Abstract
By the shock relationships, the wavy characteristics and the forming conditions of a shock wave are analyzed. The wavy characteristics of an Euler system are studied theoretically. The present research focuses on the wavy characteristics of Tollmien-Schlichting (T-S) waves, the excitation conditions of shocklets in compressible boundary layers, and the viscous effect on shock. The possibility of existence of shocklets in the compressible boundary layer and the physical mechanism of formation are theoretically interpreted.
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Fu, D. X. and Ma, Y. W. Methods of group velocity controlling and numerical simulation of threedimensional planar mixing layer. Proceedings of Modern Mechanics and Science and Technology Progress Conference, China Academy of Mechanics, Beijing, 533–538 (1997)
Yuan, X. J. and Zhou, H. A numerical study for small amplitude T-S waves in a supersonic boundary layer. Applied Mathematics and Mechanics (English Edition), 21(12), 1211–1214 (2000) DOI 10.1007/BF02459212
Shen, Q., Zhang, H. X., and Yuan, X. J. Numerical simulation of shock-lets within the supersonic boundary layer. Acta Aerodynamica Sinica, 18, 103–108 (2000)
Huang, Z. F. and Zhou, H. Evolution of a 2-D disturbance in a supersonic boundary layer and the generation of shocklets. Applied Mathematics and Mechanics (English Edition), 25(1), 1–8 (2004) DOI 10.1007/BF02437288
Cao, W. and Zhou, H. A numerical investigation of the evolution of 2-D disturbances in hypersonic boundary-layers and the effect on the flow structure due to the existence of shocklets. Science in China (Series G), 47(2), 244–255 (2004)
Whitham, G. B. On the propagation of weak shock wave. Journal of Fluid Mechanics, 1, 290–318 (1956)
Liepmann, H. W. and Roshko, A. Elements of Gasdynamics, Wiley, New York (1957)
Mack, L. M. Stability of the compressible laminar boundary layer according to a direct numerical simulation. Recent Developments in Boundary Layer Research, 97, 329–362 (1965)
Yuan, X. J., Tian, J. W., Shen, Q., and Li, Y. Shocklets in compressible flows. Applied Mathematics and Mechanics (English Edition), 34(12), 1453–1464 (2013) DOI 10.1007/s10483-013-1759-7
Lighthill, M. J. Viscosity effects in sound waves of finite amplitude. Surveys in Mechanics (eds. Batchelor, G. K. and Davies, R. M.), Cambridge University Press, London (1956)
Coleman, B. D., Herrera, I., and Truesdell, C. Wave Propagation in Dissipative Materials, Springer, New York (1965)
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Project supported by the National Natural Science Foundation of China (No. 10872018)
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Yuan, Xj., Liu, Zy., Shen, Q. et al. Theoretical investigation on shocklets in compressible boundary layers. Appl. Math. Mech.-Engl. Ed. 35, 935–946 (2014). https://doi.org/10.1007/s10483-014-1843-7
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DOI: https://doi.org/10.1007/s10483-014-1843-7