Wave packets and supersonic second modes in a high-speed boundary layer

Research output: Chapter in Book/Report/Conference proceedingConference contribution

5 Scopus citations


An initial-value problem is formulated for a wave packet in a two-dimensional compressible boundary layer flow. The problem is solved using the Fourier transform with respect to the streamwise and spanwise coordinates and eigenfunction expansion into modes of continuous and discrete spectra of temporal stability theory. The spectra of two-dimensional perturbations are analyzed numerically for a hypersonic flow with Mach number M = 6 and the wall-to-edge temperature ratio Tw/Te = 0.5. An example of a two-dimensional temperature spot is considered. The inverse Fourier transform is obtained numerically for a portion of the wave packet comprised of the second Mack modes. Solution in the physical domain reveals existence of a satellite wave packet with an acoustic-like beam protruding into the outer flow as it was observed in earlier DNS results. The wave packet structure is attributed to branching of unstable discrete mode F at the point of synchronization with the slow acoustic mode leading to the appearance of a local maximum in the growth rate of supersonic second modes. Although there is a mechanism of energy transfer from a perturbation to the outer flow, the leading part of the wave packet is dominated by subsonic second modes confined inside the boundary layer.

Original languageEnglish (US)
Title of host publicationAIAA Scitech 2020 Forum
PublisherAmerican Institute of Aeronautics and Astronautics Inc, AIAA
Number of pages13
ISBN (Print)9781624105951
StatePublished - 2020
EventAIAA Scitech Forum, 2020 - Orlando, United States
Duration: Jan 6 2020Jan 10 2020

Publication series

NameAIAA Scitech 2020 Forum


ConferenceAIAA Scitech Forum, 2020
Country/TerritoryUnited States

ASJC Scopus subject areas

  • Aerospace Engineering


Dive into the research topics of 'Wave packets and supersonic second modes in a high-speed boundary layer'. Together they form a unique fingerprint.

Cite this