Inviscid instability of the hyperbolic-tangent velocity profile-spectral "tau" solution

• Autorzy: Bogusławski A.
• Języki publikacji: EN

Abstrakty

EN

The paper presents a spectral solution of the Rayleigh equation for the case of parallel, free shear layer with the hyperbolic-tangent mean velocity profile. The expansion of the eigenfunction into the Chebyshev polynomial series allowed transformation of the differential eigenvalue problem into the general algebraic one. The standard algebraic eigenvalue problem was obtained by the use of Gary & Helgasson transformation. The results were compared with the shooting method. Although the calculations were carried out in order to validate the method, some additional study of the velocity ratio and momentum thickness influence on the temporal eigenmode growth rate was also performed.

Słowa kluczowe

EN

parallel free shear layer; free shear layer; linear stability theory; spectral approximation; Tau method; Q-R algorithm

• Wydawca: Politechnika Gdańska
• Czasopismo: TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk
• Rocznik: 2001
• Tom: Vol. 5, No 2
• Strony: 155--164
• Opis fizyczny: Bibliogr. 20 poz., rys., tab.

Twórcy

autor

Bogusławski A.

• Institute of Thermal Machinery, Technical University of Częstochowa, Armii Krajowej 36, 42-200 Częstochowa, Poland

Bibliografia

• [1] Schlichting H 1979 Boundary-Layer Theory Mc Graw-Hill Book Company
• [2] Michalke A 1964 J. Fluid Mech. 19 543
• [3] Michalke A 1965 J. Fluid Mech. 23 521
• [4] Monkewitz P A and Huerre P 1982 Phys. Fluids 25 1137
• [5] Michalke A and Herman G 1982 J. Fluid Mech. 114 343
• [6] Ho Ch-M and Huerre P 1984 Ann. Rev. Fluid Mech. 16 365
• [7] Landau L and Lifshitz E M 1959 Fluid Mechanics Pergamon, London
• [8] Bers A 1975 Linear Waves and Instabilities In Physique des Plasmas, ed. C. DeWitt, J. Peyraud, New York: Gordon & Breach, pp. 117-215
• [9] Briggs R J 1964 Electron-Stream Interaction With Plasmas Mass: MIT Press, Cambridge
• [10] Monkewitz P A and Sohn K D 1988 AIAA Journal 26 (8) 911
• [11] Jendoubi S and Strykowski P J 1994 Phys. Fluids 6 (9) 3000
• [12] Gary J and Helgason R 1970 J. Comput. Phys. 5 169
• [13] Monkewitz P A, Bechert D W, Barsikow B and Lehman B 1990 J. Fluid Mech. 213 611
• [14] Boyd J P 1989 Chebyshev and Fourier Spectral Methods Lecture Notes in Engineering, vol. 49, Springer-Verlag
• [15] Gottlieb D and Orszag S A 1977 Numerical Analysis of Spectral Methods: Theory and Applications SIAM Philadelphia, Pensylwania
• [16] Canuto C, Quarteroni A, Hussaini M Y and Zang T A 1988 Spectral Methods in Fluid Dynamics Springer-Verlag
• [17] Orszag S A 1971 J. Fluid Mech. 50 (4) 689
• [18] Press W H, Teukolsky S A, Vetterling W T and Flannary B P 1992 Numerical Recipes in C. The art of scientific computing Cambridge University Press
• [19] Wilkinson J H 1965 The Algebraic Eigenvalue Problem Oxford University Press
• [20] Kyle D M and Sreenivasan K R 1993 J. Fluid Mech. 249 619