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Spatial optimal growth in three-dimensional compressible boundary layers. (English) Zbl 1246.76025
Summary: This paper represents a continuation of the work by D. Tempelmann et al. [J. Fluid Mech. 646, 5–37 (2010; Zbl 1189.76221)] on spatial optimal growth in incompressible boundary layers over swept flat plates. We present an extension of the methodology to compressible flow. Also, we account for curvature effects. Spatial optimal growth is studied for boundary layers over both flat and curved swept plates with adiabatic and cooled walls. We find that optimal growth increases for higher Mach numbers. In general, extensive non-modal growth is observed for all boundary layer cases even in subcritical regions, i.e. where the flow is stable with respect to modal crossflow disturbances. Wall cooling, despite stabilizing crossflow modes, destabilizes disturbances of non-modal nature. Curvature acts similarly on modal as well as non-modal disturbances. Convex walls have a stabilizing effect on the boundary layer whereas concave walls have a destabilizing effect. The physical mechanisms of optimal growth in all studied boundary layers are found to be similar to those identified for incompressible flat-plate boundary layers.

MSC:
76E09 Stability and instability of nonparallel flows in hydrodynamic stability
76N20 Boundary-layer theory for compressible fluids and gas dynamics
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References:
[1] DOI: 10.1023/A:1011434805046 · Zbl 1094.76513
[2] Hanifi, FFA TN (1994)
[3] DOI: 10.1063/1.869698
[4] DOI: 10.1017/S0022112009994228 · Zbl 1189.76217
[5] Haj-Hariri, Stud. Appl. Math. 92 pp 41– (1994) · Zbl 0802.76025
[6] DOI: 10.1016/S0376-0421(99)00002-0
[7] DOI: 10.2514/2.6443
[8] DOI: 10.1017/S0022112092002453 · Zbl 0754.76029
[9] DOI: 10.1007/s10808-008-0023-5 · Zbl 1271.76095
[10] DOI: 10.1007/BF00271620 · Zbl 0748.76050
[11] Flügge, Handbuch der Physik, vol. VIII/1, Strömungsmechanik I (1959) · Zbl 0103.22504
[12] DOI: 10.1017/S0022112006009451 · Zbl 1147.76050
[13] DOI: 10.1023/A:1004367704897 · Zbl 0920.76025
[14] DOI: 10.1063/1.869908 · Zbl 1147.76308
[15] DOI: 10.1063/1.861156 · Zbl 0308.76030
[16] DOI: 10.1145/365723.365727
[17] Anderson, Hypersonic and High-Temperature Gas Dynamics (2006)
[18] DOI: 10.1023/A:1011489309543 · Zbl 1094.76512
[19] DOI: 10.1017/S0022112001003627 · Zbl 0987.76021
[20] Tumin, Phys. Fluids 13 (2001)
[21] DOI: 10.1017/S0305004100026220
[22] DOI: 10.1126/science.261.5121.578 · Zbl 1226.76013
[23] Ting, J. Math. Phys. 44 pp 353– (1965)
[24] DOI: 10.1017/S0022112009993260 · Zbl 1189.76221
[25] Simen, Instability, Transitions, and Turbulence pp 181– (1992)
[26] DOI: 10.1017/S0022112008004345 · Zbl 1156.76378
[27] DOI: 10.2514/1.9558
[28] DOI: 10.1017/S0022112093003738 · Zbl 0789.76026
[29] DOI: 10.1063/1.858386
[30] Mack, Meth. Comput. Phys. 4 pp 247– (1965)
[31] DOI: 10.1017/S0022112099007259 · Zbl 0959.76022
[32] DOI: 10.1023/B:APPL.0000004918.05683.46 · Zbl 1113.76321
[33] DOI: 10.1017/S0022112080000122 · Zbl 0428.76049
[34] DOI: 10.1063/1.3562843 · Zbl 06421671
[35] DOI: 10.1063/1.868864 · Zbl 1025.76536
[36] DOI: 10.1063/1.868205 · Zbl 0846.76026
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