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