Convective layered flows of a vertically whirling viscous incompressible fluid. Temperature field investigation

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The paper discusses a class of exact solutions of the Oberbeck–Boussinesq equations suitable for describing three-dimensional nonlinear layered flows of a vertically swirling viscous incompressible fluid. An inhomogeneous distribution of the velocity field (there is a dependence of the field components on the horizontal coordinates) generates a vertical swirl in the fluid without external rotation (excluding Coriolis acceleration). Setting the linearly distributed heat field and the field of shear stresses at the boundaries of the flow region is one of the reasons inducing convection in a viscous incompressible fluid. The main attention is paid to the study of the properties of the temperature field. The effect of vertical twist on the distribution of isolines of this field is studied. It is shown that the homogeneous component of the temperature field can be stratified into several zones relative to the reference value, and the number of such zones does not exceed nine. The inclusion of inhomogeneous components of the temperature field can only decrease this number. It is also demonstrated that the class discussed in the paper allows one to generalize the previously obtained results on modeling convective flows of viscous incompressible fluids.

About the authors

Natal'ya Vladimirovna Burmasheva

Institute of Engineering Science, Urals Branch, Russian Academy of Sciences; Ural Federal University named after the First President of Russia B. N. Yeltsin

Email: nat_burm@mail.ru
Candidate of technical sciences

Eugenii Yurevich Prosviryakov

Institute of Engineering Science, Urals Branch, Russian Academy of Sciences

Email: evgen_pros@mail.ru
Doctor of physico-mathematical sciences, no status

References

  1. Landau L. D., Lifshits E. M., Course of Theoretical Physics, v. 6, Fluid Mechanics, Pergamon Press, New York, 1959, 539 pp.
  2. Gershuni G. Z., Zhukhovitskii E. M., Convective Stability of Incompressible Fluids, Israel Program for Scientific Translations, Keter Publishing House, Jerusalem, 1976, 330 pp.
  3. Kochin N. E., Kibel I. A., Roze N. V., Theoretical Hydromechanics, Wiley Interscience, New York, 1964, 577 pp.
  4. Falkovich G., Fluid Mechanics: A Short Course for Physicists, Cambridge University Press, Cambridge, 2011, xii+180 pp
  5. Navier M., "Memoire sur les lois du mouvement des fluides", Mem. Acad. Sci. Inst. France, 6 (1827), 389-440
  6. Stokes G. G., "On the theories of internal friction of fluids in motion, and of the equilibrium and motion of elastic solids", Mathematical and Physical Papers, v. 1, Cambridge University Press, Cambridge, 2009, 75-129
  7. Drazin P. G., Introduction to hydrodynamic stability, Cambridge University Press, Cambridge, 2002, xviii+258 pp
  8. Chandrasekhar S., Hydrodynamic and hydromagnetic stability, Dover Publications, New York, 1981, 708 pp.
  9. Poisson M., "Memoire sur les equations generales de l'equilibre et du mouvement des corps solides elastiques et des fluides", Journ. de l'Ecole Polytechn., 13 (1831), 1-174
  10. Lin C. C., "Note on a class of exact solutions in magneto-hydrodynamics", Arch. Rational Mech. Anal., 1 (1858), 391-395
  11. de Saint-Venant B., "Note à joindre au Memoire sur la dynamique des fluides", Comptes rendus, 17:22 (1843), 1240-1244
  12. 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)
  13. Burmasheva N. V., Prosviryakov E. Yu., "Temperature field investigation in layered flows of a vertically swirling viscous incompressible fluid under two thermocapillar forces at a free boundary", Diagnostics, Resource and Mechanics of Materials and Structures, 2019, no. 1, 6-42 (In Russian)
  14. 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)
  15. Burmasheva N. V., Prosviryakov E. Yu., "Investigation of a velocity field for the Marangoni shear convection of a vertically swirling viscous incompressible fluid", AIP Conf. Proc., 2053 (2018), 040011
  16. Burmasheva N.V., Prosviryakov E. Yu., "Exact solution for the layered convection of a viscous incompressible fluid at specified temperature gradients and tangential forces on the free boundary", AIP Conf. Proc., 1915 (2017), 040005
  17. Burmasheva N.V., Prosviryakov E. Y., "Exact solutions for layered large-scale convection induced by tangential stresses specified on the free boundary of a fluid layer", IOP Conf. Ser.: Mater. Sci. Eng., 208 (2017), 012010
  18. Burmasheva N. V., Prosviryakov E. Yu., "Convective layered flows of a vertically whirling viscous incompressible fluid. Velocity field investigation", Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 23:2 (2019), 341-360
  19. Burmasheva N. V., Prosviryakov E. Yu., "Thermocapillary convection of a vertical swirling liquid", Theor. Found. Chem. Eng., 54:1 (2020), 230–239
  20. Liapidevskii V. Y., "A mixing layer in a homogeneous fluid", J. Appl. Mech. Tech. Phys., 41:4 (2000), 647–657
  21. Georgievsky D. V., "Tensor-nonlinear shear flows: Material functions and the diffusion-vortex solutions", Rus. J. Nonlin. Dyn., 7:2 (2011), 451-463
  22. Taylor G. I., "The transport of vorticity and heat through fluids in turbulent motion", Proc. Roy. Soc. London. Ser. A, 135:828 (1932), 685-705
  23. Kuznetsova Yu. L., Skul'skiy O. I., "Effect of different flows on the shear branding of a liquid with a non-monotonic flow curve.", J. Appl. Mech. Tech. Phys., 60:1 (2019), 22-30
  24. Rodi W., Hydrodynamic and Hydromagnetic Stability, CRC Press, Boca Raton, 1973, 124 pp.
  25. Georgievsky D. V., "Generalized Joseph Estimates of Stability of Plane Shear Flows with Scalar Nonlinearity", Bull. Russ. Acad. Sci. Phys., 75:1 (2011), 149-152
  26. Knutova N. S., Shvarts K. G., "A study of behavior and stability of an advective thermocapillary flow in a weakly rotating liquid layer under microgravity", Fluid Dyn., 50:3 (2015), 340-350
  27. Chikulaev D. G., Shvarts K. G., "Effect of rotation on the stability of advective flow in a horizontal liquid layer with solid boundaries at small Prandtl numbers", Fluid Dyn., 50:2 (2015), 215—222
  28. Sidorov A. F., "Two classes of solutions of the fluid and gas mechanics equations and their connection to traveling wave theory", J. Appl. Mech. Tech. Phys., 30:2 (1989), 197-203
  29. Knyazev D. V., "Two-dimensional flows of a viscous binary fluid between moving solid boundaries", J. Appl. Mech. Tech. Phys., 52:2 (2011), 212-217
  30. Schwarz K. G., "Plane-parallel advective flow in a horizontal incompressible fluid layer with rigid boundaries", Fluid Dyn., 49:4 (2014), 438-442
  31. Brutyan M. A., Kovalev V. E., "Vortex flows of a micropolar fluid", TsAGI Science Journal, 41:4 (2010), 52-61 (In Russian)
  32. Aristov S. N., Prosviryakov E. Y., "Stokes waves in vortical fluid", Rus. J. Nonlin. Dyn., 10:3 (2014), 309-318
  33. Nikulin V. V., "Analytical model of motion of turbulent vortex rings in an incompressible fluid", J. Appl. Mech. Techn. Phys., 55:4 (2014), 558-564
  34. Kovalev V. P., Sizykh G. B., "Axisymmetric helical flows of an ideal fluid", Trudy MFTI, 8:3 (2016), 171-179 (In Russian)
  35. Brutyan M. A., Krapivskiy P. L., "The exactsolution of the Navier-Stokes equations for the evolution of the vortex structure in a generalized shear-flow", Comput. Math. Math. Phys., 32:2 (1992), 270-272
  36. Morozov K. I., "Rotation of a droplet in a viscous fluid", J. Exp. Theor. Phys., 85:4 (1997), 728-733
  37. Greenspan H. P., The Theory of Rotating Fluids, Cambridge University Press, Cambridge, 1968, xii+328 pp.
  38. Aristov S. N., Prosviryakov E. Y., "Large-scale flows of viscous incompressible vortical fluid", Russ. Aeronaut., 58:4 (2015), 413-418
  39. Privalova V. V., Prosviryakov E. Yu., Simonov M. A., "Nonlinear gradient flow of a vertical vortex fluid in a thin layer", Rus. J. Nonlin. Dyn., 15:3 (2019), 271–283

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