On the inviscid energetics of Mack’s first mode instability

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Theoretical and Computational Fluid Dynamics
High-speed boundary layer transition is dominated by the modal, exponential amplification of the oblique Mack’s first mode waves in two-dimensional boundary layers from Mach 1 up to freestream Mach numbers of 4.5 to 6.5 depending on the wall-to-adiabatic temperature ratio. At higher Mach numbers, the acoustic, planar Mack’s second mode waves become dominant. Although many theoretical, computational and experimental studies have focused on the supersonic boundary layer transition due to the oblique Mack’s first mode, several fundamental questions about the source of this instability and the reasons for its obliqueness remain unsolved. Here, we perform an inviscid energetics investigation and classify disturbances based on their energetics signature on a Blasius boundary layer for a range of Mach numbers. This approach builds insight into the fundamental mechanisms governing various types of instability. It is shown that first mode instability is distinct from Tollmien–Schlichting instability, being driven by a phase shifting between streamwise velocity and pressure perturbations in the vicinity of the generalized inflection point and insensitive to the viscous no-slip condition. Further, it is suggested that the obliqueness of the first mode is associated with an inviscid flow invariant.
This version of the article has been accepted for publication in Theoretical and Computational Fluid Dynamics, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/s00162-022-00636-9. This article will be embargoed until 12/22/2023.
hypersonic boundary layer stability, Mack’s first mode, Mack’s second mode, Tollmien–Schlichting instability
Liang, T., Kafle, S., Khan, A.A. et al. On the inviscid energetics of Mack’s first mode instability. Theor. Comput. Fluid Dyn. (2022). https://doi.org/10.1007/s00162-022-00636-9