The scalar product of the above form of Navier-Stokes equation with ρ ρ 0 u gives the rate of increase of kinetic energy density, 1 2 ρ ρ 0 u 2 c , on the left-hand side. The last term on the right-hand side is then u ⋅ ⋅ ( J × × B ) , the local contribution to the kinetic energy due to Lorentz force.