  In the framework of relativistic ideal hydrodynamics, we study the production
mechanism for vorticity and magnetic field in relativistic ideal fluids. It is
demonstrated that in the uncharged fluids the thermal vorticity will always
satisfy the Kelvin's theorem and the circulation must be conserved. However, in
the charged fluids, the vorticity and magnetic field can be produced by the
interaction between the entropy gradients and the fluid velocity gradients.
Especially, in the multiple charged fluids, the vorticity and magnetic field
can be produced by the interaction between the inhomogenous charge density
ratio and the fluid velocity gradients even if the entropy distribution is
homogeneous, which provides another mechanism for the production of vorticity
and magnetic field in relativistic plasmas or in the early universe.
