B122 垂直平板に沿う自然対流の安定性解析

概要

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Natural convection evolving along a vertical flat plate is considered under (i) isothermal and (ii) uniform-heat-flux plate boundary conditions. Basic flow is assumed to be governed by steady boundary layer equations. Linear and weakly-nonlinear stability analysis of the basic flow is made with the aid of the Galerkin method in which the field variables are expanded in terms of Chebyshev polynomials. The Stewartson-Stuart equation for the propagating disturbance is derived for the cases of the Prandtl number Pr=0.733 and Pr=6.7. The main results are such that (i) the motion is supercritical over almost all the linearly unstable region except for a narrow boundary region defined by small wavenumbers; (ii) Iluerre's criterion shows the motion is convectively unstable along the most highly amplified path over the whole computed range of the Reynolds number; (iii) Newell's criterion shows the motion tends to be modulationally unstable at lower values of the Reynolds number especially in air.
日本流体力学会の論文
2000-07-25