The Role of conservation laws in the development of nonequilibrium and emergence of turbulence. Peculiarities of calculating nonequilibrium flows

Hidden properties of the Euler and Navier-Stokes equations

  • Ludmila Ivanovna Petrova a
Keywords: duality of functionals, conservation laws, nonidentical evolutionary relation, connection of physical fields with material media×

Abstract

It turns out that the equations of mathematical physics, which consist equations of the conservation laws for energy, linear momentum, angular momentum, and mass, possess additional, hidden, properties that enables one to describe not only a variation of physical quantities (such as energy, pressure, density) but also processes such as origination of waves, vortices, turbulent pulsations and other ones. It is caused by the conservation laws properties.

In present paper the development of nonequilibrium in gasdynamic systems, which are described by the Euler and Navier-Stokes equations, will be investigated. 

Under studying the consistence of conservation laws equations, from the Euler and Navier-Stokes equations it can be obtained the evolutionary relation for entropy (as a state functional).  The evolutionary relation possesses a certain peculiarity, namely, it turns out to be nonidentical. This fact points out to inconsistence of the conservation law equations and noncommutativity of conservation laws.

Such a nonidentical relation discloses peculiarities of the solutions to the Navier-Stokes equations due to which the Euler and Navier-Stokes equations can describe the processes the development of nonequilibrium and emergence of vortices and turbulence.

It has been shown that such processes can be described only with the help of two nonequivalent coordinate systems or by simultaneous using numerical and analytical methods.

References

[1] Clark J.F., Machesney M., The Dynamics of Real Gases. Butterworths, London, 1964.
[2] Petrova L.I., Role of skew-symmetric differential forms in mathematics, 2010, http://arxiv.org/abs/math.CM/1007.4757
[3] Petrova L.I., Relationships between discontinuities of derivatives on characteristics and trajectories. // J. Computational Mathematics and Modeling, vol. 20, Number 4, pp. 367-372, 2009.
Published
2018-05-30