Axial-Current Anomaly in Euler Fluids

We argue that a close analog of the axial-current anomaly of quantum field theories with fermions occurs in the classical Euler fluid. The conservation of the axial current (closely related to the helicity of inviscid barotropic flow) is anomalously broken by the external electromagnetic field as $∂_𝜇𝑗^𝜇_A = 2⁢E · B$ similar to that of the axial current of a quantum field theory with Dirac fermions, such as QED.