We discuss properties of a shell type model for the inviscid fluid equations. We prove that the forced system has a unique equilibrium which is an exponential global attractor. Every solution blows up in H5/6 in finite time . After this time, all solutions stay in Hs, s<5/6, and "turbulent" dissipation occurs. Onsager's conjecture is confirmed for the model system. We discuss the augmented viscous system and show that Kolmogorov's law for turbulence holds in the limit of vanishing viscosity. This is joint work with Alexey Cheskidov and Nataša Pavlović.