scholarly journals Motion trapping structures in the three-dimensional water-wave problem

2006 ◽  
Vol 58 (1-4) ◽  
pp. 67-75 ◽  
Author(s):  
P. McIver ◽  
M. McIver
Keyword(s):  
Water Wave ◽  
Three Dimensional ◽  
Wave Problem ◽  
Water Wave Problem

scholarly journals Some Explicit Solutions to the Three-Dimensional Nonlinear Water Wave Problem

2021 ◽  
Vol 23 (2) ◽  
Author(s):  
Calin I. Martin
Keyword(s):  
New York ◽  
Surface Pressure ◽  
Water Wave ◽  
Three Dimensional ◽  
Wave Climate ◽  
Explicit Solutions ◽  
Wave Problem ◽  
Water Wave Problem ◽  
Constant Vorticity ◽  
Radial Structure

AbstractWe present some explicit solutions (given in Eulerian coordinates) to the three-dimensional nonlinear water wave problem. The velocity field of some of the solutions exhibits a non-constant vorticity vector. An added bonus of the solutions we find is the possibility of incorporating a variable (in time and space) surface pressure which has a radial structure. A special type of radial structure of the surface pressure (of exponential type) is one of the features displayed by hurricanes, cf. Overland (Earle, Malahoff (eds) Overland in ocean wave climate, Plenum Pub. Corp., New York, 1979).

scholarly journals One-Dimensional Symmetry for the Solutions of a Three-Dimensional Water Wave Problem

2019 ◽  
Vol 30 (2) ◽  
pp. 1804-1835 ◽  
Author(s):  
Eleonora Cinti ◽  
Pietro Miraglio ◽  
Enrico Valdinoci
Keyword(s):  
Water Wave ◽  
Three Dimensional ◽  
Wave Problem ◽  
Water Wave Problem ◽  
One Dimensional

scholarly journals An alternative approach to study irrotational periodic gravity water waves

2021 ◽  
Vol 72 (4) ◽  
Author(s):  
Biswajit Basu ◽  
Calin I. Martin
Keyword(s):  
Free Surface ◽  
Water Waves ◽  
Water Wave ◽  
Wave Problem ◽  
Water Wave Problem ◽  
Stagnation Points ◽  
Alternative Approach ◽  
New Formulation ◽  
Bounded Below ◽  
Surface Dynamic

AbstractWe are concerned here with an analysis of the nonlinear irrotational gravity water wave problem with a free surface over a water flow bounded below by a flat bed. We employ a new formulation involving an expression (called flow force) which contains pressure terms, thus having the potential to handle intricate surface dynamic boundary conditions. The proposed formulation neither requires the graph assumption of the free surface nor does require the absence of stagnation points. By way of this alternative approach we prove the existence of a local curve of solutions to the water wave problem with fixed flow force and more relaxed assumptions.

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