Abstract
A problem of rotation of a fluid layer bounded by a solid plane and a free surface parallel to this plane is considered. The fluid can be an ideal or a viscous fluid. Conditions for the existence of solutions of the corresponding problems for the Euler and Navier–Stokes equations on an infinite time interval are formulated. Examples of the numerical solution of the problem are presented.
REFERENCES
E. N. Zhuravleva and V. V. Pukhnachev, “Problem of Deformation of a Viscous Layer," Dokl. Ross. Akad. Nauk, Fiz., Tekh. Nauki 190 (1), 66–69 (2020).
V. V. Pukhnachev and E. N. Zhuravleva, “Viscous Flows with Flat Free Boundaries," Europ. Phys. J. Plus. 554, 135–146 (2020).
L. V. Ovsiannikov, “General Equations and Examples," in Problem of Unsteady Motion of the Fluid with a Free Boundary (Nauka, Novosibirsk, 1967, pp. 5–75) [in Russian].
M. S. Longuet-Higgins, “A Class of Exact, Time-Dependent, Free-Surface Flows," J. Fluid Mech. 55, 529–543 (1972).
T. Karman, “Über Laminare und Turbulente Reibung," Z. angew. Math. Mech., No. 4, 233–252 (1921).
L. D. Landau and E. M. Lifshits, Course of Theoretical Physics, Vol. 6: Fluid Mechanics (Nauka, Moscow, 1986; Pergamon Press, Oxford-Elmsford, New York, 1987).
G. K. Batchelor, Introduction to Fluid Dynamics (Cambridge Univ. Press, Cambridge, 1967).
S. Matsumoto, K. Saito, and Y. Takashima, “The Thickness of a Viscous Liquid Film on a Rotating Disk," J. Chem. Engng Japan 6 (6), 503–507 (1974).
V. K. Andreev, O. V. Kaptsov, V. V. Pukhnachev, and A. A. Rodionov, Application Group-Theoretical Methods in Hydrodynamics (Dordrecht; Boston; L.: Kluwer Acad. Publ., 1988).
O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Uraltseva Linear and Quasi-Linear Equations of the Parabolic Type (Nauka, Moscow, 1967) [in Russian].
O. M. Lavrent’eva and G. B. Volkova, “Limiting Regimes of Layer Spreading on a Rotating Plane," in: Dynamics of Continuous Media (collected scientific papers) Inst. Hydrodynamics, Sib. Branch, Russian Acad. of Sci., No. 111, 68–77 (1996).
O. M. Lavrent’eva, “Flow of a Viscous Liquid in a Layer on a Rotating Plane," Prikl. Mekh. Tekh. Fiz. 30 (5), 41–48 (1989) [J. Appl. Mech. Tech. Phys. 30 (5), 706–712 (1989)].
Author information
Authors and Affiliations
Corresponding authors
Additional information
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2022, Vol. 63, No. 6, pp. 96-103. https://doi.org/10.15372/PMTF20220611.
Rights and permissions
About this article
Cite this article
Zhuravleva, E.N., Pukhnachev, V.V. ON ROTATION OF A FLUID LAYER. J Appl Mech Tech Phy 63, 988–994 (2022). https://doi.org/10.1134/S0021894422060116
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0021894422060116