Three-dimensional wave packet in a Mach 6 boundary layer on a flared cone

Linear, nonlinear and transitional regimes of second-mode instability

“…This observation indicates that in the presence of unbiased spanwise variations upstream, fundamental resonance is the preferable mode of breakdown for a given 2-D second-mode wave. Fundamental resonance has also been observed to arise naturally in HBLs over flared cones by Hader & Fasel (2019, 2020).…”

“…This observation indicates that in the presence of unbiased spanwise variations upstream, fundamental resonance is the preferable mode of breakdown for a given 2-D second-mode wave. Fundamental resonance has also been observed to arise naturally in HBLs over flared cones by Hader & Fasel (2019, 2020. At further downstream locations, x > 3, the frequency spectrum is broadband, with no trace of dominance of the forcing harmonic, or its multiples.…”

“…The envelope of the nonlinear wave is also asymmetric and modulated as evident in the range, 1.5 ≤ x ≤ 2. Such modulations are characteristic of nonlinear saturation (Hader & Fasel 2020) and will be further examined below in the spectral domain. Beyond x = 2 the linear response decays monotonically, whereas the nonlinear response exhibits a second region of amplification between 2 ≤ x ≤ 2.5.…”

Toward a unified interpretation of the “proper”/“smooth” orthogonal decompositions and “state variable”/“dynamic mode” decompositions with application to fluid dynamics

“…16,17 Second modes are thought to be trapped acoustic waves, which resonate within a thermoacoustic impedance well formed between the vehicle wall and the maximum boundary layer density gradient, with thermoacoustic Reynolds stresses providing the fundamental energy source. [18][19][20] As secondmode waves behave as wave packets (finite-frequency-bandwidth disturbances) in the boundary layer, [21][22][23] they exhibit a nonlinear breakdown physics that is particularly relevant to our investigation: (1) The primary 300 kHz second-mode wave packet grows linearly.…”

Wall pressure beneath a transitional hypersonic boundary layer over an inclined straight circular cone

“…The instability mechanism is accordingly much more complicated than that in extensively studied two-dimensional boundary layers (e.g. [1][2][3]), especially in hypersonic conditions. Therefore, in the last decades, considerable efforts have been made towards building a fundamental understanding to the transition of hypersonic three-dimensional boundary layers by wind tunnel experiments [4][5][6][7][8][9], theoretical analyses [10][11][12][13], direct numerical simulations (Chen et al: Transition of hypersonic boundary layer over a yawed blunt cone, submitted) (Chen et al: Stationary cross-flow breakdown in a high-speed swept-wing boundary layer, submitted) and flight tests (see overview [14]).…”