Nonlinear spectral dynamics of hypersonic laminar boundary layer flow

Abstract

Articles you may be interested inA high-order numerical method to study hypersonic boundary-layer instability including high-temperature gas effects Phys. Fluids 23, 084108 (2011); 10.1063/1.3614526On the relationship between the wall-shear-stress and transient-growth disturbances in a laminar boundary layerThe nonlinear interactions of the instability modes in a hypersonic laminar boundary layer undergoing natural transition are examined using bispectral analysis. The data are from an experiment of a boundary layer flow on a cooled-wall cone in a low-level free-stream disturbance hypersonic wind tunnel, and thus, the bispectral measurements are a good representation of the natural transition processes. The bispectral analysis shows that in the initial stages of transition the dominant nonlinear interaction is forcing by the fundamental to generate a harmonic. Subsequently, mutual forcing of the fundamental and harmonic yield a second harmonic. Difference interactions within the band of unstable disturbances centered on the fundamental and harmonic also generate a low frequency nonlinear interaction. At high amplitudes of the fundamental and harmonic a nonlinear interaction characterized by a low frequency modulation of the fundamental and harmonic then follows. This nonlinear interaction is then the most dominant and precedes the breakdown of the laminar flow.

Traveling Crossflow Instability for HIFiRE-5 in a Quiet Hypersonic Wind Tunnel

“…Quadratic phase coupling occurs when the sum of phase components of disturbances at frequencies f 1 and f 2 is equal to the phase of the disturbance at the sum or difference frequency (f 1 ± f 2 ). 57 That is,…”

Transition in Hypersonic Boundary Layers: Role of Dilatational Waves

“…Kimmel and Kendall [40] attributed the low-frequency mode to be the response of the boundary layer to the ambient tunnel disturbances and argued that the low-frequency waves modulate frequencies near the second mode and transfer energy to the sidebands. On the other hand, Chokani [41] believed that the low-frequency modes arise from nonlinear interactions within a limited band of waves centered on the fundamental and harmonic waves.…”

“…Kimmel and Kendall [40] used bispectral analysis to examine the nonlinear interactions in naturally occurring waves in boundary layers on cone shapes in a conventional Mach 8 tunnel. Chokani [41] analyzed the hot-wire data acquired in a Mach 6 quiet tunnel (M6QT) on a flared cone. The analyses showed that the harmonic generation is indeed a sum-frequency wave interaction that is a consequence of phasecoherent nonlinearity.…”

Transition of natural convection boundary layers—a revisit by Bicoherence analysis

“…The Bicoherence analysis is a relatively new statistical approach, which is able to identify and quantify the degree of quadratic phase coupling of frequencies within each power spectrum. In recent years, this approach has been used to study nonlinear processes in transitioning boundary layer flows, for instance in [16][17][18]13]. A Bicoherence spectrum is a normalized bispectrum, which is a third-order cumulant function obtained by (see [13])…”