Calcul analytique et numérique des seiches et des oscillations portuaires pour des bassins de forme rectangulaire et de profondeur constante avec des digues semi-infinies parfaitement réfléchissantes

摘要

Using the Kirchhoff-Helmholtz integral equation applied to gravity waves and taking into account the evanescent modes within the resonator, we establish a new approximation of the fundamental oscillation period of basin of rectangular shape and constant depth in the presence of perfectly reflective semi-infinite jetties. This approximation generalizes the analytical formula used by Rabinovich. The formula presented by Rabinovich corrects itself the period classically used for quarter-wave resonators. We then compare this approximation with the results of the mild slope equation of Berkhoff resolved by the finite element method. It is observed that the analytical formula presented by Rabinovich underestimates the resonance period. For finite elements calculation, a mesh density of about 10 nodes per wavelength is sufficient to achieve a good accuracy, but the mesh density must also satisfy a criterion on the number of nodes along the width. As far as the amplification factor is concerned, we find like Rabinovich that the latter is proportional to the length-to-width ratio and does not depend on the depth. We also show that the composition of the external structures can be decisive for the amplification. An experimental test in a wave tank shows, however, that in some cases a significant dissipation occurs which on the one hand reduces the seiche period and on the other hand reduces the amplification factor significantly.