Free and forced shallow-water oscillations in a rotating channel of parabolic cross-section

Free and forced oscillations of shallow water in an infinitely long rotating channel of parabolic cross-section are analyzed. The pure cross-channel oscillations ofChrystal (1905) and solutions for zero rotation first discussed byProudman (1925) andHidaka (1932) are special asymptotic solutions for the free modes of this model. However, for increasingly large, along-shore wave number, our solutions donot uniformly approach those ofReid (1958) andBall (1967) for a single shore-line and semi-infinite ocean. A method of computing eigen frequencies and eigen functions for the general problem is described, and a sufficient number of these are exhibited graphically to permit visualization of the transitions between the asymptotic regions.The forced problem consists of an incoming wave-train or surge generated at the center of the channel. Amplitude and transports near the shore are computed for a wide range of dimensionless incoming-wave frequencies and rotational frequencies.