Direct statistical simulation of out-of-equilibrium jets

We present direct statistical simulation of jet formation on a β plane, solving for the statistics of a fluid flow via an expansion in cumulants. Here we compare an expansion truncated at second order (CE2) to statistics accumulated by direct numerical simulations. We show that, for jets near equilibrium, CE2 is capable of reproducing the jet structure (although some differences remain in the second cumulant). However, as the degree of departure from equilibrium is increased (as measured by the zonostrophy parameter), the jets meander more and CE2 becomes less accurate. We discuss a possible remedy by inclusion of higher cumulants.