The spirited horse, the engineer, and the mathematician: water waves in nineteenth-century hydrodynamics
The main purpose of this article is to exemplify the symbiotic evolution of mathematical analysis and physical interpretation in the 19th century. With arguments taken from the theoretical and experimental research on water waves, it is shown that the need of solving the differential equations of certain problems of physics gave rise to new mathematical tools, and that the application of these tools to other physical phenomena provided them with a physical interpretation that greatly increased their efficiency. The paper is divided into five sections: 1. The theories of waves developed by Laplace, Lagrange, Poisson, and Cauchy; 2. The experiments on water waves that were executed by the naval engineer John Scott Russell in the 1830s and 1840s; 3. George B. Airy's wave theory of tides; 4. The problem of finite waves of permanent shape, as studied by Stokes, Boussinesq, and Rayleigh; 5. The application of optical and acoustic ideas of interference to the explanation of water wave phenomena.
scientific article; zbMATH DE number 2032491
scientific article