The Re-Examination of Determining the Coefficient of the Amplitude Evolution Equation in the Nonlinear Theory of the Hydrodynamic Stability

Luo Ji-sheng

Volume 15 Issue 8

Turn off MathJax

Article Contents

Abstract

References

Article Navigation > Applied Mathematics and Mechanics > 1994 > 15(8): 709-712

Luo Ji-sheng. The Re-Examination of Determining the Coefficient of the Amplitude Evolution Equation in the Nonlinear Theory of the Hydrodynamic Stability[J]. Applied Mathematics and Mechanics, 1994, 15(8): 709-712.

Citation:

PDF( 249 KB)

The Re-Examination of Determining the Coefficient of the Amplitude Evolution Equation in the Nonlinear Theory of the Hydrodynamic Stability

Luo Ji-sheng

Department of Mechanics, Tianjin University, Tianjin

Received Date: 1993-03-24
Publish Date: 1994-08-15

Abstract

Abstract

One of the key problems in the nonlinear theory qf 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.
- disturbance velocity amplitude,
- Landau coefficient,
- solvability condition

FullText(HTML)

References(6)

References

[1]	Reynolds,W.C.and M.C.Potter,Finite amplitude instability of parallel shear flows,J.F.M.,27(1967),465-492.
[2]	Iton,N.,SlSatial growth of finite wave disturbances in parallel and nearly parallel flows,Part I.Theoreti,cal analysis and the numerical results for plane Poiseuille flow,Trans.Japan Soc.Aero.Space Sci.,17(1974),160-174.
[3]	Itoh,N.,Nonlinear stability of parallel flows with subcritical Reynolds.number,Part 1.An asymptotic theory valid for small amplitude disturbances,J.F.M.,89.(1977),455-467.
[4]	Davey,A.,On Itoh's finite amplitude stability theory for pipe flow,J.F.M..86(1978),695-703.
[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.
[6]	Herbert,T.,On perturbation methods in nonlinear stability theory,J.F.M.,126(1983),167-186.

Relative Articles

[1]	LI Yuanfei, XIAO Shengzhong, CHEN Xuejiao. Existence and Blow-Up Phenomena of Solutions to Heat Equations With Variable Coefficients Under Nonlinear Boundary Conditions[J]. Applied Mathematics and Mechanics, 2021, 42(1): 92-101. doi: 10.21656/1000-0887.410091
[2]	ZOU Li, WANG Zhen, ZONG Zhi, WANG Xi-jun, ZHANG Shuo. Analytical and Numerical Investigation of the Variable Coefficient Burgers Equation Under Cauchy Condition With the Exponential Homotopy Method[J]. Applied Mathematics and Mechanics, 2014, 35(7): 777-789. doi: 10.3879/j.issn.1000-0887.2014.07.007
[3]	LI Wang, YU Bo, WANG Xin-ran, SUN Shu-yu. Technique to Calculate Cell Face Velocity of a Non-Staggered Grid System[J]. Applied Mathematics and Mechanics, 2012, 33(8): 933-942. doi: 10.3879/j.issn.1000-0887.2012.08.003
[4]	DAI Zhen-xiang, XU Yuan-fen. Bifurcations of Traveling Wave Solutions and Exact Solutions of Generalized Zakharov Equation and Ginzburg-Landau Equation[J]. Applied Mathematics and Mechanics, 2011, 32(12): 1509-1516. doi: 10.3879/j.issn.1000-0887.2011.12.011
[5]	YAO Qing-liu. Solvability of a Class of Second-Order Quasilinear Boundary Value Problems[J]. Applied Mathematics and Mechanics, 2009, 30(8): 990-996. doi: 10.3879/j.issn.1000-0887.2009.08.012
[6]	LI Ji-bin. Exact Traveling Wave Solutions for an Integrable Nonlinear Evolution Equation Given by M. Wadati[J]. Applied Mathematics and Mechanics, 2008, 29(4): 393-397.
[7]	JIANG Wei-hua, GUO Yan-ping, QIU Ji-qing. Solvability of 2n-Order m-Point Boundary Value Problem at Resonance[J]. Applied Mathematics and Mechanics, 2007, 28(9): 1087-1094.
[8]	GUO Li-hui, FAN Tian-you. Solvability on Boundary-Value Problems of Elasyicity of Three-Dimensional Quasicrystals[J]. Applied Mathematics and Mechanics, 2007, 28(8): 949-957.
[9]	XU Gui-qiong, LI Zhi-bin. Explicit Solutions to the Coupled KdV Equations with Variable Coefficients[J]. Applied Mathematics and Mechanics, 2005, 26(1): 92-98.
[10]	LI Ming-an, WANG Zhong-min, GUO Zhi-yong]. A Semi-Analysis Method of Differential Equations With Variable Coefficients Under Complicated Boundary Conditions[J]. Applied Mathematics and Mechanics, 2003, 24(2): 215-220.
[11]	LI Hong-da, YE Zheng-lin, GAO Hang-shan. On the Continuity and Differentiability of a Kind of Fractal Interpolation Function[J]. Applied Mathematics and Mechanics, 2002, 23(4): 422-428.
[12]	Si Jianguo. Discussion on the Periodic Solutions for Linear Equation of Neutral Type with Constant Coefficients[J]. Applied Mathematics and Mechanics, 1996, 17(1): 29-37.
[13]	Zhou Zhi-hu. Solutions of the General n-th Order Variable Coefficients Linear Difference Equation[J]. Applied Mathematics and Mechanics, 1994, 15(3): 221-231.
[14]	Huang Yong-nian. The Explicit Solution of Homogeneous Linear Ordinary Differential Equations with Constant Coefficients[J]. Applied Mathematics and Mechanics, 1992, 13(12): 1069-1074.
[15]	Zhang Shi-xiong. Accurate Computation and Interpolation Technique of Finite Analytic Coefficients[J]. Applied Mathematics and Mechanics, 1992, 13(5): 421-428.
[16]	Zhang Hong-qing, Yang Guang. Constructions of the General Solution for a System of Partial Differential Equations with Variable Coefficients[J]. Applied Mathematics and Mechanics, 1991, 12(2): 135-139.
[17]	Cheng Chong-qing. Hopf-Landau Bifurcations of Higher Dimensional Tori[J]. Applied Mathematics and Mechanics, 1989, 10(6): 531-538.
[18]	Cheng Bao-long. The Continual Differentiate Peak-Unimodal Solutions of Feigenbaum’s Functional Equations[J]. Applied Mathematics and Mechanics, 1989, 10(5): 403-409.
[19]	Chen Song-qiang, Chou Kuan-wen. Inf-Dif-Stability of Oblique Perturbation[J]. Applied Mathematics and Mechanics, 1989, 10(9): 767-772.
[20]	Liao Zong-huang, Lu De-yuan. Instability of Solution for the Third Order Linear Differential Equation with Varied Coefficient[J]. Applied Mathematics and Mechanics, 1988, 9(10): 909-923.