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arXiv · 2511.13438

The dispersion relation of Tollmien-Schlichting waves

Dongfen Bian·Shouyi Dai·Emmanuel Grenier
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Abstract

It is well-known that shear flows in a strip or in the half plane are unstable for the Navier-Stokes equations if the viscosity $\nu$ is small enough, provided the horizontal wave number $\alpha$ lies in a small interval, between the so called lower and upper marginal stability curves. The corresponding instabilities are called Tollmien-Schlichting waves. In this letter, we give a simple presentation of the dispersion relation of these waves and study its mathematical properties.

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Dongfen Bian, Shouyi Dai, Emmanuel Grenier. 2025-11-17. The dispersion relation of Tollmien-Schlichting waves. https://arxiv.org/abs/2511.13438

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