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Mack modes in supersonic boundary layer

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arxiv 2405.04853 v1 pith:LS6TW4LD submitted 2024-05-08 math.AP

Nader Masmoudi , Yuxi Wang , Di Wu , Zhifei Zhang This is my paper · ORCID
classification math.AP
keywords boundarylayermodessupersonicmacktransitionacousticaircraft
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Understanding the transition mechanism of boundary layer flows is of great significance in physics and engineering, especially due to the current development of supersonic and hypersonic aircraft. In this paper, we construct multiple unstable acoustic modes so-called Mack modes, which play a crucial role during the early stage of transition in the supersonic boundary layer. To this end, we develop an inner-outer gluing iteration to solve a hyperbolic-elliptic mixed type and singular system.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Unstable mode around the 3D boundary layer flow

    math.AP 2025-09 conditional novelty 8.0 of 10

    A class of 3D boundary layer profiles with independent streamwise and spanwise shear supports Navier-Stokes eigenmodes growing at rate exp(C alpha^3 t/sqrt(nu)), an instability absent in two dimensions.

  2. Structural stability of boundary layers in the entire subsonic regime

    math.AP 2025-01 conditional novelty 8.0 of 10

    A rigorous proof that subsonic boundary layer profiles are structurally stable for the steady compressible Navier-Stokes equations, plus a low Mach number limit with a Prandtl layer.

  3. Tollmien-Schlichting waves near neutral stable curve

    math.AP 2025-02 conditional novelty 7.0 of 10

    For small viscosity, exact Tollmien-Schlichting wave solutions exist for wavenumbers from ν^{1/8} to ν^{1/12}, with imaginary phase speed crossing zero at the lower and upper neutral branches.

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