ON GRAVITY-WAVES IN CHANNELS

This paper is concerned with the free surface oscillations under gravity of a body of water in basins of variable depth, as well as the corresponding travelling gravity waves in canals of variable depth, employing the linearized version of a more general system of equations of the theory of directed fluid sheets derived in [11, 12] instead of the linearized special theory (with a single constrained director) utilized in [7]. In particular, the linearized equations of the theory of directed fluid sheets with four directors are applied to the problem of two-dimensional free surface oscillations in basins of variable depth which include those with triangular and parabolic profiles. Some tract solutions of these equations are found to be in agreement with known exact results in the linear three-dimensional theory.