Dynamic equilibria of a nonisothermal fluid
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 22 (2018) no. 4, pp. 735-749.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, stationary dynamic equilibria of the rotating mass of a nonisothermal fluid are discussed within the accuracy limits of the Boussinesq approximation. It is demonstrated that, in this case, a fluid exhibits a finite number of counterflows, higher values of velocities than those specified on the boundary and the formation of zones of positive and negative pressures and temperatures.
Keywords: dynamic equilibrium, rotating fluid flow, counterflows, increased velocities.
Mots-clés : exact solution, Boussinesq approximation
@article{VSGTU_2018_22_4_a6,
     author = {E. Yu. Prosviryakov},
     title = {Dynamic equilibria of a nonisothermal fluid},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {735--749},
     publisher = {mathdoc},
     volume = {22},
     number = {4},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2018_22_4_a6/}
}
TY  - JOUR
AU  - E. Yu. Prosviryakov
TI  - Dynamic equilibria of a nonisothermal fluid
JO  - Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
PY  - 2018
SP  - 735
EP  - 749
VL  - 22
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VSGTU_2018_22_4_a6/
LA  - en
ID  - VSGTU_2018_22_4_a6
ER  - 
%0 Journal Article
%A E. Yu. Prosviryakov
%T Dynamic equilibria of a nonisothermal fluid
%J Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences
%D 2018
%P 735-749
%V 22
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VSGTU_2018_22_4_a6/
%G en
%F VSGTU_2018_22_4_a6
E. Yu. Prosviryakov. Dynamic equilibria of a nonisothermal fluid. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 22 (2018) no. 4, pp. 735-749. http://geodesic.mathdoc.fr/item/VSGTU_2018_22_4_a6/

[1] Newton I., Opera quae exstant omnia, Faksimile-Neudruck der Ausgabe von Samuel Horsley, London 1779–1785 in fünf Bänden. Band 1, 4, Friedrich Frommann Verlag (Günther Holzboog), Stuttgart-Bad Cannstatt, 1964, xx+592 pp. (In German) | MR | Zbl

[2] The Correspondence of Isaac Newton, v. 1. 1661-1675, ed. H. W. Turnbull, Cambridge Univ. Press, New York, 1959, xxxviii+468 pp. | MR

[3] Poincaré H., Cinématique et mécanismes. Potentiel et mécanique des fluides, Cours professé à la Sorbonne, G. Carré et C. Naud, Paris, 1899, iv+385 pp. (In French) | Zbl

[4] Lyapunov A. M., “On the stability of ellipsoidal equilibrium forms of rotating fluid”, Collected works. Vol. III, Akad. Nauk SSSR, Moscow, 1959, 5–113 (In Russian) | MR | Zbl

[5] Lyapunov A. M., “On the equilibrium figures of rotating homogeneous liquid mass slightly different from ellipsoids”, Collected works. Vol. IV, Akad. Nauk SSSR, Moscow, 1959, 5–645 (In Russian) | Zbl

[6] Chandrasekhar S., Ellipsoidal figures of equilibrium, Yale University Press, New Haven, London, 1969, ix+252 pp. | Zbl

[7] Hagihara Y., Theories of equilibrium figures of a rotating homogeneous fluid mass, NASA Special Publication, 186, US Government Printing Office, Washington, 1970

[8] Borisov A. V., Kilin A. A., Mamaev I. S., “The Hamiltonian Dynamics of Self-gravitating Liquid and Gas Ellipsoid”, Regul. Chaotic Dyn., 14:2 (2009), 179–217 | DOI | MR | Zbl

[9] Appell P., Traité de mécanique rationnelle, Tome IV, 1: Figures d'équilibre d'une masse liquide homogène en rotation, Gauthier-Villars, Paris, 1932, viii+342 pp. (In French) | Zbl

[10] Betti E., “Sopra i moti che conservano la figura ellissoidale a una massa fluida eterogenea”, Brioschi Ann, 1879, (2) X, 173–187 (In Italian) | Zbl

[11] Volterra V., “Sur la stratification dúne masse fluide en équilibre”, Acta Math., 27:1 (1903), 105–124 | MR

[12] Liouville J., “Sur la figure dúne masse fluide homogéne, en équilibre et douée dún mouvement de rotation”, J. de l'École Polytech., 14 (1834), 289–296

[13] Dirichlet G. L., “Untersuchungen über ein Problem der Hydrodynamik (Aus dessen Nachlass hergestellt von Herrn R. Dedekind zu Zürich)”, J. Reine Angew. Math. (Crelle's Journal), 58 (1861), 181–216 | MR

[14] Arnold V. I., Khesin B. A., Topological Methods in Hydrodynamics, Springer, New York, 1999, 392 pp. | MR

[15] Dolzhansky F. V., “On the mechanical prototypes of fundamental hydrodynamic invariants and slow manifolds”, Physics–Uspekhi, 48:12 (2005), 1205–1234 | DOI

[16] Hadamard J., “Mouvement permanent lent d'une sphère liquide et visqueuse dans un liquide visqueux”, C. R. Acad. Sci., Paris, 152:25 (1911), 1735–1738 | Zbl

[17] Rybcziński, W., “Über die fortschreitende Bewegung einer flüssigen Kugel in einem zähen Medium”, Bull. Int. Acad. Sci. Cracovie. Ser. A, 1 (1911), 40–46 | Zbl

[18] Aristov S. N., Prosviryakov E. Yu., “A New Class of Exact Solutions for Three Dimensional Thermal Diffusion Equations”, Theor. Found. Chem. Eng., 50:3 (2016), 286–293 | DOI

[19] Aristov S. N., Knyazev D. V., Polyanin A. D., “Exact solutions of the Navier-Stokes equations with the linear dependence of velocity components on two space variables”, Theor. Found. Chem. Eng., 43:5 (2009), 642–662 | DOI

[20] Polyanin A. D., Zaitsev V. F., Handbook of ordinary differential equations. Exact solutions, methods, and problems, CRC Press, Boca Raton, FL, 2018, xxix+1456 pp. | MR | Zbl

[21] Aristov S. N., Prosviryakov E. Yu., “Unsteady Layered Vortical Fluid Flows”, Fluid Dyn., 51:2 (2016), 148–154 | DOI | MR

[22] Aristov S. N., Prosviryakov E. Yu., Spevak L. F., “Unsteady-State Bénard–Marangoni Convection in Layered Viscous Incompressible Flows”, Theor. Found. Chem. Eng., 50:2 (2016), 132–141 | DOI

[23] Aristov S. N., Prosviryakov E. Yu., “On one class of analytic solutions of the stationary axisymmetric convection Bénard–Marangoni viscous incompressible fluid”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 3(32) (2013), 110–118 (In Russian) | DOI | Zbl

[24] Aristov S. N., Privalova V. V., Prosviryakov E. Yu., “Stationary nonisothermal Couette flow. Quadratic heating of the upper boundary of the fluid layer”, Nelin. Dinam., 12:2 (2016), 167–178 (In Russian) | DOI | MR

[25] Burmasheva N. V., Prosviryakov E. Yu., “A large-scale layered stationary convection of an incompressible viscous fluid under the action of shear stresses at the upper boundary. Velocity field investigation”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 21:1 (2017), 180–196 (In Russian) | DOI

[26] Burmasheva N. V., Prosviryakov E. Yu., “A large-scale layered stationary convection of a incompressible viscous fluid under the action of shear stresses at the upper boundary. Temperature and presure field investigation”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 21:4 (2017), 736–751 (In Russian) | DOI | Zbl

[27] Gorshkov A. V., Prosviryakov E. Yu., “Ekman Convective Layer Flow of a Viscous Incompressible Fluid”, Izv. Atmos. Ocean. Phys., 54:2 (2018), 89–195 | DOI

[28] Aristov S. N., Knyazev D. V., “Localized convective flows in a nonuniformly heated liquid layer”, Fluid Dyn., 49:5 (2014), 565–575 | DOI | MR