The linear instability of the three-dimensional boundary-layer over the HIFiRE-5 flight test geometry, i.e. a rounded-tip 2:1 elliptic cone, at Mach 7, has been analyzed through spatial BiGlobal analysis, in a effort to understand transition and accurately predict local heat loads on next-generation flight vehicles. The results at an intermediate axial section of the cone, Re_x ≈ 8 × 10~5, show three different families of spatially amplified linear global modes, the attachment-line and cross-flow modes known from earlier analyses, and a new global mode, peaking in the vicinity of the minor axis of the cone, termed "center-line mode". We discover that a sequence of symmetric and anti-symmetric centerline modes exist and, for the basic flow at hand, are maximally amplified around F~* = 130 kHz. The wavenumbers and spatial distribution of amplitude functions of the centerline modes are documented.
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