On Galilean invariance of mean kinetic helicity
Published in Physics of Fluids, 2023
While kinetic helicity is not Galilean invariant locally, it is known [Moffatt, J. Fluid Mech. 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 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.
Recommended citation: Soltani Tehrani, D., & Aluie, H. (2023). On Galilean invariance of mean kinetic helicity. Physics of Fluids, 35(12). https://doi.org/10.1063/5.0178926