Empirical Challenges and Concept Formation in the History of Hydrodynamics

Abstract

Abstract Although the fundamental equations of hydrodynamics were known at an early stage of its history, this theory long remained irrelevant to most of the practical problems of flow. The advent of a more efficient fluid mechanics in the early twentieth century depended on conceptual schemes that could not be read directly from the basic equations. Attention to concrete problems of flow, rather than purely mathematical deduction or purely intuitive guessing, permitted the gradual introduction of relevant substructures and their ultimate combination in powerful approximation schemes. This history is in part singular, owing to the extreme difficulty of dealing with non-linear systems with infinitely many degrees of freedom. But it is also typical as an illustration of the futility of reducing a physico-mathematical theory to its fundamental equations. Any advanced theory of physics must include an evolving modular structure that plays an essential role in melding the formal with the empirical.

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