Abstract
The goal of this chapter is to present a deeper study of the relationship between viscous and nonviscous flows. We begin with a more detailed study of inviscid irrotational flows, i.e., potential flows. Then we go on to study boundary layers, where the main difference between slightly viscous and inviscid flows originates.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Reference
C. Anderson and C. Greengard, SIAM J. SIal. Compo 22[1985], 413
R. Abraham and J. Marsden, Foundations of Mechanics, 2nd Edition [1978]
J.E. Marsden and A. Weinstein, Coadjoint orbits, vortices and Clebsch variables for incompressible fluids, Physica 7D [1983] 305–323,.
L. Onsager, Nuovo Cimento 6 (Suppl.) [1949]229
A.J. Chorin, J. Fluid Mech.57[1973]781
AJ. Chorin, SIAM J. Sci. Stat. Comp. 1[1980]1.
O.H. Hald, SIAM J. Num. An. 16[1979]726
T. Beale and A. Majda, Math. Comp. 39[1982]1–28,29–52
K. Gustaffson and J. Sethian, Vortex Flows, SIAM Publications, 1989.
J. Heywood, Arch. Rat. Mech. 37[1970] 48–60, and Acta Math. 129[1972] 11–34
O.A. Olejnik, Soviet Math. Dokl. [1968]
J. Lamperti [1966] Probability, a Survey of the Mathematical Theory, Benjamin.
G.K. Batchelor [1967] An Introduction to Fluid Mechanics, Cambridge Univ. Press
J. Lighthill [1963] Introduction to Boundary Layer Theory, in Laminar Boundary Layers, edited by L. Rosenhead, Oxford Univ. Press.
A.J. Chorin, J. Compo Phys.27[1978]428.
A.J. Chorin, T.J.R. Hughes, M.J. McCracken and J.E. Marsden, Comm. Pure. Appl. Math. 31[1978]205
C. Anderson, J. Compo Phys. 80[1989]72
C. Marchioro and M. Pulvirenti, Vortex Methods in 2-dimensional Fluid Mechanics, Springer-Verlag, [1984]
K. Gustaffson and J. Sethian, Vortex Flows, SIAM publications [1990].
A. Chorin, J. Fluid Mech. 57[1973]785–796
J. Marsden, Bull. Am. Math. Soc. 80[1974]154–158
G. Benfauo and M. Pulvirenti, Convergence of the Chorin-Marsdcn product fromula in the half plane, Comm. Math. Phys. 106[1986]427–458.
J. Marsden and M. McCracken [1976] The Hopf Bifurcation. Springer Applied Mathematics Series
D. Sallinger [1973] Lectures on Stability and Bifurcation Theory. Springer Lecture Notes 309.
C.C. Lin [1955] The Theory of Hydrodynamic Stability, Cambridge
S. Chandrasekar [1961] Hydrodynamic and Hydromagnetic Stability, Oxford.
J. Marsden and T J.R. Hughes [1983] Mathematical Foundations of Elasticity, Prentice Hall
M. Golubitsky. I. Stewart and D. Schaeffer [1988] Symmetry and Groups in Bifurcation Theory, Vol. II, Springer-Verlag for further infonnation and references.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1990 Springer-Verlag New York Inc.
About this chapter
Cite this chapter
Chorin, A.J., Marsden, J.E. (1990). Potential Flow and Slightly Viscous Flow. In: A Mathematical Introduction to Fluid Mechanics. Texts in Applied Mathematics, vol 4. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-0364-0_2
Download citation
DOI: https://doi.org/10.1007/978-1-4684-0364-0_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4684-0366-4
Online ISBN: 978-1-4684-0364-0
eBook Packages: Springer Book Archive