New approach to interpretation of the nature of the Navier-Stokes equation and its solution

As was indicated in [17,18], this is possible only in case, when one starts from the assumption that viscosity constant , entering the relation of Hagen-Poiseuille (4) and specific resistance , entering the formula of Ohm's law are the quantities proportionally dependent on the concentration of excited atoms per unit volume. We assume, that the high the concentration in the system the higher the value of and , i.e. assume that one can start from assumption , .

For the computation , using the relation (35,б), we obtain

,

.

Furthermore, jointly considering the formulae (4), (70) and formulae of Ohm's law and, we obtain

,

In our view, in these relations potentially are contained the ideas and results whose analysis can be used to satisfactorily understand the main difference between the phenomena of superfluidity and superconductivity and the phenomena of ordinary fluidity and ordinary conductivity. In other words, we think that for the transfer of the system from the state of ordinary fluidity and ordinary conductivity to the state of superfluidity and superconductivity the main role belongs to the concentration of phonons, as particles of heat determining the temperature of the system. In case, when we deal with temperature higher than critical, the concentration of phonons, as particles of heat is sufficiently high and all particles of both helium-4 and crystal lattice perform chaotic vibrational motion and this is exhibited in the form of resistance to fluidity and conductivity. If we deal with the critical temperature, then to this corresponds the state when due to very low concentration of phonons or their disappearance, concentration of helium particles or atoms of crystal lattice which do not perform the chaotic vibrational motion will be high. It is this process that leads to the disappearance of resistance exhibited in the form of viscosity and specific resistance . As a consequence the phenomenon is exhibited of superfluidity and superconductivity.

Speaking in other word, we think, that helium-4 which under low critical temperature has the properties of superfluidity is the ideal example of the theory of ideal Euler liquid. Hence, in this meaning superfluid liquid is the ideal example of liquid where all the conditions of laminar regime of flowing are satisfied. From the viewpoint of this conceptions at temperature higher than critical we deal with the system, where the share of liquid has the place, which flows in turbulent regime.

In our view, now taking as the foundation new ideas and results, it is easy to understand why until present time all the efforts to obtain the analytical solution from Navier-Stokes equation (3) on the basis of which it would be possible to understand the nature of turbulent fluidity were unsuccessful. The main reason of this is the following. In this equation in the role of the main factor using which the factor of non-ideality was accounted was the factor containing in itself the information about the nature of turbulent fluidity was accounted using the viscosity constants. Hence, in order to understand the nature of the processes occurring in turbulent regime it was necessary to utilize the solutions of the form, which are obtained from equation of Gibbs statistical mechanism for the interpretation of constant . But until that time trying to obtain the solution from equation 3 based on which it would be possible to understand the nature of turbulent fluidity, and this factor was overlooked.

Let us note, that in the above mentioned results the main difference of the phenomena of laminar and turbulent regime of fluidity we tried to explain on the example that the system where such processes occur was considered to be the superfluid liquid and ordinary liquid. While the main reason due to which the laminar flow transforms to turbulent flow of fluidity was considered to be the temperature factor. It was clarified, that the increase of temperature above critical the order inherent to laminar flow, i.e. superfluid regime is destroyed and as a result the system transfers to turbulent flow of fluidity. But in practice often one has to deal with systems where as the example of laminar flow of fluidity and turbulent regime of fluidity are considered the systems at high temperatures. In such cases usually as the example of laminar flow the case is considered, when the ordered motion of particles is observed with neglecting the fact that these particles are able to perform the chaotic vibration in three-dimensional space. Certainly, in such cases talking about the turbulent flow of fluidity we must keep in mind the decomposition of the ordered motion of liquid due to certain other reasons.

As is known, based on the analysis of experimental data it is clarified that the reasons due to which the ordered regime can be destroyed are in great amount. During this it is clarified that such factors affect the time when laminar regime of flow will get transformed into turbulent regime of flow. We understand, that the formulae of the form can not be used for theoretical description of such processes. Nevertheless, there are grounds to supposes that these results have the value as the result based on which it became possible to understand the fundamental differences of processes, occurring in laminar and turbulent flow based on the possibilities of ideas and results of the foundations of theoretical physics.

Here we want to say that we succeeded in obtained results to understand the nature of processes occurring in laminar regime of flow assuming that there is a deep analogy between the fundamental equations of Hamilton-Jacobi-Schrodinger (11) obtained from equations of Hamilton (10) and equations of Euler and Navier-Stokes (2), (3) obtained from Newton equation (1). During this the facts were kept in mind that on the basis of fundamental equations obtained from equation (11) and equation (3), it became possible to understand that phenomenon conditioned by ordered motion of the set of particles appears in systems where the motion of these particles occurs under the influence of external force and р. We want to say, that in obtained results the nature of processes occurring in turbulent regime of flow was understood using the possibility of solutions of obtained from the fundamental equations of Gibbs statistical mechanics.

Literature

1. Problems of turbulent flow. Collection of articles. - M.: Nauka, 1987.

2. Altaev N.K. Universal method of disclosure of hidden truths. - Shymkent, 2005.

3. Altaev N.K. Algebraic and arithmetic equations of the foundation of the theory of cognition. - Shymkent, 2012.

4. Decartus P. Rules for manual of mind. “Selected works”. - M., 1959. - p.77.-171.

5. Decartus P. Discussing the method. “Selected works”. - M., 1950.- p.257-319.

6. Decartus P. Beginnings of philosophy. “Selected works”. - M., 1950.-p.409-545.

7. Altaev N.K. Method of reduction of variables. Publ. In book “Universal method of disclosure of hidden truths”. - Shymkent, 2012. - p.271-277.

8. Altaev N,K. On the interpretation of the nature of main equations of matrix mechanics) //Proceedings of international congress - 1912 “Fundamental problems of natural science and technology”. - Saint-Petersburg, 2012. - p.47-57;57-65.

9. Altaev N.K. Statistical theory of chemical equilibrium and kinetics of chemical reactions. Publ. in book. “Universal method of disclosure of hidden truths”- Shymkent, 2012. - p.141-174.

10. Nesie E.I. Methods of mathematical physics. - M.:Prosvetschenie, 1977.

11. Altaeve N.K. Logical criterion of completeness of solution of mathematical and physical problems. Publ. in book. “Universal method of disclosure of hidden truths”. - Shymkent, 2012. - p.277-284.

12. Terletski Ya.P. Statistical physics.- M.: Vyschaya schkola, 1966.

13. Heizenberg W. On quantum-theoretical interpretation of kinematic and mechanical relations. - SPS, 1977. - V.122. - p.574-586.

14. Diract P. Lectures on quantum theory of fields. - M.:Mir, 1971.

15. Bogolyubov N.N. On the theory of superfluidity. - M.-Bull AS USSR. Physical series. -1947, 11(1).77.

16. Bardin J, Cooper L., Shriffer J. Theory of superconductivity //Coll. Of papers. - M., 1969. - p.103-172.- IL.

17. (J.Bardeen, L.Cooper, J.Schrieffer. Phys. Rev., 108, 1775-1204 (1957)).

18. Altaev N.K. Statistical theory of conductivity and superconductivity. Publ. in book “Universal method of disclosure of hidden truths”. - Shymkent, 2005. - p.66-78.

19. Altaev N.K. Statistical theory of flow and superfluidity. Publ. in book “Universal method of disclosure of hidden truths”. - Shymkent, 2005. - p.66-78.

20. Nikitin E.E. Theory of elementary atomic-molecular processes in gases. - M.: Himia, 1970.

21. Schlichting G. Theory of boundary layer.- М.: Наука, 1969.

22. Bogolyubov N.N., Tolmachev B.B., Shirkov D.V. New approach in the theory of superconductivity. - M.: AS USSR, 1958.

Размещено на Allbest.ru