Formation of Jets by Baroclinic Turbulence

Farrell, Brian F.; Ioannou, Petros J.

doi:10.1175/2008jas2611.1

Cited by 42 publications

(31 citation statements)

References 112 publications

(125 reference statements)

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“…(c) The attractor of the SSST system dynamics may be a fixed point, a limit cycle or be chaotic. Examples of each type have been found in the SSST dynamics of geophysical and plasma turbulence (Farrell & Ioannou 2003, 2008a). (d) The SSST system introduces a new stability concept: the stability of an equilibrium between a streamwise-averaged flow and its associated field of turbulence.…”

Section: Formulation Of the Ssst Dynamicsmentioning

confidence: 99%

“…However, in the absence of feedback between the amplifying streak and streamwise roll this powerful growth mechanism does not result in instability. Owing to the large streak growth produced by a streamwise roll perturbation, placing even a weak coupling of the streak back to the roll, such as is provided by a small spanwise frame rotation, produces destabilization (Komminaho, Lundbladh & Johansson 1996;Farrell & Ioannou 2008a). The close association between the growing streak and oblique waves suggests that these waves are involved in providing the feedback destabilizing the streamwise roll and streak in the presence of turbulent perturbations (Schoppa & Hussain 2002).…”

Section: Introductionmentioning

confidence: 99%

“…We refer to this dynamical system as the stochastic structural stability theory (SSST) system. This method for analysing the dynamics of turbulence was developed to study the phenomenon of spontaneous jet formation in planetary atmospheres (Farrell & Ioannou 2003, 2008aBakas & Ioannou 2011) and has also been applied to the problem of spontaneous jet formation from drift wave turbulence in magnetic fusion devices (Farrell & Ioannou 2009). In SSST, the turbulence is simulated using a stochastic turbulence model (STM) (Farrell & Ioannou 1993c, 1996aDelSole & Farrell 1996;Bamieh & Dahleh 2001;DelSole 2004;Gayme et al 2010).…”

Section: Introductionmentioning

confidence: 99%

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Dynamics of streamwise rolls and streaks in turbulent wall-bounded shear flow

2012

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Streamwise rolls and accompanying streamwise streaks are ubiquitous in wall-bounded shear flows, both in natural settings, such as the atmospheric boundary layer, as well as in controlled settings, such as laboratory experiments and numerical simulations. The streamwise roll and streak structure has been associated with both transition from the laminar to the turbulent state and with maintenance of the turbulent state. This close association of the streamwise roll and streak structure with the transition to and maintenance of turbulence in wall-bounded shear flow has engendered intense theoretical interest in the dynamics of this structure. In this work, stochastic structural stability theory (SSST) is applied to the problem of understanding the dynamics of the streamwise roll and streak structure. The method of analysis used in SSST comprises a stochastic turbulence model (STM) for the dynamics of perturbations from the streamwise-averaged flow coupled to the associated streamwise-averaged flow dynamics. The result is an autonomous, deterministic, nonlinear dynamical system for evolving a second-order statistical mean approximation of the turbulent state. SSST analysis reveals a robust interaction between streamwise roll and streak structures and turbulent perturbations in which the perturbations are systematically organized through their interaction with the streak to produce Reynolds stresses that coherently force the associated streamwise roll structure. If a critical value of perturbation turbulence intensity is exceeded, this feedback results in modal instability of the combined streamwise roll/streak and associated turbulence complex in the SSST system. In this instability, the perturbations producing the destabilizing Reynolds stresses are predicted by the STM to take the form of oblique structures, which is consistent with observations. In the SSST system this instability exists together with the transient growth process. These processes cooperate in determining the structure of growing streamwise roll and streak. For this reason, comparison of SSST predictions with experiments requires accounting for both the amplitude and structure of initial perturbations as well as the influence of the SSST instability. Over a range of supercritical turbulence intensities in Couette flow, this instability equilibrates to form finite amplitude time-independent streamwise roll and streak structures. At sufficiently high levels of forcing of the perturbation field, equilibration of the streamwise roll and streak structure does not occur and the flow transitions to a time-dependent state. This time-dependent state is self-sustaining in the sense that it persists when the forcing is removed. Moreover, this self-sustaining state rapidly evolves toward a minimal representation of wall-bounded shear flow turbulence in which the dynamics is limited to interaction of the streamwise-averaged flow with a perturbation structure at one † Email address for correspondence: pjioannou@phys.uoa.gr 150 B. F. Farrell and P. J. Ioannou st...

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Section: Formulation Of the Ssst Dynamicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Dynamics of streamwise rolls and streaks in turbulent wall-bounded shear flow

2012

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“…Analysis of the SSD and the resulting instability is only possible through a closure assumption for the dynamics, as a straightforward calculation leads to an infinite hierarchy of equations for the moments and is therefore intractable (Hopf 1952;Kraichnan 1964;Frisch 1995). There is now a large number of studies of barotropic turbulence (Farrell & Ioannou 2007;Marston 2010;Srinivasan & Young 2012), shallow-water turbulence (Farrell & Ioannou 2009a), baroclinic turbulence (DelSole 1996;Farrell & Ioannou 2008Marston et al 2016), turbulence in pipe flows (Constantinou et al 2014b;Farrell et al 2016, turbulence in a convectively unstable flows (Herring 1963;Fitzgerald & Farrell 2014;Ait-Chaalal et al 2016) and turbulence in plasma and astrophysical flows (Farrell & Ioannou 2009b;Tobias et al 2011;Parker & Krommes 2013) providing evidence that whenever there is a coherent flow coexisting with the turbulent field, the SSD can be accurately captured by a second-order closure. Such closures of the SSD are either termed Stochastic Structural Stability Theory (S3T) (Farrell & Ioannou 2003) or second-order cumulant expansion (CE2) (Marston et al 2008).…”

Section: Introductionmentioning

confidence: 99%

Is spontaneous generation of coherent baroclinic flows possible?

Bakas

Ioannou

2019

J. Fluid Mech.

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Geophysical turbulence is observed to self-organize into large-scale flows such as zonal jets and coherent vortices. Previous studies on barotropic beta-plane turbulence, a simple model that retains the basic self-organization dynamics, have shown that coherent flows emerge out of a background of homogeneous turbulence as a bifurcation when the turbulence intensity increases and the emergence of large scale flows has been attributed to a new type of collective, symmetry breaking instability of the statistical state dynamics of the turbulent flow. In this work we extend the analysis to stratified flows and investigate turbulent self-organization in a two-layer fluid with no imposed mean north-south thermal gradient and turbulence supported by an external random stirring. We use a second order closure of the statistical state dynamics (S3T) with an appropriate averaging ansatz that allows the identification of statistical turbulent equilibria and their structural stability. The bifurcation of the statistically homogeneous equilibrium state to inhomogeneous equilibrium states comprising of zonal jets and/or large scale waves when the energy input rate of the excitation passes a critical threshold is analytically studied. The theory predicts that when the flow transitions to a statistical state with large-scale structures, these states are barotropic if the scale of excitation is larger than the deformation radius. Mixed barotropic-baroclinic states with jets and/or waves arise when the excitation is at scales shorter than the deformation radius with the baroclinic component of the flow being subdominant for low energy input rates and non-significant for higher energy input rates. The results of the S3T theory are compared to nonlinear simulations. The theory is found to accurately predict both the critical transition parameters and the scales of the emergent structures but underestimates their amplitude.

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“…In S3T, and the related system referred to as CE2 (second-order cumulant expansion, Marston 2010), nonlinearity due to perturbation-perturbation advection is either set to zero or stochastically parameterized, so that the SSD is closed at second order. This second-order closure has proven useful in the study of coherent structure emergence in barotropic turbulence (Farrell & Ioannou 2007;Marston et al 2008;Srinivasan & Young 2012;Tobias & Marston 2013;Bakas & Ioannou 2013;Constantinou et al 2014;Parker & Krommes 2014;Bakas et al 2018), two-layer baroclinic turbulence (Farrell & Ioannou 2008, 2009aMarston 2010Marston , 2012Farrell & Ioannou 2017c), turbulence in the shallow-water equations on the equatorial beta-plane (Farrell & Ioannou 2009b), drift wave turbulence in plasmas (Farrell & Ioannou 2009;Parker & Krommes 2013), unstratified 2D turbulence (Bakas & Ioannou 2011), rotating magnetohydrodynamics (Tobias et al 2011;Squire & Bhattacharjee 2015;Constantinou & Parker 2018), 3D wall-bounded shear flow turbulence (Farrell & Ioannou 2012;Thomas et al 2014Thomas et al , 2015, and the turbulence of stable ion-temperature-gradient modes in plasmas (St-Onge & Krommes 2017). In the present work we place 2D stratified Boussinesq turbulence into the mechanistic and phenomenological context of the mean flow-turbulence interaction mechanism that has been identified in these other turbulent systems.…”

Section: Introductionmentioning

confidence: 99%

Statistical state dynamics of vertically sheared horizontal flows in two-dimensional stratified turbulence

Fitzgerald

Farrell

2018

J. Fluid Mech.

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Simulations of strongly stratified turbulence often exhibit coherent large-scale structures called vertically sheared horizontal flows (VSHFs). VSHFs emerge in both twodimensional (2D) and three-dimensional (3D) stratified turbulence with similar vertical structure. The mechanism responsible for VSHF formation is not fully understood. In this work, the formation and equilibration of VSHFs in a 2D Boussinesq model of stratified turbulence is studied using statistical state dynamics (SSD). In SSD, equations of motion are expressed directly in the statistical variables of the turbulent state. Restriction to 2D turbulence makes available an analytically and computationally attractive implementation of SSD referred to as S3T, in which the SSD is expressed by coupling the equation for the horizontal mean structure with the equation for the ensemble mean perturbation covariance. This second order SSD produces accurate statistics, through second order, when compared with fully nonlinear simulations. In particular, S3T captures the spontaneous emergence of the VSHF and associated density layers seen in simulations of turbulence maintained by homogeneous large-scale stochastic excitation. An advantage of the S3T system is that the VSHF formation mechanism, which is wavemean flow interaction between the emergent VSHF and the stochastically excited largescale gravity waves, is analytically understood in the S3T system. Comparison with fully nonlinear simulations verifies that S3T solutions accurately predict the scale selection, dependence on stochastic excitation strength, and nonlinear equilibrium structure of the VSHF. These results facilitate relating VSHF theory and geophysical examples of turbulent jets such as the ocean's equatorial deep jets.

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Formation of Jets by Baroclinic Turbulence

Cited by 42 publications

References 112 publications

Dynamics of streamwise rolls and streaks in turbulent wall-bounded shear flow

Dynamics of streamwise rolls and streaks in turbulent wall-bounded shear flow

Is spontaneous generation of coherent baroclinic flows possible?

Statistical state dynamics of vertically sheared horizontal flows in two-dimensional stratified turbulence

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