TY - JOUR
T1 - Nonlinear two-dimensional water waves with arbitrary vorticity
AU - Ionescu-Kruse, Delia
AU - Ivanov, Rossen
N1 - Publisher Copyright:
© 2023 The Authors
PY - 2023/9/25
Y1 - 2023/9/25
N2 - We consider the two-dimensional water-wave problem with a general non-zero vorticity field in a fluid volume with a flat bed and a free surface. The nonlinear equations of motion for the chosen surface and volume variables are expressed with the aid of the Dirichlet-Neumann operator and the Green function of the Laplace operator in the fluid domain. Moreover, we provide new explicit expressions for both objects. The field of a point vortex and its interaction with the free surface is studied as an example. In the small-amplitude long-wave Boussinesq and KdV regimes, we obtain appropriate systems of coupled equations for the dynamics of the point vortex and the time evolution of the free surface variables.
AB - We consider the two-dimensional water-wave problem with a general non-zero vorticity field in a fluid volume with a flat bed and a free surface. The nonlinear equations of motion for the chosen surface and volume variables are expressed with the aid of the Dirichlet-Neumann operator and the Green function of the Laplace operator in the fluid domain. Moreover, we provide new explicit expressions for both objects. The field of a point vortex and its interaction with the free surface is studied as an example. In the small-amplitude long-wave Boussinesq and KdV regimes, we obtain appropriate systems of coupled equations for the dynamics of the point vortex and the time evolution of the free surface variables.
UR - http://www.scopus.com/inward/record.url?scp=85162110294&partnerID=8YFLogxK
U2 - 10.1016/j.jde.2023.05.047
DO - 10.1016/j.jde.2023.05.047
M3 - Article
AN - SCOPUS:85162110294
SN - 0022-0396
VL - 368
SP - 317
EP - 349
JO - Journal of Differential Equations
JF - Journal of Differential Equations
ER -