Standing Gravity Waves in a Horizontal Circular Eccentric Annular Tank

Abstract

Standing gravity waves in halffull horizontal cylindrical containers with eccentric tube are analyzed using the linear theory of water waves. The problem solution is obtained by the method of conformal coordinate transformation, leading to standard truncated matrix Eigenvalue problem from which fluid motion characteristics (Eigenfrequencies and wave modes) are calculated. The effects of tube eccentricity and radius ratio upon the three lowest antisymmetric and symmetric sloshing frequencies and the associated hydrodynamic pressure mode shapes are examined. Also, convergence of the adopted approach with respect to the eccentricity condition, and radius ratio is discussed. Accuracy of the present analysis is checked by comparison with the known results of the limiting cases.