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Incompressible Viscous Flows

  • Chung FangEmail author
Chapter
Part of the Springer Textbooks in Earth Sciences, Geography and Environment book series (STEGE)

Abstract

Flows of viscous fluids are discussed in this chapter, in which the fluid viscosity is intrinsically important. For simplicity, fluid density is considered constant, and the focus is on the characteristics of incompressible viscous flows. First, a general formulation of the field equations for viscous flows is presented, and the vorticity equation is derived, which provides a useful perspective in describing viscous flows. The exact solutions to the full Navier-Stokes equation for selected problems are presented. The approximate solutions to the Navier-Stokes equation for low-Reynolds-number flows, in the context of Stokes’ approximation, are discussed for selected problems. Similarly, large-Reynolds-number flows are introduced in the context of boundary-layer theory and Prandtl’s boundary-layer equations. These are considered equally an approximation to the Navier-Stokes equation, and some exact solutions to the obtained boundary-layer equations are presented by using similarity methods. On the other hand, the momentum integral and the Kármán-Pohlhausen method are introduced as the approximate methods in solving the boundary-layer equations, with a discussion on the stability of boundary layer. Buoyancy-driven flows, which are induced essentially by density variation, are discussed in the context of the Boussinesq approximation to the Navier-Stokes and thermal energy equations. The solutions to the resulting equations are presented for some problems with simple geometric configurations. The stability of a horizontal fluid layer is explored to study the conditions of the onset of thermal convection.

Further Reading

  1. P. Bradshaw, An Introduction to Turbulence and its Measurements (Pergamon Press, New York, 1971)zbMATHGoogle Scholar
  2. I.G. Currie, Fundamental Mechanics of Fluids, 2nd edn. (McGraw-Hill, Singapore, 1993)zbMATHGoogle Scholar
  3. O. Darrigol, Worlds of Flow: A History of Hydrodynamics from the Bernoulli to Prandtl (Oxford University Press, Oxford, 2005)zbMATHGoogle Scholar
  4. R.W. Fox, P.J. Pritchard, A.T. McDonald, Introduction to Fluid Mechanics, 7th edn. (Wiley, New York, 2009)zbMATHGoogle Scholar
  5. R.J. Goldstein (ed.), Fluid Mechanics Measurements, 2nd edn. (Taylor & Francis, New York, 1996)Google Scholar
  6. J. Happel, Low Reynolds Number Hydrodynamics (Prentice-Hill, New Jersey, 1965)Google Scholar
  7. J.O. Hinze, Turbulence, 2nd edn. (McGraw-Hill, New York, 1975)Google Scholar
  8. W.M. Kays, M.E. Crawford, Convective Heat and Mass Transfer, 3rd edn. (McGraw-Hill, Singapore, 1993)Google Scholar
  9. B.R. Munson, D.F. Young, T.H. Okiishi, Fundamentals of Fluid Mechanics, 3rd edn. (Wiley, New York, 1990)zbMATHGoogle Scholar
  10. R.L. Panton, Incompressible Flow, 2nd edn. (Wiley, New York, 1996)zbMATHGoogle Scholar
  11. R.H.F. Pao, Fluid Mechanics (Wiley, New York, 1961)Google Scholar
  12. L. Rosenhead, Laminar Boundary Layers (Dover, New York, 1963)zbMATHGoogle Scholar
  13. H. Schlichting, Boundary Layer Theory, 7th edn. (McGraw-Hill, New York, 1979)zbMATHGoogle Scholar
  14. F.S. Sherman, Viscous Flow (McGraw-Hill, New York, 1990)zbMATHGoogle Scholar
  15. Z. Sorbjan, Structure of the Atmospheric Boundary Layer (Prentice-Hall, New Jersey, 1989)Google Scholar
  16. H. Tennkes, J.L. Lumley, A First Course in Turbulence (The MIT Press, Cambridge, 1972)Google Scholar
  17. D.J. Tritton, Physical Fluid Dynamics (Oxford University Press, Oxford, 1988)zbMATHGoogle Scholar
  18. C. Tropea, A. Yarin, J.F. Foss (eds.), Springer Handbook of Experimental Fluid Mechanics (Springer, Berlin, 2007)Google Scholar
  19. A. Tsinober, An Informal Conceptual Introduction to Turbulence, 2nd edn. (Springer, Berlin, 2009)CrossRefGoogle Scholar
  20. J.M. Wallace, P.V. Hobbs, Atmospheric Science: An Introductory Survey, 2nd edn. (Elsevier, New York, 2006)Google Scholar
  21. F.M. White, Viscous Fluid Flow, 3rd edn. (McGraw-Hill, New York, 2006)Google Scholar
  22. M. Van Dyke, Perturbation Methods in Fluid Mechanics (The Parabolic Press, Stanford, 1975)zbMATHGoogle Scholar
  23. M. Van Dyke, An Album of Fluid Motion (The Parabolic Press, Stanford, 1988)Google Scholar

Copyright information

© Springer International Publishing AG 2019

Authors and Affiliations

  1. 1.Department of Civil EngineeringNational Cheng Kung UniversityTainanTaiwan

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