From Euler to Navier-Stokes : A Spatial Analysis of Conceptual Changes in Nineteenth-century Fluid Dynamics

Abstract

This article provides a spatial analysis of the conceptual framework of fluid dynamics during the nineteenth century, focusing on the transition from the Euler equation to the Navier–Stokes equation. A dynamic version of Peter Gärdenfors's theory of conceptual spaces is applied which distinguishes changes of five types: addition and deletion of special laws; change of metric; change in importance; change in separability; addition and deletion of dimensions. The case instantiates all types but the deletion of dimensions. We also provide a new view upon limiting case reduction at the conceptual level that clarifies the relation between the predecessor and successor conceptual framework. The nineteenth-century development of fluid dynamics is argued to be an instance of normal science development.