2023/11/05 by Dina Soltani Tehrani, Tehrani, Dina Soltani, Hussein Aluie +1 · 1 citation
Engineering · Environmental Science · Physics and Astronomy · #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Plant Water Relations and Carbon Dynamics #Solar and Space Plasma Dynamics
paper · pdf · doi:10.48550/arxiv.2311.02550
openalex publication_date 2023/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
While kinetic helicity is not Galilean invariant locally, it is known (K. Moffatt, Journal of Fluid Mechanics, 35, 117 (1969)) that its spatial integral quantifies the degree of knottedness of vorticity field lines. Being a topological property of the flow, mean kinetic helicity is Galilean invariant. Here, we provide a direct mathematical proof that kinetic helicity is Galilean invariant when spatially integrated over regions enclosed by vorticity surfaces, i.e., surfaces of zero vorticity flux. We also discuss so-called ``relative'' kinetic helicity, which is Galilean invariant when integrated over any region in the flow.