Non-linear mechanisms in a non-conservative quasi-geostrophic flow which possesses 30 degrees of freedom

Abstract

In order to evidence the influence of scale interactions on fluid motions, the behaviours of two spectral models of the Lorenz type (1963) are compared by numerical integration for various rotation rates and thermal forcings. The representation of the fields of motion in the first model (Lorenz' model, L.M.) involves one zonal wave of the first two modes while the second model (the polyharmonic model, P.M.) involves three zonal waves of the first two modes. It is found that, at intense or moderate thermal forcing and slow rotation rates, the steady Rossby regimes are maintained up to higher rotation rates in the P.M. then in the L.M., whereas at weak thermal forcings and high rotation rates, scale interactions de-stabilize the flow in the P.M. In all cases, the wave resulting from the interaction of two unstable scales plays essentially a relay role, transferring energy between the unstable scales but only retaining for itself a very modest amount of energy. When the role of the scale interactions is examined in terms of energetic processes, it is recognized that the stabilization at the low rotation rate is a pure baroclinic process while de-stabilization at the high rotation rate is a mixed baroclinic and barotropic process, the latter being presumably dominant at a high rotation rate and weak thermal forcing. Finally, it has to be emphasized that the effects of scale interactions critically depend on the initial conditions of integration. DOI: 10.1111/j.2153-3490.1973.tb00639.x