Statistical State Dynamics of Jet–Wave Coexistence in Barotropic Beta-Plane Turbulence

Abstract

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) which comprises the dynamics of the interaction between coherent and incoherent components in the turbulent state. In this work the S3T implementation of SSD for barotropic beta-plane turbulence is used to develop a theory for the jet/wave coexistence regime by separating the coherent motions consisting of the zonal jets together with a selection of large-scale waves from the smaller scale motions which constitute the incoherent component. It is found that 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. This mechanism of destabilization differs fundamentally and serves to augment the more familiar S3T instabilities in which jets and waves arise from homogeneous turbulence with energy source exclusively from the incoherent eddy field and provides further insight into the cooperative dynamics of the jet/waves coexistence regime in planetary turbulence.

Magnetic Suppression of Zonal Flows on a Beta Plane

“…The eddy-mean flow interaction between the coherent flow and the incoherent eddy field is so robust that it manifests itself even when the mean flow is weak. This fact has been revealed in previous studies of unmagnetized flows (Bakas & Ioannou 2013b;Constantinou et al 2014). For example, Constantinou et al (2014) compared predictions of ZI with fully nonlinear direct numerical simulations and showed that the bifurcation to zonation (i.e., when zonal flows are still very weak) is indeed well captured in the quasilinear model, so long as the eddy field is modified to match that in nonlinear simulations.…”

“…This fact has been revealed in previous studies of unmagnetized flows (Bakas & Ioannou 2013b;Constantinou et al 2014). For example, Constantinou et al (2014) compared predictions of ZI with fully nonlinear direct numerical simulations and showed that the bifurcation to zonation (i.e., when zonal flows are still very weak) is indeed well captured in the quasilinear model, so long as the eddy field is modified to match that in nonlinear simulations. Here, the agreement of the magnetized ZI with the simulations results by Tobias et al (2007) indicates that in magnetized fluids, the eddy-mean flow interaction retained within the quasilinear approximation is the dominant process responsible for driving or opposing zonal flows.…”

Wave kinetics of drift-wave turbulence and zonal flows beyond the ray approximation

“…This stimulated formulations of full-wave statistical theories, which remain manageable within the quasilinear approximation, i.e., when eddy-eddy interactions are ignored. A particularly notable example is the second-order cumulant expansion (CE2), which has been used in both geophysics and plasma physics [20][21][22][23]. However, the CE2 is formulated in terms of the two-point correlation function, so it is not an obvious generalization of the WKE, which describes the DW dynamics in the ray phase space.…”

On the Rayleigh–Kuo criterion for the tertiary instability of zonal flows

“…In particular, Refs. [11][12][13][14] reported that the ZF-turbulence system undergoes a structural instability even when the laminar ZF with the same amplitude would be RK-stable. Also, Ref.…”

“…Also, Ref. [14] shows that the least-damped eigenmode changes its structure in the presence of the ambient turbulence and hence can become unstable. Correspondingly, the stability criterion that we report here can be considered as determining the upper bound of the ZF amplitude in a stable equilibrium.…”