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Liquid surface waves in parabolic tanks
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View: Figures


Image of FIG. 1.
FIG. 1.

Surface wave in a parabolic tank. The basin’s cross section is formed by two confocal parabolas with axes along the axis. is the fluid depth.

Image of FIG. 2.
FIG. 2.

Eigenvalues of Eq. (15) under the variation of the geometry factor . Dashed (solid) lines represent eigenvalues for the odd (even) modes. The labels indicate the excitation in the parabolic degrees of freedom and , respectively.

Image of FIG. 3.
FIG. 3.

Eigenvalues of Eq. (15) under variation of . Same notation as in Fig. 2.

Image of FIG. 4.
FIG. 4.

Calculated 3D stationary elongation of the liquid surface in a parabolic-shape tank with geometry factor . The normal modes are identified by the labels of Fig. 2.

Image of FIG. 5.
FIG. 5.

Frequency modes in units of as function of . Two spectral region representing gravity and capillary waves are shown. Solid lines correspond to the exact solution of Eq. (22). Dotted lines indicate the gravity or capillary wave approximations. Mode labeling as in Fig. 2.

Image of FIG. 6.
FIG. 6.

Contour plots for the modulus of the amplitude in a parabolic-shape tank of the first 12 gravity wave modes labeled by the parabolic wave numbers (as in Figs. 2 and 5) for . and .

Image of FIG. 7.
FIG. 7.

Contour plot of the static amplitude of the capillary wave mode (50,50) in a tank with parabolic cross section and geometric factor . and .


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Liquid surface waves in parabolic tanks