Perturbation growth in terms of barotropic alignment properties

In order to study the error growth due to initial uncertainties in the model state, this paper examines the alignment dynamics of the perturbation velocity vector in quasi-geostrophic flows. In a barotropic context, the time evolution of the perturbation velocity field is the sum of two terms: (i) the stretching of the perturbation velocity vector by the basic-state velocity-gradient tensor (denoted ∇ū) and (ii) the perturbation ageostrophic pressure gradient, which also depends on ∇ū. Different analytical results show that such a system has two types of preferred orientation that induce kinetic-energy growth: one orientation concerns one eigenvector of ∇ū, the other one is linked to a fixed point of the orientation equation of the perturbation velocity vector written in strain coordinates. This analytical diagnostic is confirmed by using Monte-Carlo techniques in a quasi-geostrophic oceanic-basin model of a stratified wind-driven double-gyre circulation, and these orientations are shown to be the most probable. These preferred orientations are of great importance for diagnosing the most probable kinetic-energy generation rate at each grid point. An interesting outcome is that the kinetic-energy error field is localized in regions where the norm of ∇ū is large.