Systems of interacting networks of strings such as cosmic strings or quantum vortices can be approximated in a certain regime as an anisotropic fluid with an equation of state depending on a conserved flux. The equations for ideal magnetohydrodynamics are shown to be another example of a fluid of this type. Previous work on these fluids is now extended to include dissipative effects. The new dissipative terms are discussed in terms of both standard resistive magnetohydrodynamics and small-scale structure formation in networks of cosmic strings. Conditions are derived for the stationary solutions of the fluid. The requirement of frame invariance restricts second-order corrections to the theory, and is used to calculate the speed of second sound for an idealized cosmic string model.

26 pages, 1 figure; typos corrected