1966/06/01 by D. H. Peregrine · 3 citations
Engineering · Mathematics · Physics and Astronomy · #Development (topology) #Elevation (ballistics) #Finite difference #Flow (mathematics) #Free surface #Geology #Geometry #Hydraulic flow and structures #Mathematical analysis #Mathematics #Mechanics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Partial differential equation #Physics
paper · doi:10.1017/s0022112066001678
openalex publication_date 1966/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
If a long wave of elevation travels in shallow water it steepens and forms a bore. The bore is undular if the change in surface elevation of the wave is less than 0·28 of the original depth of water. This paper describes the growth of an undular bore from a long wave which forms a gentle transition between a uniform flow and still water. A physical account of its development is followed by the results of numerical calculations. These use finite-difference approximations to the partial differential equations of motion. The equations of motion are of the same order of approximation as is necessary to derive the solitary wave. The results are in general agreement with the available experimental measurements.