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This study analysed a three-dimensional Taylor decaying vortex under anapplied magnetic field as a benchmark test problem to verify the calculationmethod of an electromagnetic fluid flow and investigated the validity of thedecaying magnetic field model. First, we observed the flow structure of athree-dimensional Taylor decaying vortex without an applied magnetic field. Weinvestigated the changes in the error between the calculation result and theexact solution when the number of grid points and the Reynolds number variedand showed the effectiveness of the benchmark test. Next, we analysed athree-dimensional Taylor decaying vortex under an applied magnetic field andclarified the characteristics of the decaying magnetic field. When a magneticfield is applied, low magnetic pressure regions are connected in a meshpattern, and the magnetic pressure distribution with a distorted cubicstructure occurs to surround a high magnetic pressure region. In a stagnationregion, the magnetic energy becomes low, and the magnetic flux line is similarto the streamline of the velocity field. High current densities occur in a gridpattern, and the magnetic flux lines swirl around the high current densityregion. The magnetic pressure and magnetic energy are high in the high currentdensity region. When the Reynolds number and the magnetic Reynolds number vary,the decay trends of various energies agree well with the exact solution. Thetransition to turbulent flow occurs at a high Reynolds number, and the kineticand total energies decrease rapidly. After the dissipation rate of kineticenergy becomes maximum, the vortex structure decays, and the flow fieldapproaches a stationary state without magnetic fields. The three-dimensionalTaylor decaying magnetic field belonging to the Beltrami flow is a valuablemodel for verifying the calculation method of electromagnetic fluid flows.

Three-dimensional decaying magnetic field belonging to Beltrami flow