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.
Highlights
It is well known that the the equations of mathematical physics, which consist equations of the conservation law equations for energy, linear momentum, angular momentum, and mass, are used for describing material systems such as thermodynamical, gas-dynamical, cosmical, and other ones
From the evolutionary relation it follows that the Euler and Navier-Stokes equations possess solutions of two types, namely, the solutions that are not functions and the solutions that are discrete functions
In present paper it is shown that the Euler and Navier-Stokes equations possess additional, hidden, properties that enables one to describe a variation of physical quantities and processes such as origination of waves, vortices, turbulent pulsations and other ones
Summary
It is well known that the the equations of mathematical physics, which consist equations of the conservation law equations for energy, linear momentum, angular momentum, and mass, are used for describing material systems such as thermodynamical, gas-dynamical, cosmical, and other ones. The nonidentity of the evolutionary relation points to the fact that the conservation law equations for energy and linear momentum (entered into the set of Euler and Navier-Stokes equations) appear to be inconsistent. They cannot be contracted into an identical relation (which is built by differentials) and integrated directly. The Euler and Navier-Stokes equations can have exact solutions (which are functions) in the case if from ω the evolutionary skew-symmetric form in the right-hand side of nonidentical evolutionary relation it is realized a closed skew-symmetric form, which is a differential.
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