5 turbulence %T The Appearance and Development of Turbulence in a Flow Around a Body: Problems and the Existing Approaches to Their Solution %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=221 %X The direct numerical integration of the Navier-Stokes equations for unstable flows has become possible as late as recent years. The results of numerical integration of the Navier-Stokes equations and integration of the pair functions theory equations were evaluated against experimental data for the problem of a flow around a hard sphere at rest in an unstable regime 1-2. Experiments record three stable medium states for a flow around a sphere. Each of these three states, after losing the stability, starts to evolve in its own direction. The turbulence development inevitably goes through the regime of periodic vortex shedding. Each of three turbulence development directions has its own distinctive features of vortex shedding, inherent to it only. Calculations based on the Navier-Stokes equations satisfactorily reproduced three stable medium states observed for a flow around a sphere. They were, however, incapable of reproducing any of the three directions of turbulence development recorded experimentally. Namely, calculations were unable to reproduce any of six periodic regimes of the vortex shedding observed in three directions. As it follows from the analysis 2, most likely, the reason for calculations failure is the Navier-Stokes equations themselves. The possibility that an inaccuracy crept into the derivation of the Boltzmann equation is discussed, namely, the molecular chaos hypothesis (ŤStosszahlansatzť) may be responsible for the failure of classic hydrodynamics. The ŤStosszahlansatzť is a closure to the Boltzmann equation that allows classic hydrodynamics to be constructed on three main hydrodynamic values. The inaccuracy mentioned introduced no substantial error into stable flow calculations. The error, however, increased rapidly after stability loss. It is explained by the property of the nonlinear equations to bring apart the close solutions even in a limited phase space region. This sensitivity to initial conditions was called earlier the Lorentz butterfly effect. I suggest the use of hydrodynamic equations based on the pair functions theory as an alternative for unstable modes. These equations were earlier derived without any additional assumptions such as the ŤStosszahlansatzť 3. As distinct from classic hydrodynamics, solutions of pair functions theory equations predict the direction of turbulence development close to that observed experimentally. 1) I.V.Lebed Physica A 315 (1-2), 2002.\\ 2) I.V.Lebed, S.Ya.Umanskii RJ of Physical Chemistry B 1 (1), 2007.\\ 3) I.V.Lebed Chem. Phys. Letters 165 (2-3), 1990.

@incollection{statphys23_0221, abstract = {The direct numerical integration of the Navier-Stokes equations for unstable flows has become possible as late as recent years. The results of numerical integration of the Navier-Stokes equations and integration of the pair functions theory equations were evaluated against experimental data for the problem of a flow around a hard sphere at rest in an unstable regime [1-2]. Experiments record three stable medium states for a flow around a sphere. Each of these three states, after losing the stability, starts to evolve in its own direction. The turbulence development inevitably goes through the regime of periodic vortex shedding. Each of three turbulence development directions has its own distinctive features of vortex shedding, inherent to it only. Calculations based on the Navier-Stokes equations satisfactorily reproduced three stable medium states observed for a flow around a sphere. They were, however, incapable of reproducing any of the three directions of turbulence development recorded experimentally. Namely, calculations were unable to reproduce any of six periodic regimes of the vortex shedding observed in three directions. As it follows from the analysis [2], most likely, the reason for calculations failure is the Navier-Stokes equations themselves. The possibility that an inaccuracy crept into the derivation of the Boltzmann equation is discussed, namely, the molecular chaos hypothesis (ŤStosszahlansatzť) may be responsible for the failure of classic hydrodynamics. The ŤStosszahlansatzť is a closure to the Boltzmann equation that allows classic hydrodynamics to be constructed on three main hydrodynamic values. The inaccuracy mentioned introduced no substantial error into stable flow calculations. The error, however, increased rapidly after stability loss. It is explained by the property of the nonlinear equations to bring apart the close solutions even in a limited phase space region. This sensitivity to initial conditions was called earlier the Lorentz butterfly effect. I suggest the use of hydrodynamic equations based on the pair functions theory as an alternative for unstable modes. These equations were earlier derived without any additional assumptions such as the ŤStosszahlansatzť [3]. As distinct from classic hydrodynamics, solutions of pair functions theory equations predict the direction of turbulence development close to that observed experimentally. 1) I.V.Lebed Physica A 315 (1-2), 2002.\\ 2) I.V.Lebed, S.Ya.Umanskii RJ of Physical Chemistry B 1 (1), 2007.\\ 3) I.V.Lebed Chem. Phys. Letters 165 (2-3), 1990.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Lebed, I.V.}, biburl = {https://www.bibsonomy.org/bibtex/25ba7663316ef0554fcc487d5fbe9f164/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {781cff78fd4eeab9ecbf68975599c98e}, intrahash = {5ba7663316ef0554fcc487d5fbe9f164}, keywords = {classic development functions hydrodynamics loss pair stability statphys23 topic-5 turbulence}, month = {9-13 July}, timestamp = {2007-06-20T10:16:14.000+0200}, title = {The Appearance and Development of Turbulence in a Flow Around a Body: Problems and the Existing Approaches to Their Solution}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=221}, year = 2007 }