Free wave modes in elliptic cylindrical containers

• Gravity–capillary waves in cylindrical containers with elliptical cross-section are studied.
• We show the dependence of the natural frequencies and the frequency shift on the eccentricity ee.
• We retrieve the well-known case of a circular basin for e=0e=0.
• The elliptical confinement can be used to modulate the damping ratio.

The linear theory of unforced surface gravity–capillary waves in cylindrical containers with an elliptical cross-section is studied in detail. General solutions for the velocity potential and the free surface amplitude are given in terms of Mathieu functions. Our numerical results show the dependence of the natural frequencies on the fluid properties and the eccentricity ee of the container cross-section. The well-known case of a circular tank for e=0e=0 is retrieved and remarkable crossings of the mode frequencies for certain values of ee are found. The frequency shift and the wall damping ratio due to viscous dissipation in the Stokes boundary layers are evaluated numerically. The effect of the viscous dissipation in the bulk, the wall damping ratio, is estimated.