Note on Discrepancies between Two Theories on the Stability of Plane Poiseuille Flow

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概要

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• Existing theories of the hydrodynamical stability of plane Poiseuille flow are divided into two groups by their quite different conclusions. Results attained by Lin and other earlier authors are that this flow is unstable for sufficiently large Reynolds numbers. On the other hand, Pekeris has obtained different results that the flow is stable for any value of the Reynolds number and that, in addition to the ordinary disturbances discussed by earlier authors, there exists another class of perturbation which is characterized by c_r→1 as _αR→∞. In this paper a critical survey for these conflicting. results is presented. It is shown that Pekeris's first result arises essentially from the poor convergency of his series expansion of c, namely c=c_0+α_2c_1 + . . . , and that if this procedure is avoided, the existence of Lin's stability limit is asymptotically confirmed. It is also found that Pekeris's second prediction is erroneous.

• 社団法人日本物理学会の論文
• 1952-12-25

著者

• Tatsumi Tomomasa

  Department Of Physics Faculty Of Science University Of Kyoto

• Tatsumi Tomomasa

  Department Of Physics Faculity Of Science University Of Kyoto

関連論文

• The Modified Zero-Fourth Cumulant Approximation for Burgers Turbulence
• The Stability of a Free Boundary Layer at Large Reynolds Numbers
• The Modified Cumulant Expansion For Isotropic Turbulence At Large Reynolds Numbers
• Numerical Calculation of the Laminar Inlet Flow. I
• The Modified Cumulant Expansion for Two-Dimensional Homogeneous Turbulence with a Mean Flow
• Chapter VI Magneto-Fluid Dynamical Stability and Turbulence
• Stability of the Laminar Inlet-flow prior to the Formation of Poiseuille Regime, I
• Interaction of Plane Nonlinear Waves in a Compressible Fluid and Two-Dimensional Shock Turbulence
• Note on Discrepancies between Two Theories on the Stability of Plane Poiseuille Flow

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