Shell model for quasi-two-dimensional turbulence.

We discuss the possibility to introduce geometrical constraints in shell models of turbulence in order to mimic the turbulent dynamics that takes place in fluid layers with large aspect ratio. By using a scale-dependent set of coupling parameters, we are able to resolve both scales larger and smaller than a geometrical dimension of the flow. The proposed model is able to resolve with high accuracy the split energy cascade phenomenon recently observed in such flows, and allows us to investigate in detail the scaling properties of turbulent convection confined in narrow convective cells.