Applying Models in Fluid Dynamics

Abstract

The following article treats the ‘applicational turn’ of modern fluid dynamics as it set in at the beginning of the 20th century with Ludwig Prandtl’s concept of the boundary layer. It seeks to show that there is much more to applying a theory in a highly mathematical field like fluid dynamics than deriving a special case from a general explanatory theory under particular antecedent conditions. In Prandtl’s case, the decisive move was to introduce a model that provided a physical/causal conception of viscous flow at high Reynolds numbers. It facilitated an approximate solution to the Navier–Stokes equations, which in turn gave rise to many special applications. After a detailed account of Prandtl’s achievement, the article discusses the role of the physical model and its experimental and mathematical significance. It is shown that the mathematical simplification provided by the physical model greatly expanded the explanatory capacity of the theory which the Navier–Stokes equations alone could not provide.

Acknowledgements

I am grateful to Bruno Eckhardt, Michael Eckert, Moritz Epple, Axel Gelfert, Johannes Lenhard, John Michael, Gregor Schiemann, Reinhard Siegmund‐Schultze, and the participants of the workshop on ‘Applying Science’, at the PSA 2004 in Austin, Texas, but above all to Mohamed Gad‐el‐Hak of Virginia Commonwealth University, for valuable comments on a former version of the paper.

Additional information

Notes on contributors

Michael Heidelberger

Michael Heidelberger is at Universität Tübingen, Germany.