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# The Stabilization Law for Transonic Flow

L. Pamela Cook and F. J. Zeigler
SIAM Journal on Applied Mathematics
Vol. 46, No. 1 (Feb., 1986), pp. 27-48
Stable URL: http://www.jstor.org/stable/2101485
Page Count: 22
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## Abstract

In this paper, the dependence of two-dimensional transonic flow over a thin airfoil on the free stream Mach number is analyzed. It is shown that for free stream Mach numbers (M) close to one, the flow near the airfoil and ahead of the shock differs from that at sonic (M = 1) to order K3 where K = (1 - M2)/δ2/3 and δ is the thickness ratio of the wing. This weak dependence explains the stabilization law or the freezing of the local Mach number near the airfoil and ahead of the shock at free stream Mach numbers near one. The result is obtained by the method of matched asymptotic expansions applied to the transonic small disturbance equations, in the physical plane for $M_\infty \lesssim 1$ and in the hodograph plane for $M_\infty \gtrsim 1$. Boundary value problems for the corrections are formulated and undetermined constants are found by use of Germain's conservation laws.

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