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Register a new userStatistical state dynamics based theory for the formation and equilibration of Saturns north polar jet
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Coherent jets with most of the kinetic energy of the flow are common in atmospheric turbulence. In the gaseous planets these jets are maintained by incoherent turbulence excited by small-scale convection. Large-scale coherent waves are sometimes observed to coexist with the jets; a prominent example is Saturns hexagonal North polar jet (NPJ). The mechanism responsible for forming and maintaining such a turbulent state remains elusive. The coherent planetary-scale component of the turbulence arises and is maintained by interaction with the incoherent small-scale turbulence component. Theoretical understanding of the dynamics of the jet/wave/turbulence coexistence regime is gained by employing a statistical state dynamics (SSD) model. Here, a second-order closure implementation of a two-layer beta-plane SSD is used to develop a theory that accounts for the structure and dynamics of the NPJ. Asymptotic analysis of the SSD equilibrium in the weak jet damping limit predicts a universal jet structure in agreement with NPJ observations. This asymptotic theory also predicts the wavenumber (six) of the prominent jet perturbation. Analysis with this model of the jet/wave/turbulence regime dynamics reveals that jet formation is controlled by the effective value of $beta$; the required value of this parameter for correspondence with observation is obtained. As this is a robust prediction it is taken as an indirect observation of a deep poleward sloping stable layer beneath the NPJ. The slope required is obtained from observations of NPJ structure as is the small-scale turbulence excitation required to maintain the jet. The observed jet structure is then predicted by the theory as is the wave-six disturbance. This wave, which is identified with the least stable mode of the equilibrated jet, is shown to be primarily responsible for equilibrating the jet with the observed structure and amplitude.
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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 only exist 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.
Zonal jets in a barotropic setup emerge out of homogeneous turbulence through a flow-forming instability of the homogeneous turbulent state (`zonostrophic instability) which occurs as the turbulence intensity increases. This has been demonstrated using the statistical state dynamics (SSD) framework with a closure at second order. Furthermore, it was shown that for small supercriticality the flow-forming instability follows Ginzburg-Landau (G-L) dynamics. Here, the SSD framework is used to study the equilibration of this flow-forming instability for small supercriticality. First, we compare the predictions of the weakly nonlinear G-L dynamics to the fully nonlinear SSD dynamics closed at second order for a wide ranges of parameters. A new branch of jet equilibria is revealed that is not contiguously connected with the G-L branch. This new branch at weak supercriticalities involves jets with larger amplitude compared to the ones of the G-L branch. Furthermore, this new branch continues even for subcritical values with respect to the linear flow-forming instability. Thus, a new nonlinear flow-forming instability out of homogeneous turbulence is revealed. Second, we investigate how both the linear flow-forming instability and the novel nonlinear flow-forming instability are equilibrated. We identify the physical processes underlying the jet equilibration as well as the types of eddies that contribute in each process. Third, we propose a modification of the diffusion coefficient of the G-L dynamics that is able to capture the asymmetric evolution for weak jets at scales other than the marginal scale (side-band instabilities) for the linear flow-forming instability.
We continue our investigation into the nonlinear evolution of the Goldreich-Schubert-Fricke (GSF) instability in differentially rotating radiation zones. This instability may be a key player in transporting angular momentum in stars and giant planets, but its nonlinear evolution remains mostly unexplored. In a previous paper we considered the equatorial instability, whereas here we simulate the instability at a general latitude for the first time. We adopt a local Cartesian Boussinesq model in a modified shearing box for most of our simulations, but we also perform some simulations with stress-free, impenetrable, radial boundaries. We first revisit the linear instability and derive some new results, before studying its nonlinear evolution. The instability is found to behave very differently compared with its behaviour at the equator. In particular, here we observe the development of strong zonal jets (layering in the angular momentum), which can considerably enhance angular momentum transport, particularly in axisymmetric simulations. The jets are, in general, tilted with respect to the local gravity by an angle that corresponds initially with that of the linear modes, but which evolves with time and depends on the strength of the flow. The instability transports angular momentum much more efficiently (by several orders of magnitude) than it does at the equator, and we estimate that the GSF instability could contribute to the missing angular momentum transport required in both red giant and subgiant stars. It could also play a role in the long-term evolution of the solar tachocline and the atmospheric dynamics of hot Jupiters.
Extreme events provide relevant insights into the dynamics of climate and their understanding is key for mitigating the impact of climate variability and climate change. By applying large deviation theory to a state-of-the-art Earth system model, we define the climatology of persistent heatwaves and cold spells in key target geographical regions by estimating the rate functions for the surface temperature, and we assess the impact of increasing CO$_2$ concentration on such persistent anomalies. Hence, we can better quantify the increasing hazard {color{black}due} to heatwaves in a warmer climate. We show that two 2010 high impact events - summer Russian heatwave and winter Dzud in Mongolia - are associated with atmospheric patterns that are exceptional compared to the typical ones, but typical compared to the climatology of extremes. Their dynamics is encoded in the natural variability of the climate. Finally, we propose and test an approximate formula for the return times of large and persistent temperature fluctuations from easily accessible statistical properties.
In this paper we advance physical background of the energy- and flux-budget turbulence closure based on the budget equations for the turbulent kinetic and potential energies and turbulent fluxes of momentum and buoyancy, and a new relaxation equation for the turbulent dissipation time-scale. The closure is designed for stratified geophysical flows from neutral to very stable and accounts for the Earth rotation. In accordance to modern experimental evidence, the closure implies maintaining of turbulence by the velocity shear at any gradient Richardson number Ri, and distinguishes between the two principally different regimes: strong turbulence at Ri << 1 typical of boundary-layer flows and characterised by the practically constant turbulent Prandtl number; and weak turbulence at Ri > 1 typical of the free atmosphere or deep ocean, where the turbulent Prandtl number asymptotically linearly increases with increasing Ri (which implies very strong suppression of the heat transfer compared to the momentum transfer). For use in different applications, the closure is formulated at different levels of complexity, from the local algebraic model relevant to the steady-state regime of turbulence to a hierarchy of non-local closures including simpler down-gradient models, presented in terms of the eddy-viscosity and eddy-conductivity, and general non-gradient model based on prognostic equations for all basic parameters of turbulence including turbulent fluxes.
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