Asymptotic Solution of the Instability Problem of Channel Flows with Antisymmetric Velocity Profile

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概要

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• Instability of channel flows of an incompressible viscous fluid with antisymmetric velocity profile U(y) is investigated at large values of Reynolds number R. The wave number α of the neutral disturbance of zero phase velocity is obtained as α^2=α_0^2-K(αR)^<-1/3>+O[(αR)^<-2/3>], where K=0.672[φ'(1)]^2/[∣U'(1)∣^<1/3>∫^1_0φ^2(y)dy], and α_0 and φ are respectively the eigenvalue of α and the eigenfunction in the limit αR=∞. The result is applied to the instability of a thermal convection between two parallel vertical plates kept at different temperatures, and it is found that α^2=5.20-9.83(αR)^<-1/3>+O[(αR)^<-2/3>]. Full neutral curve for this problem is obtained by numerical integration of the disturbance equations.

• 社団法人日本物理学会の論文
• 1972-03-05

著者

• Gotoh Kanefusa

  Research Institue For Mathematical Sciences University Of Kyoto

• IKEDA Norito

  Department of Physics, Faculty of Science, University of Kyoto

• Ikeda Norito

  Department Of Physics Faculty Of Science University Of Kyoto

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• Nonlinear Evolution of the Disturbance in a Natural Convection Induced in a Vertical Fluid Layer
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• The Stability of a Natural Convection between Two Parallel Vertical Planes
• Hydromagnetic Stability of Free Flows at Large Reynolds Numbers. : III. Free Boundary Layer with Small Magnetic Prandtl Number
• A Stability Condition in Parallel Flows of Small Magnetic Reynolds Number
• On the Effect of Pulsation upon the Instability of the Two-Dimensional Parallel Flow
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• Secondary Convection in a Fluid between Parallel Vertical Plates of Different Temperatures
• Thermal Convecion in a Horizontal Layer of Magnetic Fluids

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