Airfoil in a sonic shear flow jet: a mixed boundary value problem for the generalized Tricomi equation
Authors:
C. C. Chang and T. S. Lundgren
Journal:
Quart. Appl. Math. 17 (1960), 375-392
MSC:
Primary 76.00; Secondary 35.00
DOI:
https://doi.org/10.1090/qam/109564
MathSciNet review:
109564
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Abstract: In this paper, small perturbations of a non-uniform two-dimensional flow of a compressible inviscid fluid are considered. It is shown that for a particular class of main stream Mach number distributions, which are characterized by a sonic line along the $x$-axis, the linearized shear flow equation may be transformed into the generalized Tricomi equation. The mixed boundary value problem which results from considering perturbations generated by a two-dimensional camber surface is formulated and solved by utilizing the Wiener-Hopf technique.
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- Chieh-Chien Chang and Jack Werner, A solution of the telegraph equation with application to two dimensional supersonic shear flow, J. Math. Physics 31 (1952), 91–101. MR 0049458
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F. Tricomi, On linear partial differential equations of second order of mixed type, translation A9–T–26 Graduate Division of Applied Mathematics, Brown University, 1948
R. Paley and N. Wiener, The Fourier-transform in the complex domain, Am. Math. Soc., Colloquium Publ., 1934
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G. N. Watson, Bessel functions, Cambridge Univ. Press, 1954
- J. A. Lewis and G. F. Carrier, Some remarks on the flat plate boundary layer, Quart. Appl. Math. 7 (1949), 228–234. MR 34160, DOI https://doi.org/10.1090/S0033-569X-1949-34160-7
A. Erdelyi, W. Magnus, etc., Tables of integral transforms, vols. 1, 2, McGraw-Hill, New York, 1954
E. T. Whittaker and G. N. Watson, Modern analysis, Cambridge Univ. Press, 1935
M. J. Lighthill, Reflection at a laminar boundary layer of a weak steady disturbance to a supersonic stream, neglecting viscosity and heat conduction, Quart. J. Mech. and Appl. Math. III–,305–325 (1950)
C. C. Chang and J. Werner, A solution of the telegraph equation with application to two dimensional supersonic shear flow, J. Math, and Phys. 31, 91–101 (1952)
G. N. Ward, Linearized theory of steady high-speed flow, Cambridge Univ. Press, 1955
F. Tricomi, On linear partial differential equations of second order of mixed type, translation A9–T–26 Graduate Division of Applied Mathematics, Brown University, 1948
R. Paley and N. Wiener, The Fourier-transform in the complex domain, Am. Math. Soc., Colloquium Publ., 1934
P. M. Morse and H. Feshbach, Methods of theoretical physics, McGraw-Hill, New York, 1953
G. F. Carrier, A generalization of the Wiener-Hopf technique, Quart. Appl. Math. 7, 105–109 (1949)
G. N. Watson, Bessel functions, Cambridge Univ. Press, 1954
J. A. Lewis and G. F. Carrier, Some remarks on the flat plate boundary layer, Quart. Appl. Math. 7, 228–234 (1949)
A. Erdelyi, W. Magnus, etc., Tables of integral transforms, vols. 1, 2, McGraw-Hill, New York, 1954
E. T. Whittaker and G. N. Watson, Modern analysis, Cambridge Univ. Press, 1935
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© Copyright 1960
American Mathematical Society
