TY - UNPB
T1 - Large-amplitude steady gravity water waves with general vorticity and critical layers
AU - Weber, Jörg
AU - Wahlén, Erik
PY - 2022
Y1 - 2022
N2 - We consider two-dimensional steady periodic gravity waves on water of finite depth with a prescribed but arbitrary vorticity distribution. The water surface is allowed to be overhanging and no assumptions regarding the absence of stagnation points and critical layers are made. Using conformal mappings and a new Babenko-type reformulation of Bernoulli's equation, we uncover an equivalent formulation as "identity plus compact", which is amenable to Rabinowitz' global bifurcation theorem. This allows us to construct a global connected set of solutions, bifurcating from laminar flows with a flat surface. Moreover, a nodal analysis is carried out for these solutions under a monotonicity assumption on the vorticity function.
AB - We consider two-dimensional steady periodic gravity waves on water of finite depth with a prescribed but arbitrary vorticity distribution. The water surface is allowed to be overhanging and no assumptions regarding the absence of stagnation points and critical layers are made. Using conformal mappings and a new Babenko-type reformulation of Bernoulli's equation, we uncover an equivalent formulation as "identity plus compact", which is amenable to Rabinowitz' global bifurcation theorem. This allows us to construct a global connected set of solutions, bifurcating from laminar flows with a flat surface. Moreover, a nodal analysis is carried out for these solutions under a monotonicity assumption on the vorticity function.
U2 - 10.48550/arXiv.2204.10071
DO - 10.48550/arXiv.2204.10071
M3 - Preprint (in preprint archive)
BT - Large-amplitude steady gravity water waves with general vorticity and critical layers
PB - arXiv.org
ER -