In this study, the fictitious time integration method (FTIM) is applied to investigate wave propagation over an arbitrary bathymetry with measured uncertainty. The FTIM is used to convert the higher-order elliptic mild-slope equation (EMSE) into a FTIM like EMSE (FTIMEMSE). It has the advantage to describe wave transformation from deep water to shallow water region in a large coastal area with numerical efficiency. The validity of the noise resistance for the measured uncertainty of the bathymetry is also studied. In addition, typical examples for waves propagating over an elliptic shoal rest on a horizontal and sloping bottom is presented. It is concluded that the FTIM is robust in the numerical stability and capable of against the noise of the measurement.

We introduce the entropy of a family of planar curves in terms of the number of intersections of the family with a random line, calculate it for key examples, and discuss the entropy of a pattern of rings produced by an impulse on the surface of still water.

Les instruments de mesures des courants en mer permettent d'obtenir un nombre d'informations de plus en plus important grâce à des techniques de mesures de plus en plus sophistiquées. En particulier, les mesures ponctuelles de vitesses et de pression permettent d'obtenir des informations sur l'énergie de la houle et sa direction de propagation. Nous avons montré dans ce travail que le caractère partiellement stationnaire des houles réelles peut être mesuré de façon quantitative à partir de données synchrones de vitesse et/ou de pression. Ces capacités sont illustrées par des exemples de mesures à partir de différents appareils immergés en zone littorale (S4, ADV, ligne de capteurs de pression).