COMPLETE SYSTEM OF NAVIER-STOKES EQUATIONS: LINEARIZATION AND CONSTRUCTION OF SOLUTIONS
https://doi.org/10.26583/vestnik.2025.1.6
EDN: RUGZUE
Abstract
Modeling of atmospheric phenomena is carried out on the basis of systems of ordinary differential equations and partial differential equations with their subsequent numerical study. As a result of discretization of these equations, we arrive at systems with millions and even billions of unknowns. Due to the nonlinearity of the complete system of Navier-Stokes equations, constructing its solutions is quite labor-intensive. As a consequence, the linearization procedure is applied on the exact solution (homogeneous rest). For the linearized system, taking into account the action of gravity and Coriolis forces, the emergence and development of ascending swirling flows of different intensity is numerically modeled using blowing up the pipe. Numerical calculation of the velocity characteristics of a three-dimensional unsteady flow of viscous heat-conducting gas in an ascending swirling flow initiated by vertical blowing showed that the gas swirl occurs in the positive direction and is due to the presence of terms in the linearized complete system of Navier-Stokes equations describing the Coriolis acceleration. Thus, the pattern of the occurrence of an ascending swirling flow is once again numerically confirmed. A conclusion is also made about the possibility of applying this approach to the study of ascending swirling flows such as tornadoes and tropical cyclones
About the Authors
A. A. Bugaenko
Federal State Unitary Enterprise "Russian Federal Nuclear Center - All-Russian Research Institute of Technical Physics named after Academician E.I. Zababakhin";
FSBEI HE "Snezhinsk Institute of Physics and Technology of the National Research Nuclear University MEPhI"
Russian Federation
Russian Federation
I. Yu. Krutova
FSBEI HE "Snezhinsk Institute of Physics and Technology of the National Research Nuclear University MEPhI"
Russian Federation
Russian Federation
References
1. Bautin S.P., Krutova I.Yu. Linearizovannaya sistema uravnenij gazovoj dinamiki pri uchete dejstviya sily Koriolisa. [Linearized system of gas dynamics equations taking into account the Coriolis force]. Snezhinsk, SFTI Publ., 2019. 60 p.
2. Bautin S.P., Krutova I.Yu., Obukhov A.G. Gazodinamicheskaya teoriya voskhodyashchih zakruchennyh potokov. [Gas-dynamic theory of ascending swirling flows]. Yekaterinburg, UrGUPS Publ., 2020. 400 p.
3. Obukhov A.G. Raschet skorostnyh harakteristik voskhodyashchego zakruchennogo potoka gaza v usloviyah bokovogo vetrovogo vozdejstviya. [Calculation of the velocity characteristics of an ascending swirling gas flow under lateral wind conditions]. Matematicheskie struktury i modelirovanie, 2020. No. 3 (55). Pp. 61-71.( In Russian)
4. Bautin S.P. Tornado i sila Koriolisa .[Tornado and the Coriolis force]. Novosibirsk, Nauka Publ., 2008. 96 p.
5. Bautin S.P., Krutova I.Yu., Obukhov A.G., Bautin K.V. Razrushitel'nye atmosfernye vihri: teoremy, raschety, eksperimenty. [Destructive atmospheric vortices: theorems, calculations, experiments]. Novosibirsk, Nauka Publ., Ekaterinburg, UrGUPS Publ., 2013. 216 p.
6. Abdubakova L.V., Obukhov A.G. Chislennyj raschet termodinamicheskih parametrov zakruchennogo potoka gaza, iniciirovannogo holodnym vertikal'nym produvom.[Numerical calculation of thermodynamic parameters of swirling gas flow initiated by cold vertical blowing]. Izvestiya vysshih uchebnyh zavedenij. Neft' i gaz, 2014. No. 5 (107). Pp. 57-62. ( In Russian)
7. Bautin S.P., Deryabin S.L., Krutova I.Yu., Obukhov A.G. Razrushitel'nye atmosfernye vihri i vrashchenie Zemli vokrug osi. [Destructive atmospheric vortices and the Earth's rotation around the axis]. Ekaterinburg, UrGUPS Publ., 2017. 336 p.
8. Bautin S.P., Krutova I.Yu. Analiticheskoe i chislennoe modelirovanie techenij gaza pri uchete dejstviya sily Koriolisa. [Analytical and numerical modeling of gas flows taking into account the Coriolis force]. Ekaterinburg, UrGUPS Publ., 2019. 182p.
9. Abdubakova L.V., Obukhov A.G. Chislennyj raschet plotnosti, temperatury i davleniya zakruchennogo potoka gaza pri vertikal'nom produve [Numerical calculation of density, temperature and pressure of swirling gas flow during vertical blowing].Fundamental'nye i prikladnye issledovaniya: problemy i rezul'taty, 2014. No. 12. Pp. 108-112. (In Russian)
10. Abdubakova L.V., Obukhov A.G. Raschet skorostej i linij toka trekhmernogo voskhodyashchego zakruchennogo potoka gaza pri vertikal'nom produve.[Calculation of velocities and streamlines of three-dimensional ascending swirling gas flow during vertical blowing]. Innovacii i investicii, 2014. No. 9. Pp. 139-142. (In Russian)
11. Bautin S.P., Obukhov A.G. Matematicheskoe modelirovanie razrushitel'nyh atmosfernyh vihrej. [Mathematical modeling of destructive atmospheric vortices]. Novosibirsk, Nauka Publ., 2012. 152 p.
12. Bautin S.P. Harakteristicheskaya zadacha Koshi i ee prilozheniya v gazovoj dinamike [Characteristic Cauchy problem and its applications in gas dynamics]. Novosibirsk, Nauka Publ., 2009. 368 p.
13. Bautin S.P., Obukhov A.G. Chislennoe modelirovanie trekhmernyh nestacionarnyh techenij szhimaemogo vyazkogo teploprovodnogo gaza [Numerical modeling of three-dimensional unsteady flows of compressible viscous heat-conducting gas]. Ekaterinburg, Ural State Transport University Publ., 2020. 287p.
14. Varaksin A.Yu., Romash M.E., Kopeitsev V.N., Gorbachev M.A. Fizicheskoe modelirovanie vozdushnyh smerchej: nekotorye bezrazmernye parametry.[Physical modeling of air tornadoes: some dimensionless parameters]. TVT, 2011. Vol. 49. No. 2. Pp. 317. (In Russian)
15. Rotunno R. Numerical Simulation of a Laboratory Vortex. J. Atmos. Sci. 1977. Vol 34. Pp. 1942.
Review
For citations:
Bugaenko A.A., Krutova I.Yu. COMPLETE SYSTEM OF NAVIER-STOKES EQUATIONS: LINEARIZATION AND CONSTRUCTION OF SOLUTIONS. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2025;14(1):64-78. (In Russ.) https://doi.org/10.26583/vestnik.2025.1.6. EDN: RUGZUE
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