Co-oscillating tides in long, narrow bays : Taylor problem revisited

In a small, rectangular, mid-latitude bay too narrow and too deep for Poincaré modes to propagates semidiurnal tidal energy, the co-oscillating semidiurnal tide must be primarily a superposition of oppositely travelling Kelvin waves. We generalize Taylor's (1921) study of the reflection of Kelvin waves at the head of such a bay, now allowing the boundary at the head to absorb a variable portion of the power flux incident upon it. In a bay of uniform depth, the resulting displacement of amphidromic points away from the central axis of the bay becomes a unique measure of the total energy loss at the head of the bay. This displacement explains the marked difference between semidiurnal tides in the Adriatic Sea and in the Gulf of California; a Kelvin wave fit to these tides yields both the tidal energy incident at the mouth of each basin and the tidal energy dissipated within each basin.