2023/08/24 by Michele Dolce, Dolce, Michele · 5 citations
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · Engineering · #Geomagnetism and Paleomagnetism Studies #Theoretical and Computational Physics #Characterization and Applications of Magnetic Nanoparticles
paper · pdf · doi:10.48550/arxiv.2308.12589
We consider a 2D incompressible and electrically conducting fluid in the domain \mathbbT×ℝ. The aim is to quantify stability properties of the Couette flow (y,0) with a constant homogenous magnetic field (β,0) when |β|>1/2. The focus lies on the regime with small fluid viscosity ν, magnetic resistivity μ and we assume that the magnetic Prandtl number satisfies μ2\lesssimPrm=ν/μ≤ 1. We establish that small perturbations around this steady state remain close to it, provided their size is of order ε≪ν2/3 in HN with N large enough. Additionally, the vorticity and current density experience a transient growth of order ν-1/3 while converging exponentially fast to an x-independent state after a time-scale of order ν-1/3. The growth is driven by an inviscid mechanism, while the subsequent exponential decay results from the interplay between transport and diffusion, leading to the dissipation enhancement. A key argument to prove these results is to reformulate the system in terms of symmetric variables, inspired by the study of inhomogeneous fluid, to effectively characterize the system's dynamic behavior.