Added mass: a complex face of tidal conversion

TL;DR

This study investigates how finite water depth and ridge shape influence tidal conversion and added mass coefficients, revealing conditions where tidal energy transfer is enhanced, reduced, or nullified.

Contribution

It provides experimental insights into the effects of ridge shape and water depth on tidal conversion and added mass, highlighting scenarios of null conversion.

Findings

Shallow depth weakly enhances tidal conversion at low frequency for semi-circular ridge

Vertical ridge shows similar added mass coefficients to semi-circular ridge

Tidal conversion can be nullified for specific ridge shapes, depths, and frequencies

Abstract

This paper revisits the problem of tidal conversion at a ridge in a uniformly stratified fluid of limited depth using measurements of complex-valued added mass. When the height of a sub-marine ridge is non negligible with respect to the depth of the water, the tidal conversion can be enhanced in the supercritical regime or reduced in the subcritical regime with respect to the large depth situation. Tidal conversion can even be null for some specific cases. Here, we study experimentally the influence of finite depth on the added mass coefficients for three diffierent ridge shapes. We first show that at low forcing frequency the tidal conversion is weakly enhanced by shallow depth for a semi-circular ridge. In addition, added mass coefficients measured for a vertical ridge show strong similarities with the ones obtained for the semi-circular ridge. Nevertheless, the enhancement of the tidal conversion at low forcing frequency for the vertical ridge has not been observed, in contrast with its supercritical shape. Finally, we provide the experimental evidence of a lack of tidal conversion due to the specific shape of a ridge for certain depth and frequency tuning.