1999/11/10 by Didier Clamond · 26 citations
Earth and Planetary Sciences · Physics and Astronomy · Mathematics · #Ocean Waves and Remote Sensing #Nonlinear Waves and Solitons #Oceanographic and Atmospheric Processes #Waves and shallow water #Amplitude #Renormalization #Laplace transform #Transformation (genetics) #Physics #Korteweg–de Vries equation #Field (mathematics) #Mathematical analysis #Seabed #Velocity potential #Shallow water equations #Domain (mathematical analysis) #Mechanics #Classical mechanics #Geology #Mathematics #Mathematical physics #Nonlinear system #Boundary value problem #Optics
paper · doi:10.1017/s0022112099006151
published in Journal of Fluid Mechanics 398, 45-60 (Cambridge University Press)
openalex publication_date 1999/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
From shallow-water gravity wave theories it is shown that the velocity field in the whole fluid domain can be reconstructed using an analytic transformation (a renormalization). The resulting velocity field satisfies the Laplace equation exactly, which is not the case for shallow-water approximations. Applying the renormalization to the first-order shallow-water solution of limited accuracy, gives accurate simple solutions for both long and short waves, even for large amplitudes. The KdV and Airy solutions are special limiting cases.