arXiv subjects

Petros J. Ioannou

Publications and source records attributed to Petros J. Ioannou.

28 records · Page 2Linked to original sources

arXiv2015

Emergence of non-zonal coherent structures

Planetary turbulence is observed to self-organize into large-scale structures such as zonal jets and coherent vortices. One of the simplest models that retains the relevant dynamics of turbulent self-organization is a barotropic flow in a beta-plane channel with turbulence sustained by random stirring. Non-linear integrations of this model show that as the energy input rate of the forcing is increased, the homogeneity of the flow is first broken by the emergence of non-zonal, coherent, westward propagating structures and at larger energy input rates by the emergence of zonal jets. The emergence of both non-zonal coherent structures and zonal jets is studied using a statistical theory, Stochastic Structural Stability Theory (S3T). S3T directly models a second-order approximation to the statistical mean turbulent state and allows the identification of statistical turbulent equilibria and study of their stability. Using S3T, the bifurcation properties of the homogeneous state in barotropic beta-plane turbulence are determined. Analytic expressions for the zonal and non-zonal large-scale coherent flows that emerge as a result of structural instability are obtained and the equilibration of the incipient instabilities is studied through numerical integrations of the S3T dynamical system. The dynamics underlying the formation of zonal jets are also investigated. It is shown that zonal jets form from the upgradient momentum fluxes that result from the shearing of the eddies by the emerging infinitesimal large-scale flow. Finally, numerical simulations of the nonlinear equations confirm the characteristics (scale, amplitude and phase speed) of the structures predicted by S3T, even in highly non-linear parameter regimes such as the regime of zonostrophic turbulence.

physics.ao-ph↗

arXiv2015

A minimal model of self-sustaining turbulence

In this work we examine the turbulence maintained in a Restricted Nonlinear (RNL) model of plane Couette flow. This model is a computationally efficient approximation of the second order statistical state dynamics (SSD) obtained by partitioning the flow into a streamwise averaged mean flow and perturbations about that mean, a closure referred to herein as the RNL$_\infty$ model. The RNL model investigated here employs a single member of the infinite ensemble that comprises the covariance of the RNL$_\infty$ dynamics. The RNL system has previously been shown to support self-sustaining turbulence with a mean flow and structural features that are consistent with DNS. This paper demonstrates that the RNL system's self-sustaining turbulent state is supported by a small number of streamwise varying modes, which form the natural support for the self-sustaining process maintaining RNL turbulence. Remarkably, truncation of the RNL system's support to a single streamwise varying mode can suffice to sustain the turbulent state. The close correspondence between RNL simulations and DNS that has been previously observed along with the results presented here suggest that the fundamental mechanisms underlying wall-turbulence can be analyzed using these highly simplified RNL systems.

physics.flu-dyn↗

arXiv2014

S3T stability of the homogeneous state of barotropic beta-plane turbulence

Zonal jets and non-zonal large-scale flows are often present in forced-dissipative barotropic turbulence on a beta-plane. The dynamics underlying the formation of both zonal and non-zonal coherent structures is investigated in this work within the statistical framework of Stochastic Structural Stability Theory (S3T). Previous S3T studies have shown that the homogeneous turbulent state undergoes a bifurcation at a critical parameter and becomes inhomogeneous with the emergence of zonal and/or large-scale non-zonal flows and that these statistical predictions of S3T are reflected in direct numerical simulations. In this paper, we study the dynamics underlying the S3T statistical instability of the homogeneous state as a function of parameters. It is shown that for weak planetary vorticity gradient, $β$, both zonal jets and non-zonal large-scale structures form from upgradient momentum fluxes due to shearing of the eddies by the emerging infinitesimal flow. For large $β$, the dynamics of the S3T instability differs for zonal and non-zonal flows but in both the destabilizing vorticity fluxes decrease with increasing $β$. Shearing of the eddies by the mean flow continues to be the mechanism for the emergence of zonal jets while non-zonal large-scale flows emerge from resonant and near resonant triad interactions between the large-scale flow and the stochastically forced eddies. The relation between the formation of large-scale structure through modulational instability and the S3T instability of the homogeneous state is also investigated and it is shown that the modulational instability results are subsumed by the S3T results.

physics.ao-ph↗

arXiv2014

Turbulence in the highly restricted dynamics of a closure at second order: comparison with DNS

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.

physics.flu-dyn↗

arXiv2013

Emergence and equilibration of jets in beta-plane turbulence: applications of Stochastic Structural Stability Theory

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.

physics.flu-dyn↗

arXiv2013

A theory for the emergence of coherent structures in beta-plane turbulence

Planetary turbulent flows are observed to self-organize into large scale structures such as zonal jets and coherent vortices. One of the simplest models of planetary turbulence is obtained by considering a barotropic flow on a beta-plane channel with turbulence sustained by random stirring. Non-linear integrations of this model show that as the energy input rate of the forcing is increased, the homogeneity of the flow is broken with the emergence of non-zonal, coherent, westward propagating structures and at larger energy input rates by the emergence of zonal jets. We study the emergence of non-zonal coherent structures using a non-equilibrium statistical theory, Stochastic Structural Stability Theory (S3T, previously referred to as SSST). S3T directly models a second order approximation to the statistical mean turbulent state and allows identification of statistical turbulent equilibria and study of their stability. Using S3T, the bifurcation properties of the homogeneous state in barotropic beta-plane turbulence are determined. Analytic expressions for the zonal and non-zonal large scale coherent flows that emerge as a result of structural instability are obtained. Through numerical integrations of the S3T dynamical system, it is found that the unstable structures equilibrate at finite amplitude. Numerical simulations of the nonlinear equations confirm the characteristics (scale, amplitude and phase speed) of the structures predicted by S3T.

physics.ao-ph↗

arXiv2013

Emergence of large scale structure in planetary turbulence

Planetary and magnetohydrodynamic drift-wave turbulence is observed to self-organize into large scale structures such as zonal jets and coherent vortices. In this Letter we present a non-equilibrium statistical theory, the Stochastic Structural Stability theory (SSST), that can make predictions for the formation and finite amplitude equilibration of non-zonal and zonal structures (lattice and stripe patterns) in homogeneous turbulence. This theory reveals that the emergence of large scale structure is the result of an instability of the interaction between the coherent flow and the associated turbulent field. Comparison of the theory with nonlinear simulations of a barotropic flow in a beta-plane channel with turbulence sustained by isotropic random stirring, demonstrates that SSST predicts the threshold parameters at which the coherent structures emerge as well as the characteristics of the emerging structures (scale, amplitude, phase speed). It is shown that non-zonal structures (lattice states or zonons) emerge at lower energy input rates of the stirring compared to zonal flows (stripe states) and their emergence affects the dynamics of jet formation.

physics.ao-ph↗

arXiv2011

Optimal excitation of two dimensional Holmboe instabilities

Highly stratified shear layers are rendered unstable even at high stratifications by Holmboe instabilities when the density stratification is concentrated in a small region of the shear layer. These instabilities may cause mixing in highly stratified environments. However these instabilities occur in limited bands in the parameter space. We perform Generalized Stability analysis of the two dimensional perturbation dynamics of an inviscid Boussinesq stratified shear layer and show that Holmboe instabilities at high Richardson numbers can be excited by their adjoints at amplitudes that are orders of magnitude larger than by introducing initially the unstable mode itself. We also determine the optimal growth that is obtained for parameters for which there is no instability. We find that there is potential for large transient growth regardless of whether the background flow is exponentially stable or not and that the characteristic structure of the Holmboe instability asymptotically emerges as a persistent quasi-mode for parameter values for which the flow is stable.

physics.flu-dyn↗

arXiv2010

Stochastic Structural Stability Theory applied to roll/streak formation in boundary layer shear flow

Stochastic Structural Stability Theory (SSST) provides an autonomous, deterministic, nonlinear dynamical system for evolving the statistical mean state of a turbulent system. In this work SSST is applied to the problem of understanding the formation of the roll/streak structures that arise from free-stream turbulence (FST) and are associated with bypass transition in boundary layers. Roll structures in the cross-stream/spanwise plane and associated streamwise streaks are shown to arise as a linear instability of interaction between the FST and the mean flow. In this interaction incoherent Reynolds stresses arising from FST are organized by perturbation streamwise streaks to coherently force perturbation rolls giving rise to an amplification of the streamwise streak perturbation and through this feedback to an instability of the combined roll/streak/turbulence complex. The dominant turbulent perturbation structures involved in supporting the roll/streak/turbulence complex instability are non-normal optimal perturbations with the form of oblique waves. The cooperative linear instability giving rise to the roll/streak structure arises at a bifurcation in the parameter of STM excitation parameter. This structural instability eventually equilibrates nonlinearly at finite amplitude and although the resulting statistical equilibrium streamwise streaks are inflectional the associated flows are stable. Formation and equilibration of the roll/streak structure by this mechanism can be traced to the non-normality which underlies interaction between perturbations and mean flows in modally stable systems.

physics.flu-dyn↗

arXiv2009

Drift wave-zonal flow dynamics

A remarkable phenomenon in turbulent flows is the spontaneous emergence of coherent large spatial scale zonal jets. Geophysical examples of this phenomenon include the Jovian banded winds and the Earth's polar front jet. In this work a comprehensive theory for the interaction of jets with turbulence, Stochastic Structural Stability Theory, is applied to the problem of understanding the formation and maintenance of the zonal jets that are crucial for enhancing plasma confinement in fusion devices.

physics.plasm-ph↗