## Two models of truncated Navier--Stokes equations on a two-dimensional torus

Two truncations of the Navier--Stokes equations for an incompressible fluid on a two-dimensional torus are numerically investigated. The two models, an eight-mode truncation and a nine-mode extension of it, exhibit almost completely different behaviors. Only two aspects appear to be common to both. First, in contrast to all the previously studied models, turbulence takes place at low Reynolds numbers and for critical values close to each other. Second, there is a parameter interval for which the same stable periodic orbit is present in both models. The main feature of the two truncations is a very rich phenomenology, with many differentmore »