Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Mathematics applied in fluid motion

Author: J. T. Stuart
Journal: Quart. Appl. Math. 56 (1998), 787-796
MSC: Primary 76F99; Secondary 76D99, 76E99
DOI: https://doi.org/10.1090/qam/1668738
MathSciNet review: MR1668738
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Over many decades, indeed for more than a century, fluid dynamics has been the subject of many beautiful experiments and has been a proving ground for a wealth of mathematical theories, both linear and nonlinear.

References [Enhancements On Off] (What's this?)

  • [1] D. J. Benney and R. F. Bergeron, A new class of nonlinear waves in parallel flows, Studies Appl. Math. 48, 181-204 (1969)
  • [2] B. Cantwell, D. Coles, and P. Dimotakis, Structure and entrainment in the plane of symmetry of a turbulent spot, J. Fluid Mech. 87, 641-672 (1978)
  • [3] V. W. Ekman, On the change from laminar to turbulent motion in liquids, Ark. Mat. Astr. Fys. 6, No. 12 (1910)
  • [4] H. W. Emmons and A. E. Bryson, The laminar-turbulent transition in a boundary layer, Proc. 1st U.S. National Cong. Appl. Mech., 859-868 (1951) MR 0052931
  • [5] M. Gaster, The development of a two-dimensional wave packet in a growing boundary layer, Proc. Roy. Soc. A384, 317-332 (1982)
  • [6] D. Henningsen, P. Spalart, and J. Kim, Numerical simulations of turbulent spots in plane Poiseuille flow, Phys. Fluids 30, 2914-2917 (1987)
  • [7] P. S. Klebanoff, K. D. Tidstrom, and L. M. Sargent, The three-dimensional nature of boundary-layer instability, J. Fluid Mech. 12, 1-34 (1962)
  • [8] O. Reynolds, An experimental investigation of the circumstances which determine whether the motion of the water shall be direct or sinuous, and of the law of resistance in parallel channels, Phil. Trans. Roy. Soc. A174, 935-982 (1883)
  • [9] L. Rosenhead, editor, Laminar Boundary Layers, Clarendon Press, Oxford, 1963 MR 0155499
  • [10] G. B. Schubauer and P. S. Klebanoff, Contributions on the mechanics of boundary layer transition, Proc. Sympos. Boundary Layer Effects in Aerodynamics, Nat. Phys. Lab. Teddington. Also Rep. Nat. Adv. Comm. Aero. Washington, No. 1289, 1955
  • [11] G. B. Schubauer and H. K. Skramstad, Laminar boundary layer oscillations and transition on a flat plate, Rep. Nat. Adv. Comm., Washington, No. 909. Also J. Res. Nat. Bur. Stand. Washington, 38, 251-292, and J. Aero. Sci. 14, 69-78 (1947)
  • [12] J. T. Stuart, Instability and transition in pipes and channels, In ``Transition and Turbulence'' (ed. R. E. Meyer), Academic Press, 1981, pp. 77-94 MR 636118
  • [13] J. T. Stuart, Evolution of vorticity in flow in a pipe, Exptl. Thermal. Fluid Sci. 13, 206-210 (1996)
  • [14] J. T. Stuart, Singularities in three-dimensional compressible Euler flows with vorticity, Theor. Comp. Fluid Dyn. 10, 385-391 (1998)
  • [15] T. Tatsumi, Stability of the laminar inlet-flow prior to the formation of Poiseuille régime, I, II, J. Phys. Soc. Japan 7, 489-495, 495-502 (1952) MR 0051077
  • [16] G. I. Taylor, Dispersion of soluble matter in solvent flowing slowly through a tube, Proc. Roy. Soc. A219, 186-203 (1953)
  • [17] G. I. Taylor, The dispersion of matter in turbulent flow through a pipe, Proc. Roy. Soc. A223, 446-468 (1954)
  • [18] I. J. Wygnanski and F. H. Champagne, On transition in a pipe. Part 1. The origin of puffs and slugs and the flow in a turbulent slug, J. Fluid Mech. 59, 281-335 (1973)
  • [19] I. J. Wygnanski, M. Sokolov, and D. Friedman, On transition in a pipe. Part 2. The equilibrium puff, J. Fluid Mech. 69, 283-304 (1975)
  • [20] F. T. Smith and R. J. Bodonyi, Amplitude-dependent neutral modes in the Hagen-Poiseuille flows through a circular pipe, Proc. Roy. Soc. A384, 463-489 (1982)

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 76F99, 76D99, 76E99

Retrieve articles in all journals with MSC: 76F99, 76D99, 76E99

Additional Information

DOI: https://doi.org/10.1090/qam/1668738
Article copyright: © Copyright 1998 American Mathematical Society

American Mathematical Society