October 3, 2025Open Access

Unstable mode around the 3D boundary layer flow

Key Points

An unstable mode exhibits rapid growth with a rate of e^{t/√ν}, indicating significant instability.
The study focuses on three-dimensional shear flows governed by the Navier-Stokes equations under small viscosity conditions.
Instability arises from interactions between spanwise flow and perturbations, distinct from two-dimensional flows.
Findings provide insights into the behavior of boundary layer flows that can influence engineering applications.

Abstract

We study the stability properties of boundary layer-type shear flows for the three-dimensional Navier-Stokes equations in the limit of small viscosity 0<ν 1. When the streamwise and spanwise velocity profiles are linearly independent near the boundary, we construct an unstable mode that exhibits rapid growth at the rate of e^t/ν. Our results reveal an analytic instability in the three-dimensional Navier-Stokes equations around generic boundary layer profiles. This instability arises from the interplay between spanwise flow and three-dimensional perturbations, and does not occur in purely two-dimensional flows.

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Cite This Study

Liu et al. (Sun,) studied this question.

synapsesocial.com/papers/68e02f3cf0e39f13e7fa2616 https://doi.org/https://doi.org/10.48550/arxiv.2509.06089

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