On the non‐existence of continuous transonic flows past profiles II
On the non‐existence of continuous transonic flows past profiles II
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DOI：
10.1002/cpa.3160090104
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发表时间：
1956-02
影响因子：
3
通讯作者：
C. Morawetz
中科院分区：
文献类型：
--
作者：
C. Morawetz
本文证明了二维定常跨声速过障流的摄动问题是不正确的。这个定理已经以各种形式被提出[1,2,3,4]来解释连续跨音速流动的破裂。在此之前还没有给出严格的证据。这个定理的表述可以在[1]中找到猜想定理C。基本的合理性论点是由Busemann [2]， Frankl[3]和Guderley[2]提出的。摄动问题可以大致描述如下。假设在无限马赫数m < 1处，有一个稳定的连续对称跨声速流，经过由y= 4y (x)给出的剖面，具有连续可微的势q和流函数v。描述这种流的解析表达式是已知的，例如参见Lighthill， Cragg和Goldstein，或Tomatika和Tamada的工作。T和V构成了一类一阶非线性椭圆双曲方程边值问题的解，V在y=-Y (x)处消失。
In this paper we shall show that the perturbation problem belonging to a two-dimensional steady transonic flow past an obstacle is not correctly posed. This theorem has been proposed in various forms'[1, 2, 3, 4] as an explanation for the breakdown of continuous transonic flow. No rigorous proof has been given before. The statement of the theorem may be found as Conjectured Theorem C in [1]. The basic plausibility arguments were developed by Busemann [2], Frankl [3] and Guderley [4]. The perturbation problem may be described roughly as follows. Suppose for some Mach number at infinity, M.< 1, there is a steady continuous symmetric transonic flow, past a profile given by y= 4 Y (x), with continuously differentiable potential q and stream function V. Analytic expressions describing such flows are known, see for example the work of Lighthill, Cragg and Goldstein, or Tomatika and Tamada. T and V form a solution of a boundary value problem for a pair of nonlinear elliptic-hyperbolic equations of first order and V vanishes on y=-Y (x).