Open AccessOn the theory of long waves and bores
Author(s) -
Lord Rayleigh
Publication year - 1914
Publication title -
proceedings of the royal society of london. series a, containing papers of a mathematical and physical character
Language(s) - English
Resource type - Journals
eISSN - 2053-9150
pISSN - 0950-1207
DOI - 10.1098/rspa.1914.0055
Subject(s) - section (typography) , elevation (ballistics) , point (geometry) , geometry , mathematics , motion (physics) , mechanics , physics , mathematical analysis , classical mechanics , advertising , business
In the theory of long waves in two dimensions, which we may suppose to be reduced to a "steady" motion, it is assumed that the length is so great in proportion to the depth of the water that the velocity in a vertical direction can be neglected, and that the horizontal velocity is uniform across each section of the canal. This, it should be observed, is perfectly distinct from any supposition as to the height of the wave. Ifl be the undisturbed depth, andh the elevation of the water at any point of the wave,u 0 ,u the velocities corresponding tol ,l +h respectively, we have, as the equation of continuity,u =lu 0 /l +h . (1) By the the principles of hydrodyamics, the increase of pressure due to retardation will be ½ρ (u 0 2 -u 2 ) =ρu 0 2 /2. 2lh +h 2 /(l +h )2 . (2)