Turbulent baker's maps

We formulate and study an elementary one-dimensional model mimicking some of the features of fluid turbulence. The underlying vorticity field corresponds to a parallel flow. Structure on all scales down to the numerical resolution is generated by the action of baker's maps acting on the vorticity of the flow. These transformations conserve kinetic energy locally in the Euler model, while viscous diffusion of vorticity occurs in the Navier-Stokes case. We apply the model to the study of homogeneous fully developed turbulence, and to turbulent channel flow.