High frequency analysis of the unsteady Interactive Boundary Layer model

TL;DR

This paper investigates the unsteady Interactive Boundary Layer (IBL) model's stability, revealing significant high-frequency instabilities that differ from classical Tollmien-Schlichting waves, impacting its numerical and theoretical applications.

Contribution

It provides the first linear stability analysis of the unsteady IBL model, identifying strong unrealistic high-frequency instabilities not previously documented.

Findings

Unsteady IBL exhibits strong high-frequency instabilities.

Instabilities are distinct from Tollmien-Schlichting waves.

Similar instabilities are found in the Prescribed Displacement Thickness model.

Abstract

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. We 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. We 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.