This paper is devoted to the study of water waves under the influence of the gravity and the Coriolis force. It is quite common in the physical literature that the rotating shallow water equations are used to study such water waves. We prove a local wellposedness theorem for the water waves equations with vorticity and Coriolis force, taking into account the dependence on various physical parameters and we justify rigorously the shallow water model. We also consider a possible non constant pressure at the surface that can be used to describe meteorological disturbances such as storms or pressure jumps for instance.
Accepté le :
DOI : 10.1051/m2an/2017024
Mots-clés : Water waves equations, quasilinear hyperbolic system, asymptotic models, shallow water asymptotic
@article{M2AN_2017__51_5_1957_0, author = {Melinand, Benjamin}, title = {Coriolis effect on water waves}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {1957--1985}, publisher = {EDP-Sciences}, volume = {51}, number = {5}, year = {2017}, doi = {10.1051/m2an/2017024}, mrnumber = {3731556}, zbl = {1382.35232}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/m2an/2017024/} }
TY - JOUR AU - Melinand, Benjamin TI - Coriolis effect on water waves JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2017 SP - 1957 EP - 1985 VL - 51 IS - 5 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an/2017024/ DO - 10.1051/m2an/2017024 LA - en ID - M2AN_2017__51_5_1957_0 ER -
Melinand, Benjamin. Coriolis effect on water waves. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 5, pp. 1957-1985. doi : 10.1051/m2an/2017024. http://archive.numdam.org/articles/10.1051/m2an/2017024/
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