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The Shallow–Water Equations (SWEs), also referred to as the de Saint-Venant equations, constitute the current governing mathematical tool for free-surface water flows. These include, e.g., flood flows in rivers and in urban zones, flows across hydraulic structures as dams or wastewater facilities, flows in the environmental fields, glaciology, or meteorology. Despite this attractiveness, the system of two partial differential equations has an exact mathematical solution only for a limited number of problems of practical relevance.This historical work on the SWEs is based on a correspondence between two 19th-century scientists, de Saint-Venant and Boussinesq. Their well-known papers are thus commented from the point of development of their theory; the input of both scientists is evidenced by their writings, and comments of both to each other that led to what is commonly known as the SWEs. Given the age difference of the two of 45 years, the experienced engineer de Saint-Venant, and the mathematician Boussinesq, two eminent researchers, met to discuss not only problems in hydraulics, but in physics generally. In addition, their correspondence embraced also questions in ethics, religion, history of sciences, and personal news.The results of the SWEs cease to hold if streamline curvature effects dominate; this includes breaking waves, solitary and cnoidal waves, or non-linear waves in general. In most other cases, however, the SWEs perfectly apply to typical flows in engineering practice; they are considered the fundamental system of equations describing open channel flows. This work thus provides a background to its birth, including lots of comments as to its improvement, physical meanings, methods of solution, and a discussion of the results. This paper also deals with the steady flow equations, gives a short account on the main persons mentioned in the Correspondence, and provides a summary of further developments of the SWEs until 1920. 相似文献
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《Helvetica chimica acta》2017,100(12)
A collection of excerpts from letters written by R. B. Woodward to his friends, colleagues, young students and others is presented. These excerpts are representative of Woodward 's lengthy correspondence and illustrate many aspects of his personality and philosophies of life. 相似文献
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This obituary-tribute for Fred Basolo (1920–2007), the Charles E. and Emma H. Morrison Professor of Chemistry Emeritus at Northwestern University and 1983 President of the American Chemical Society, who died of congestive heart failure on February 27, 2007, discusses his life and work in chemical education, coordination chemistry, inorganic reaction kinetics and mechanisms, and service to science and society. 相似文献
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