2024/10/29 by Niklas Knobel, Knobel, Niklas · 1 citation
Earth and Planetary Sciences · Engineering · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Meteorological Phenomena and Simulations #Solar and Space Plasma Dynamics
paper · pdf · doi:10.48550/arxiv.2410.21835
openalex publication_date 2024/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This article considers the ideal 2D magnetohydrodynamic equations on an infinite periodic channel close to a combination of an affine shear flow, called Couette flow, and a constant magnetic field. This setting combines important physical effects of mixing and coupling of velocity and magnetic field. We establish the existence and stability of the velocity and magnetic field for Gevrey-class perturbations of size ε, valid up to times t ∼ ε-1. Additionally, the vorticity and current grow as O(t) and there is no inviscid damping of the velocity and magnetic field. This has parallels to the above threshold case for the 3D Navier-Stokes \citebedrossian2022dynamics where growth in `streaks' leads to time scales of t∼ ε-1. In particular, for the ideal MHD equations, our article suggests that for a wide range of initial data, the scenario ``dynamo effect ⇒ vorticity and current growth ⇒ vorticity and current breakdown'' leads to instability and possible turbulences.