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Global stability of swept flow around a parabolic body: Connecting attachment-line and crossflow modes. (English) Zbl 1151.76469
Summary: The global linear stability of a three-dimensional compressible flow around a yawed parabolic body of infinite span is investigated using an iterative eigenvalue method in conjunction with direct numerical simulations. The computed global spectrum shows an unstable branch consisting of three-dimensional boundary layer modes whose amplitude distributions exhibit typical characteristics of both attachment-line and crossflow modes. In particular, global eigenfunctions with smaller phase velocities display a more pronounced structure near the stagnation line, reminiscent of attachment-line modes while still featuring strong crossflow vortices further downstream. This analysis establishes a link between the two prevailing instability mechanisms on a swept parabolic body which, so far, have only been studied separately and locally. A parameter study shows maximum modal growth for a spanwise wavenumber of \(\beta = 0.213\), suggesting a preferred disturbance length scale in the sweep direction.

MSC:
76E09 Stability and instability of nonparallel flows in hydrodynamic stability
76N15 Gas dynamics (general theory)
76M20 Finite difference methods applied to problems in fluid mechanics
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References:
[1] DOI: 10.1017/S0022112095002746 · Zbl 0850.76203
[2] DOI: 10.1063/1.2187450 · Zbl 1185.76862
[3] Hall, Proc. R. Soc. Lond. 395 pp 229– (1984)
[4] DOI: 10.1017/S0022112006001303 · Zbl 1209.76012
[5] DOI: 10.1016/S0045-7930(00)00002-5 · Zbl 0991.76056
[6] DOI: 10.1146/annurev.fluid.35.101101.161045 · Zbl 1039.76018
[7] DOI: 10.1063/1.1383592 · Zbl 1184.76152
[8] DOI: 10.1146/annurev.fl.21.010189.001315
[9] DOI: 10.1006/jcph.1994.1007 · Zbl 0792.76062
[10] Poll, Aero. Q. 30 pp 607– (1979)
[11] DOI: 10.1016/S0376-0421(99)00002-0
[12] Oswatitsch, Gas Dynamics (1956)
[13] DOI: 10.1017/S0022112096004260 · Zbl 0891.76026
[14] DOI: 10.1017/S0022112096002583 · Zbl 0953.76025
[15] DOI: 10.1146/annurev.fluid.29.1.245
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