Summary
The problem of the (relative) equilibrium of liquids in accelerating frames is examined in its entirety, and the conditions under which this equilibrium can be realized are determined in a rigorous manner. Also the question of the existence of a free surface of a liquid in relative equilibrium is answered, and expressions for the pressure, as a function of position and time, are given.
Moreover, generalized buoyancy is calculated for the most important cases of equilibrium. Two examples of practical interest are given.
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References
Batchelor, G. K.: Fluid dynamics, pp. 17–18. Cambridge: Cambridge University Press 1980.
Darwin, G. H.: On Jacobi's figure of equilibrium for a rotating mass of fluid. Proc. R. Soc.xli, 319 (1886).
Darwin, G. H.: On figures of equilibrium for a rotating mass of fluid. Phil. Trans. Aclxxviii., 379 (1887).
Greenspan, H. P., Howard, L. N.: On a time-dependent motion of a rotating fluid. J. Fluid Mech.17, 385–391 (1990).
Gunn, J. S., Albridge, K. D.: Inertial wave eigenfrequencies for a nonuniformly rotating fluid. Phys. FluidsA2, 2055–2060 (1990).
Liouville, R.: Sur la figure d'une masse fluide homogene en equilibre et dounee d'un mouvement de rotation. J. l'Ecole Polytechn.M 290 (1834).
Poincaré, H.: Figures d'equilibre. Paris 1902.
Ramsey, A. S.: Hydrostatics, pp. 107–109. London: Cambridge University Press 1936.
Stewartson, K.: On almost rigid rotations. J. Fluid Mech.3, 17–27 (1957).
Xu Y., Boyer, L., Zhang, X.: Rotating oscillatory flow past a cylinder. Phys. FluidsA 5, 868–879 (1993).
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Kapoulitsas, G.M. On the equilibrium of fluids in accelerating frames. Acta Mechanica 122, 123–136 (1997). https://doi.org/10.1007/BF01181994
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DOI: https://doi.org/10.1007/BF01181994