The effect of rotation on the simpler modes of motion of a liquid in an elliptic paraboloid

Abstract

The six simplest modes of motion are considered and three rotational effects investigated: The effect of the rotation of the earth. The effect of the rotation of the container. The effect of the rotation of the liquid within the container. The first two are shown to be equivalent for motion in a paraboloid, and the last two are also equivalent when the paraboloid iscircular. In the case of an elliptic paraboloid the last is rather more difficult and one must first derive a solution of the non-linear equations representing ‘elliptic rotation’ and then consider deviations from it.The changes in frequency consequent on the rotation are derived in all three cases for all six modes. In the case of the earth's rotation the disposition and character of the amphidromic (nodal) points and the amphidromic waves that rotate round these points are investigated in detail. One mode is particularly interesting because it has four amphidromic points, the waves rotate in a positive sense around two of these and in a negative sense round the other two.