A. (2016) 'A statistical state dynamics-based study of the structure and mechanism of largescale motions in plane Poiseuille flow', The perspective of statistical state dynamics (SSD) has recently been applied to the study of mechanisms underlying turbulence in a variety of physical systems. An SSD is a dynamical system that evolves a representation of the statistical state of the system. An example of an SSD is the second order cumulant closure referred to as stochastic structural stability theory (S3T), which has provided insight into the dynamics of wall turbulence, and specifically the emergence and maintenance of the roll/streak structure. S3T comprises a coupled set of equations for the streamwise mean and perturbation covariance, in which nonlinear interactions among the perturbations has been removed, restricting nonlinearity in the dynamics to that of the mean equation and the interaction between the mean and perturbation covariance. In this work, this quasi-linear restriction of the dynamics is used to study the structure and dynamics of turbulence in plane Poiseuille flow at moderately high Reynolds numbers in a closely related dynamical system, referred to as the restricted non-linear (RNL) system. Simulations using this RNL system reveal that the essential features of wall-turbulence dynamics are retained. Consistent with previous analyses based on the S3T version of SSD, the RNL system spontaneously limits the support of its turbulence to a small set of streamwise Fourier components giving rise to a naturally minimal representation of its turbulence dynamics. Although greatly simplified, this RNL turbulence exhibits natural-looking structures and statistics albeit with quantitative differences from those in direct numerical simulations (DNS) of the full equations. Surprisingly, even when further truncation of the perturbation support to a single streamwise component is imposed, the RNL system continues to self-sustain turbulence with qualitatively realistic structure and dynamic properties. RNL turbulence at the Reynolds numbers studied is dominated by the roll/streak structure in the buffer layer and similar very-large-scale structure (VLSM) in the outer layer. In this work, diagnostics of the structure, spectrum and energetics of RNL and DNS turbulence are used to demonstrate that the roll/streak dynamics supporting the turbulence in the buffer and logarithmic layer is essentially similar in RNL and DNS. † Email address for correspondence: pjioannou@phys.uoa.gr arXiv:1512.06018v4 [physics.flu-dyn]

Stochastic Structural Stability Theory (S3T) provides analytical methods for understanding the emergence and equilibration of jets from the turbulence in planetary atmospheres based on the dynamics of the statistical mean state of the turbulence closed at second order. Predictions for formation and equilibration of turbulent jets made using S3T are critically compared with results of simulations made using the associated quasi-linear and nonlinear models. S3T predicts the observed bifurcation behavior associated with the emergence of jets, their equilibration and their breakdown as a function of parameters. Quantitative differences in bifurcation parameter values between predictions of S3T and results of nonlinear simulations are traced to modification of the eddy spectrum which results from two processes: nonlinear eddy-eddy interactions and formation of discrete non-zonal structures. Remarkably, these non-zonal structures, which substantially modify the turbulence spectrum, are found to arise from S3T instability. Formation as linear instabilities and equilibration at finite amplitude of multiple equilibria for identical parameter values in the form of jets with distinct meridional wavenumbers is verified as is the existence at equilibrium of finite amplitude non-zonal structures in the form of nonlinearly modified Rossby waves. When zonal jets and nonlinearly modified Rossby waves coexist at finite amplitude the jet structure is generally found to dominate even if it is linearly less unstable. The physical reality of the manifold of S3T jets and non-zonal structures is underscored by the existence in nonlinear simulations of jet structure at subcritical S3T parameter values which are identified with stable S3T jet modes excited by turbulent fluctuations.

Oceanic eddies play a profound role in mixing tracers such as heat, carbon, and nutrients, thereby regulating regional and global climate. Yet, it remains unclear how global oceanic eddy kinetic energy has evolved over the past few decades. Furthermore, coupled climate model predictions generally fail to resolve oceanic mesoscale dynamics, which could limit their accuracy in simulating future climate change. Here we show a global statistically significant increase of the eddy activity using two independent observational datasets of mesoscale variability, one directly measuring currents and the other from sea surface temperature.Regions characterized by different dynamical processes show distinct evolution in the eddy field. For example, eddy-rich regions such as boundary current extensions and the Antarctic Circumpolar Current show a significant increase of 2% and 5% per decade in eddy activity, respectively. In contrast, most of the regions of observed decrease are found in the tropical oceans. Because eddies play a fundamental role in the ocean transport of heat, momentum, 1 and carbon, our results have far-reaching implications for ocean circulation and climate, and the modelling platforms we use to study future climate change.Changes in the climate system over recent decades have warmed the upper ocean and modified the wind stress, heat and freshwater fluxes that drive ocean circulation 1, 2 . These changes have the capacity to modify the ocean circulation at all scales, including the overturning circulation 3, 4 , basin-scale gyres 5,6 , boundary currents 7,8 , and the mesoscale 9 . The ocean's mesoscale incorporates motions that occur at spatial scales from ∼10 to ∼100 km. These motions include both steady flows, such as jets and re-circulations, and time-varying flows, generally referred to as eddies. Mesoscale eddies are ubiquitous in the global ocean and feed back onto all scales, from regional processes 10 up to the meridional overturning circulation 3 . Moreover, these eddies act to transport and mix tracers such as heat, salt, and nutrients 11,12 . Thus, understanding the evolution of the mesoscale circulation is crucial to better predict our changing oceans. Kinetic energy (KE) quantifies the magnitude of ocean currents 9,[13][14][15] . Kinetic energy is proportional to the square of the velocity, and is commonly separated into the mean KE (MKE; computed from the time-mean velocity field) and the KE of the time-varying velocity (known as the Eddy Kinetic Energy; EKE). The EKE is dominated by mesoscale variability and is a significant fraction of the total KE 16,17 . A recent study has inferred a global increase of KE anomaly from ocean reanalyses and ARGO floats 15 . However, these reanalyses and observations do not have the spatial resolution required to resolve the mesoscale field. Satellite observations, which can resolve the mesoscale, suggest that EKE in the Southern Ocean has a robust increasing trend 9,18,19 . How-

The mesoscale eddy field plays a key role in the mixing and transport of physical and biological properties and redistribution of energy in the ocean. Eddy kinetic energy is commonly defined as the kinetic energy of the time‐varying component of the velocity field. However, this definition contains all processes that vary in time, including coherent mesoscale eddies, jets, waves, and large‐scale motions. The focus of this paper is on the eddy kinetic energy contained in coherent mesoscale eddies. We present a new method to decompose eddy kinetic energy into oceanic processes. The proposed method uses a new eddy identification algorithm (TrackEddy). This algorithm is based on the premise that the sea level signature of a coherent eddy can be approximated as a Gaussian feature. The eddy Gaussian signature then allows for the calculation of kinetic energy of the eddy field through the geostrophic approximation. TrackEddy has been validated using synthetic sea surface height data and then used to investigate trends of eddy kinetic energy in the Southern Ocean using satellite sea surface height anomaly (AVISO+). We detect an increasing trend of eddy kinetic energy associated with mesoscale eddies in the Southern Ocean. This trend is correlated with an increase in the coherent eddy amplitude and the strengthening of wind stress over the last two decades.

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.

S3T (Stochastic Structural Stability Theory) employs a closure at second order to obtain the dynamics of the statistical mean turbulent state. When S3T is implemented as a coupled set of equations for the streamwise mean and perturbation states, nonlinearity in the dynamics is restricted to interaction between the mean and perturbations. The S3T statistical mean state dynamics can be approximately implemented by similarly restricting the dynamics used in a direct numerical simulation (DNS) of the full Navier-Stokes equations (referred to as the NS system). Although this restricted nonlinear system (referred to as the RNL system) is greatly simplified in its dynamics in comparison to the associated NS, it nevertheless self-sustains a turbulent state in wall-bounded shear flow with structures and dynamics comparable to that in observed turbulence. Moreover, RNL turbulence can be analyzed effectively using theoretical methods developed to study the closely related S3T system. In order to better understand RNL turbulence and its relation to NS turbulence, an extensive comparison is made of diagnostics of structure and dynamics in these systems. Although quantitative differences are found, the results show that turbulence in the RNL system closely parallels that in NS and suggest that the S3T/RNL system provides a promising reduced complexity model for studying turbulence in wall-bounded shear flows. arXiv:1401.7816v1 [physics.flu-dyn]

Oceanic eddies play a profound role in mixing tracers such as heat, carbon, and nutrients, thereby regulating regional and global climate. Yet, it remains unclear how global oceanic eddy kinetic energy has evolved over the past few decades. Furthermore, coupled climate model predictions generally fail to resolve oceanic mesoscale dynamics, which could limit their accuracy in simulating future climate change. Here we show a global statistically significant increase of the eddy activity using two independent observational datasets of mesoscale variability, one directly measuring currents and the other from sea surface temperature. Regions characterized by different dynamical processes show distinct evolution in the eddy field. For example, eddy-rich regions such as boundary current extensions and the Antarctic Circumpolar Current show a significant increase of 2% and 5% per decade in eddy activity, respectively. In contrast, most of the regions of observed decrease are found in the tropical oceans. Because eddies play a fundamental role in the ocean transport of heat, momentum, and carbon, our results have far-reaching implications for ocean circulation and climate, and the modelling platforms we use to study future climate change.