The importance of being thin

Stephen H. Davis*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


This article outlines a family of approximations for solutions to the incompressible Navier–Stokes equations valid for flow domains that have one small dimension. The approach is applicable to two- or three-dimensional systems, steady or unsteady flows, viscous or inviscid fluids, high or low Reynolds numbers, and internal or external domains. Among the methods in this class are lubrication theories, slender-body theories, shallow-water theories, Hele–Shaw flows, and boundary layers. By displaying the commonalities in these, one sees a systematic approach to many fluid- flow problems as well as those in other fields.

Original languageEnglish (US)
Pages (from-to)3-30
Number of pages28
JournalJournal of Engineering Mathematics
Issue number1
StatePublished - Aug 1 2017


  • Asymptotic methods
  • Fluid mechanics
  • Long-scale phenomena

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)


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