Applied Mathematics and Mechanics

, Volume 15, Issue 8, pp 745–748 | Cite as

The re-examination of determining the coefficient of the amplitude evolution equation in the nonlinear theory of the hydrodynamic stability

  • Luo Ji-sheng


One of the key problems in the nonlinear theory of the hydrodynamic stability is to determine the law of the evolution of the disturbance velocity amplitude. The methods, which have been obtained, can only be used for quasi-neutral flow and have some artificial factors. In this paper, a method is proposed for this problem.

Key words

disturbance velocity amplitude Landau coefficient solvability condition 


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  1. [1]
    Reynolds, W. C. and M. C. Potter, Finite amplitude instability of parallel shear flows,J. F. M.,27 (1967), 465–492.zbMATHCrossRefGoogle Scholar
  2. [2]
    Iton, N., Spatial growth of finite wave disturbances in parallel and nearly parallel flows, Part I. Theoretical analysis and the numerical results for plane Poiseuille flow,Trans. Japan Soc. Aero. Space Sci.,17 (1974), 160–174.Google Scholar
  3. [3]
    Itoh, N., Nonlinear stability of parallel flows with subcritical Reynolds number, Part I. An asymptotic theory valid for small amplitude disturbances,J. F. M.,82 (1977), 455–467.zbMATHCrossRefGoogle Scholar
  4. [4]
    Davey, A., On Itoh's finite amplitude stability theory for pipe flow,J. F. M.,86 (1978), 695–703.zbMATHCrossRefGoogle Scholar
  5. [5]
    Zhou, H., On the nonlinear theory of stability of plane Poiseuille flow in subcritical range,Proc. Soc. Roy. Lond., A,318 (1982), 407–418.CrossRefGoogle Scholar
  6. [6]
    Herbert, T., On perturbation methods in nonlinear stability theory,J. F. M.,126 (1983), 167–186.zbMATHMathSciNetCrossRefGoogle Scholar

Copyright information

© SUT 1994

Authors and Affiliations

  • Luo Ji-sheng
    • 1
  1. 1.Department of MechanicsTianjin UniversityTianjin

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