Unification of the Fluid Flow Field, the Electromagnetic Field-Strength Tensors, and the Field Dynamic Equations

Either mechanical waves or electromagnetic waves propagate in space at a finite speed. The wave propagation speed and particle flow velocity form a four-vector. Using the four-vector, we can obtain the fluid flow field and the electromagnetic field strength tensor. Both tensors share the same mathematical structure and can be unified into a single mathematical frame. The field dynamic equations, either for fluid flow or for the charged particle motions, are a combination of the translational and the rotational motion. The rotational motion behaves as wave properties. The strength tensor contraction (inner product) forms a hypersurface. It is an indefinite quadratic form (saddle-shaped surface) that can take positive or negative values to reveal the dominating moving types. The electromagnetic waves are located at the saddle points, and the strength tensor for electromagnetic waves is zero. In general, the motion in the field obeys the weak form of Newton’s action and reaction law, namely, the field has an induced secondary flow, due to the interactions between vorticity and velocity for fluid flow or the magnetic field and the charge flow for the electromagnetic field. It is found that this approach is equivalent to the Euler-Lagrangian method, which is expressed by \(D_t\vec{p} = \nabla\mathcal{L}\)_._ Both methods will produce the same field dynamic equations.