Surface waves in a square container due to its resonant horizontal elliptic motion

Abstract eng:
Surface waves in a square container due to its resonant horizontal elliptic motion are examined theoretically. The motion of the container is characterized by the ratio of the lengths of the major and minor axes of its elliptic orbit, and by the angle between the directions of the major axis and one of its sidewalls. Using the reductive perturbation method, nonlinear time evolution equations for the complex amplitudes of two degenerate modes excited by this motion are derived with the inclusion of linear damping. Solutions to these equations expressing regular co—rotating or counter—rotating waves and waves with periodic or chaotic variations in their amplitudes are obtained. Counter—rotating waves are not observed for the circular motion of the container. Chaotic waves are obtained frequently when the container’s motion is close to linear.

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