High Frequency Analysis of the Unsteady Interactive Boundary Layer Model | Zendy

Anne-Laure Dalibard | Zendy; Helge Dietert | Zendy; David GérardVaret | Zendy; Frédéric Marbach | Zendy

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High Frequency Analysis of the Unsteady Interactive Boundary Layer Model

Author(s) -

Anne-Laure Dalibard,

Helge Dietert,

David GérardVaret,

Frédéric Marbach

Publication year - 2018

Publication title -

siam journal on mathematical analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.882

H-Index - 92

eISSN - 1095-7154

pISSN - 0036-1410

DOI - 10.1137/17m1157477

Subject(s) - boundary layer , prandtl number , mechanics , stability (learning theory) , physics , displacement (psychology) , boundary (topology) , flow (mathematics) , instability , linear stability , boundary value problem , mathematics , classical mechanics , mathematical analysis , computer science , convection , psychology , machine learning , psychotherapist

The present paper is about a famous extension of the Prandtl equation, the so-called Interactive Boundary Layer model (IBL). This model has been used intensively in the numerics of steady boundary layer flows, and compares favorably to the Prandtl one, especially past separation. consider here the unsteady version of the IBL, and study its linear well-posedness, namely the linear stability of shear flow solutions to high frequencyperturbations. show that the IBL model exhibits strong unrealistic instabilities, that are in particular distinct from the Tollmien-Schlichting waves. We also exhibit similar instabilities for a Prescribed Displacement Thickness model (PDT), which is one of the building blocks of numerical implementations of the IBL model.

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