Lower bound of the eigenfrequencies of plane oscillations of a fluid in a channel

A method is proposed for estimating the lower bound of the eigenfrequencies of free plane oscillations of an ideal fluid in a channel of constant cross-section. The method is based on the identity [1] which is used to prove the theorem of uniqueness in the problem of radiation and scattering of the waves by a body completely immersed in the fluid. Unlike in the estimates obtained earlier [2, 3], here the bottom of the channel is not explicitly specified. It is shown that in a number of cases the estimate can be substantially improved when it is used together with the principle of monotony [4, 5]. The method developed here can also be used for a three-dimensional problem. Examples are solved and the results compared with the known exact and approximate values [5, 6] and with the estimates obtained by others [7]. A lower bound of a different type was obtained in [8]. A bibliography of the problems of eigenfrequencies of the oscillations of an ideal fluid can be found in [5, 9].