  The fundamental difference between incompressible ideal magnetohydrodynamics
and the dynamics of a non-conducting fluid is that magnetic fields exert a
tension force that opposes their bending; magnetic fields behave like elastic
strings threading the fluid. It is natural, therefore, to expect that a
magnetic field tangled at small length scales should resist a large-scale shear
in an elastic way, much as a ball of tangled elastic strings responds
elastically to an impulse. Furthermore, a tangled field should support the
propagation of `magnetoelastic waves', the isotropic analogue of Alfv\'en waves
on a straight magnetic field. Here, we study magnetoelasticity in the idealised
context of an equilibrium tangled field configuration. In contrast to previous
treatments, we explicitly account for intermittency of the Maxwell stress, and
show that this intermittency necessarily decreases the frequency of
magnetoelastic waves in a stable field configuration. We develop a mean-field
formalism to describe magnetoelastic behaviour, retaining leading-order
corrections due to the coupling of large- and small-scale motions, and solve
the initial-value problem for viscous fluids subjected to a large-scale shear,
showing that the development of small-scale motions results in anomalous
viscous damping of large-scale waves. Finally, we test these analytic
predictions using numerical simulations of standing waves on tangled, linear
force-free magnetic-field equilibria.
