Scaling and symmetry breaking in a vortex dipole

A vortex dipole is experimentally studied in a layer of salt water driven by time independent electromagnetic forcing. In particular, we characterize the flow along the dipole axis by measuring the Reynolds number $Re$ as a function of the Chandrasekhar number $Ch$ (the ratio of Lorentz to viscous forces). We find $Re \sim Ch^{\alpha}$, with the scaling exponent $\alpha$ ranging from $\alpha=1$ (viscous regime) to $\alpha = 1/2$ (advective regime). The underlying transition emerges as a symmetry breaking of the axial flow, which we quantify via the skewness of the axial velocity profile.