Abstract
A new approach to the study of electrically induced flows is opened by the use of cylindrical coordinates. First, substantially more variants of axisymmetric electric current distributions (compared to the spherical case) are available, which, at least partly, have immediate practical implications. Second, in cylindrical coordinates there are several methods for the separation of variables in the Navier-Stokes and Maxwell equations that allow us to construct solutions in a similarity form. In choosing the coordinate system the role played by the geometrical form of the liquid conductor domain is by no means unimportant; a cylindrical form often occurs in practical high-current technology.
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References
Abdullah A. J.: Some aspects of the dynamics of tornadoes. Month. Weather Rev. (1955), No. 83, pp. 83–88.
Axford W. I.: Axisymmetric stagnation point flow in magnetohydrodynamics. Appl. Sci. Research (1961), 9, sect. B, No. 1, pp. 213–229.
Bacon F.: Natural history of winds — Extraordinary winds and sudden blasts. In: 1622. The Works of Francis Bacon, Carey and Hart. Philadelphia, 1844, vol. 3, p. 449.
Batchelor G. K.: An Introduction to Fluid Dynamics. Cambridge at the University Press, 1970.
Bojarevičs V. V. and Millere R. P.: Electrovortex flow in Karman’s class. 10th Riga Conference on MHD. Salaspils, 1981, vol. 1, pp. 157–158 (In Russian).
Bojarevičs V. V. and Sharamkin V. I.: MHD flow due to the discharge of an electric current in an axially symmetric layer of finite thickness. Magnitnaya Gidrodinamika (1977), No. 2, pp. 55–60.
Bojarevičs V. V., Freibergs J. Ž., Shilova E. I., and Shcherbinin E. V.: Electro-Vortex Flows. Riga: Zinatne, 1985 (In Russian).
Brady J. F. and Acrivos A.: Steady flow in a channel or tube with an accelerating surface velocity. J. Fluid Mech. (1981), 112, pp. 127–150.
Brady J. F.: Flow development in a porous channel and tube. Phys. Fluids (1984), 27(5), pp. 1061–1067.
Braham R. R.: The water and energy budgets of the thunderstorm and their relation to thunderstorm development. J. Meteorol. (1952), No. 9, pp. 237–243.
Brooks E. M.: The tornado-cyclone. Weatherwise (1949), 2, pp. 32–33.
Bucenieks I. E., Petersons D. E., Sharamkin V. I., and Shcherbinin E. V.: MHD flows caused by diverging currents passing through closed volumes of liquid. Magnitnaya Gidrodinamika (1976), No. l, pp. 92–97.
Cham T. S.: The laminar boundary layer of a source and vortex flow. Aeronautical Quart. (1971), 22(2), pp. 196–206.
Glazov O. A.: Rotation of conducting liquid under the stationary disc in the presence of magnetic field. Magnitnaya Gidrodinamika (1967), No. 2, pp. 75–80.
Goldshtik M. A.: A class of exact solutions of Navier-Stokes equations. Zhurnal Prikladnoj Mekhaniki i Tekhnicheskoj Fiziki (1966), No. 2, pp. 106–109.
Goldshtik M. A.: Vortex Flows. Novosibirsk: Nauka, 1981 (In Russian).
Golubinskij A. A. and Sychev V. V.: About a similarity solution of Navier-Stokes equations. Uchenye Zapiski TSAGI (1976), 7(6), pp. 11–17.
Greenspan H. P.: The Theory of Rotating Fluids. Cambridge at the University Press, 1968.
Gribben R. J.: Magnetohydrodynamic stagnation-point flow. Quart. J. Mech. Appl. Math. (1965), 18(3), pp. 357–384.
Gutman L. N.: Theoretical Model of Tornado. Izvestiya Akademii Nauk SSSR, Ser. Geophys. (1957), N 1, pp. 79–93.
Gutman L. N.: Introduction to the Nonlinear Theory of Mesometeorological Processes. Leningrad: Gidrometeoizdat, 1969 (In Russian).
Hare R.: On the causes of the tornado or waterspout. Amer. J. Sci. Arts (1837), 32, pp. 153–158.
Intense Atmospheric Vortices. Ed. by Bengtsson L., Lighthill J. Berlin-Heidelberg: Springer Verlag, 1982.
Kakutani T.: Axially symmetric stagnation-point flow of an electrically conducting fluid under transverse magnetic field. J. Phys. Soc. Jpn. (1960), 15(4), pp. 688–695.
Karman Th.: Über laminare und turbulente Reibung. ZAMM (1921), 1, S. 233–251.
Kislykh V. I. and Smulskij I. I.: To the hydrodynamics of vortex chamber. Inzhenerno-Fizicheskij Zhurnal (1978), 35(3), pp. 543–544.
Lentini M. and Keller H. B.: Computation of Karman swirling flows. Lecture Notes in Computer Sci. Ed. by Goos G., Hartmanis J., 1979, vol. 76, pp. 89–100.
Lewellen W. S. and King W. S.: Boundary-layer similarity solution for rotating flows with and without magnetic interaction. Phys. Fluids (1964), 7(10), pp. 1674–1680.
Lin C. C: Note on a class of exact solutions in magnetohydrodynamics. Arch. Rational Mech. Anal. (1958), 1(4), pp. 391–395.
Loitsyanskij L. G.: Laminar Boundary Layer. Moscow: GIFML, 1962 (In Russian).
Lucretius: On Nature of Objects. Part I. Moscow: Akademiya Nauk SSSR, 1946 (Russian translation).
Malbakhov V. M.: Investigation of tornado structure. Izvestiya Akademii Nauk SSSR. Fizika Atmosfery i Okeana (1972), 8(1), pp. 17–28.
Malbakhov V. M. and Gutman L. N.: Nonstationary problem of mesoscale atmospheric vortices with vertical axis. Idem (1968), 4(6), pp. 586–598.
Meksyn D.: Integration of the boundary-layer equations. Proc. Roy. Soc. London, ser. A (1956), 237(1211), pp. 543–559.
Mikhailov A.O.: About Storms. MorskojSbornik, SPb., 1888, No. 3, pp. 1–37.
Millere R. P., Sharamkin V. I., and Shcherbinin E. V.: Effect of longitudinal magnetic field on electrovortex flow in a cylindrical volume. Magnitnaya Gidrodinamika (1980), No. 1, pp. 81–85.
Millsaps K. and Nydahl J. E.: Heat transfer in a laminar cyclone, ZAMM (1973), 53, pp. 241–246.
Nalivkin D. V.: Hurricanes, Storms and Tornadoes. Leningrad: Nauka, 1963 (In Russian).
Nanbu K.: Vortex flow over a flat surface with suction. AIAA J. (1971), 9(8), pp. 1642–1645.
Pao H. P.: Magnetohydrodynamic Flows over a Rotating Disc. AIAA J. (1968), 6(7).
Peltier J. C. A.: Translation by Robert Hare. Amer. J. Sci. Arts (1840), 38, p. 73.
Petrovskij I. G.: Lectures in the Theory of Ordinary Differential Equations. Moscow: Nauka, 1964.
Reznikov B. I.: A method to integrate asymptotically the equations of laminar boundary layer. Aerophysical Investigations of Supersonic Flows. Ed. by Dunaev Yu. A. Leningrad: Nauka, 1967, pp. 284–300 (In Russian).
Reznikov B. I. and Smyslov Yu. N.: Magnetohydrodynamic flow in the vicinity of critical point in purely azimuthal magnetic field. Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza (1967), No. 4, pp. 3–8.
Sandler V. Yu.: Numerical study of temperature and velocity fields in a slag pool. Magnitnaya Gidrodinamika (1982), No. 2, pp. 113–119.
Schlichting H.: Laminare Strahlungsbreitung. ZAMM (1933), 13, S. 260–263.
Schlichting H.: Boundary Layer Theory. New York: McGraw-Hill, 1960.
Shcherbinin E. V.: Viscous Fluid Jet Flows in Magnetic Field. Riga: Zinatne, 1973 (In Russian).
Shilova E. I. and Shcherbinin E. V.: Some aspects of theoretical study of MHD flow in a diffuser. Magnitnaya Gidrodinamika (1971), No. 1, pp. 11–17.
Shilova E. I. and Shcherbinin E. V.: MHD model of weak whirlwind. Magnitnaya Gidrodinamika (1974), No. 2, pp. 77–86.
Sychev V. V.: On viscous electrically conducting fluid motion under the action of rotating disc in the presence of magnetic field. Prikladnaya Matematika i Mekhanika (1960), 24, No. 5, pp. 906–908.
Smirnov E. M.: Similarity solutions of Navier-Stokes equations for a swirling flow of incompressible fluid in a circular tube. Idem (1981), 45, No. 5, pp. 833–839.
Smyslov Yu. N. and Shcherbinin E. V.: Nonlinear magnetohydrodynamic model of tornado. Problems of Mathematical Physics. Leningrad: Nauka, 1976, pp. 271–282 (In Russian).
Sozou C.: Electrical discharges and intense vortices. Proc. Roy. Soc. London (1984), A392, pp. 415–426.
Srivastava A. C. and Sharma S. K.: The effect of a transverse magnetic field on the flow between two infinite discs — one rotating and the other at rest. Bull. Acad. Polon. Sci., Ser. Sci. Techn. (1961), 9(11), pp. 639–645.
Uman M. A.: Lightning. New York: McGraw-Hill Book Co., 1969.
Van Dyke M.: Semi-analytical applications of the computer. Fluid Dynamics Trans. Ed. by W. Fiszdon et al., Warszawa, 1978, vol. 9, pp. 305–320.
Vlasyuk V. Kh.: Effect of melting electrode radius on the electrically induced vortical flow in a cylindrical container. Magnitnaya Gidrodinamika (1987), No. 4, pp. 101–106.
Vonnegut B.: Electrical theory of tornadoes. J. Geophys. Research (1960), 65(1), pp. 203– 212.
Wegener A.: Wind und Wassershosen in Europa. In: Die Wissenschaft. Braunschweig, 1917, Bd. 60, S. 301.
Yuan S. W., Finkelstein A. B.: Laminar pipe flow with injection and suction through a porous wall. Trans. ASME (1956), 78(4), pp. 719–724.
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Bojarevičs, V., Freibergs, J.A., Shilova, E.I., Shcherbinin, E.V. (1989). Flows with cylindrical symmetry. In: Electrically Induced Vortical Flows. Mechanics of Fluids and Transport Processes, vol 9. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1163-5_5
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DOI: https://doi.org/10.1007/978-94-009-1163-5_5
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