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Free vibrations of a meniscus with edge constraints. (English) Zbl 0592.76024

Summary: The gravity capillary small vibrations of the meniscus of a fluid contained in a trough, when the line of contact on the lateral walls is fixed, are studied for the incompressible inviscid case. The two cases when the bottom end of the trough is closed or open are considered. It is found that the vibration frequencies and modes may be determined as eigenmodes and eigenvalues of a linear operator whose components, in a suitable basis of \(L_ 2(-1,1)\), are given analytically. The influence of the relevant nondimensional parameters and the distinguishing features of the case of an open channel are then determined, and substantiated by numerical results.

MSC:

76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76M99 Basic methods in fluid mechanics
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References:

[1] Benjamin T.B., Scott J.C., 1979, J. Fluid Mech., 92, 241–267. · Zbl 0409.76020 · doi:10.1017/S0022112079000616
[2] Benjamin T.B.,Scott J.C., 1981, Trends in applications of pure Mathematics to Mechanics, vol. III, Pitman.
[3] Lamb H., 1932, Hydrodynamics, 6-th Edition, Dover.
[4] Strani M., Sabetta F., 1984, J. Fluid Mech., 141, 233–247. · Zbl 0571.76101 · doi:10.1017/S0022112084000811
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