Global stability of swept flow around a parabolic body: connecting attachment-line and crossflow modes

Abstract

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 β = 0.213, suggesting a preferred disturbance length scale in the sweep direction.