HYDRODYNAMICS AND ACOUSTICS

This document is licensed under CC BY-NC-ND 4.0

2026 ◊ Volume 4 (94) ◊ Issue 1 ◊ p. 52-74  

https://doi.org/10.15407/jha2026.01.052

  T. S. Krasnoplolskaya^*,   Yu. V. Gorskiy^**

^* Institute of Hydromechanics of NAS of Ukraine, Kyiv, Ukraine

^** Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

Forced waves and cross-waves on a liquid surface in a partially filled ``singing wineglass''

Gidrodin. akust. 2026, 4(1):052-074

TEXT LANGUAGE: Ukrainian

ABSTRACT

The occurrence and structure of the forced and cross waves on a free surface of the liquid poured into the thin-walled cylindrical reservoir with a finite depth are explained using the superposition method. The chosen configuration of the system approximates the so-called ``singing wineglasses,'' famous due to the tonal sound radiation when exciting it by the wet finger evenly moving along the free edge of the wall. The theoretical analysis is complemented by the study held on the created special experimental benchmark that allows the photographic imaging of the free liquid surface displacements. The offered graphic representation of the height of the free surfaces depicts the main features of the wave distributions observed in the ``singing wineglass.'' The forced waves are shown to have the four knots in the azimuthal direction. Those knots correspond to the lowest bending mode of the circumferential vibration of the elastic shell and match with a modal structure of eigen oscillations of the liquid in the finite domain. The peculiarity of of the cross-waves is the ultimate orthogonality of their crests to the vibrating wall. The principal characteristics of the forced waves on the free liquid surface in the glass may be qualitatively described within the limits of the linearized theoretical model. At the same time, the cross-waves may be adequately modeled only by the nonlinear mathematical approaches describing the parametric resonance. The two-mode resonant model developed in this paper offers the most plausible mechanism of the occurrence of cross-waves. The obtained mathematical relations form the basis for simulation of the surface waves in the partially filled reservoirs in a wide range of the geometric and physical parameters. The expected results may be of use for prognostication of the behavior of the oil storage reservoirs, water towers, fuel tanks, and so on.

KEY WORDS

``singing wineglass'', forced surface waves, cross-waves, superposition method, parametric resonance, eigenmodes

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