On “radiational” tides and their interpretation as frictional effects

Abstract

When the observed sea levels are fitted linearly with the tidal potential, using cross-spectral methods, an apparent discontinuity in the response of neighbouring harmonics, like S 2 and K 2, becomes noticeable. The hypothesis of radiational tides would reproduce this discontinuity by introducing an additional input. However, a closer scrutiny of the hypothesis shows it to be untenable: it would require a diffuse and irregular source of energy, the radiation at the water surface, to induce oscillations of a fixed frequency, of constant amplitude and phase lag. The radiational tides calculated, assuming a linear response to gravitational inputs by the ocean, would reach amplitudes of 15–20 cm around the North Sea and of only 1–2 cm in the subtropics; they should even exist in the High Canadian Arctic. A more plausible cause for the discontinuity in response is quadratic friction: friction creates a linkage between the spectral elements of the observed water levels, which is evident for pairs of close frequency. In fact such linkage exists right across the tidal bands. Consequently the spectra of water levels, whenever nonlinear effects are present, will exhibit unusual features such as discontinuities in amplitude and phase, line splitting, besides other irregularities.