A Statistical State Dynamics Based Theory for Jet--Wave Coexistence in Beta-Plane Turbulence

Jets coexist with planetary scale waves in the turbulence of planetary atmospheres. The coherent component of these structures arises from cooperative interaction between the coherent structures and the incoherent small-scale turbulence in which they are embedded. It follows that theoretical understanding of the dynamics of jets and planetary scale waves requires adopting the perspective of statistical state dynamics (SSD), that is the study of the dynamics that governs the statistics of the flow rather than the dynamics of individual flow realizations. SSD comprises the dynamics of the interaction between coherent and incoherent components in the turbulent state. Here, using the SSD perspective, we develop a theory for the jet--wave coexistence regime in barotropic beta-plane turbulence. We find that the mean flow--turbulence interaction gives rise to jets that coexist with large-scale coherent waves in a synergistic manner: Large-scale waves that would exist only as damped modes in the laminar jet are found to be transformed into exponentially growing waves by interaction with the incoherent small scale turbulence which results in a change in the mode structure allowing the mode to tap the energy of the mean jet.