  Low-Reynolds-number polymer solutions exhibit a chaotic behaviour known as
'elastic turbulence' when the Weissenberg number exceeds a critical value. The
two-dimensional Oldroyd-B model is the simplest constitutive model that
reproduces this phenomenon. To make a practical estimate of the resolution
scale of the dynamics requires an assumption that an attractor of the Oldroyd-B
model exists : numerical simulations show that the quantities on which this
assumption is based are bounded. We estimate the Lyapunov dimension of this
assumed attractor as a function of the Weissenberg number by combining a
mathematical analysis of the model with direct numerical simulations.
