Abstract
In a recent paper (Li et al., Acta Mech. Sin. 31, 32–44, 2015), the authors claimed that the general solution of steady Stokes flows can be compactly expressed using only two harmonic functions. They present two cases of a flat plate translating through a viscous fluid. The present paper shows that such a two-harmonic solution does not describe the rotation of a circular plate in an unbounded fluid and thus confirms that at least three independent harmonics are required to express the general solution of Stokes equations.
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References
Palaniappan, D., Nigam, S.D., Amaranath, T.: Lamb’s solution of Stokes’s equations: a sphere theorem. Q. J. Mech. Appl. Math. 45, 47–56 (1992)
Padmavathi, B.S., Raja Sekhar, G.P., Amaranath, T.: A note on complete general solutions of Stokes equations. Q. J. Mech. Appl. Math. 51, 383–388 (1998)
Almansi, E.: Sull integrazione dell’ equazione differenziale \(\nabla ^{2n}F=0\). Ann. di Math. Ser. 3, 1–51 (1899) (in Italian)
Venkatalaxmi, A., Padmavathi, B.S., Amaranath, T.: Complete general solution of Stokes equations for plane boundaries. Mech. Res. Commun. 31, 465–475 (2004)
Li, X.Y., Ren, S.C., He, Q.C.: A general solution for Stokes flow and its application to the problem of a rigid plate translating in a fluid. Acta Mech. Sin. 31, 32–44 (2015)
Milne-Thomson, L.M.: Theoretical Hydrodynamics, 4th edn. Macmillan, London (1960)
Lamb, H.: Hydrodynamics. Dover, New York (1945)
Acknowledgements
The project was supported by the National Natural Science Foundation of China (Grant 11372186) and the Specialized Research Fund for the Doctoral Program of Higher Education (Grant 20130073110059).
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Qin, Y., Sun, R. On the solution of Stokes equations for plane boundaries. Acta Mech. Sin. 33, 62–64 (2017). https://doi.org/10.1007/s10409-016-0622-y
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DOI: https://doi.org/10.1007/s10409-016-0622-y