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

Fitzgerald, Joseph G.; Farrell, Brian F.

doi:10.1017/jfm.2018.560

Cited by 13 publications

(27 citation statements)

References 80 publications

(112 reference statements)

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“…This behavior is in contrast to the usual observation in β -plane turbulence that jets transition to lower wavenumber as the excitation strength is increased (Farrell and Ioannou 2007). Our previous analysis of VSHF formation with matrix S3T is consistent with this interpretation, and also suggests that additional turbulent equilibria consisting of lower-wavenumber, more energetic VSHFs may be simultaneously stable with the equilibria shown in Figure 8 (Fitzgerald and Farrell 2016).…”

Section: Stability Boundaries a Iresupporting

confidence: 71%

“…Although this result appears to contradict the results of the NL simulation shown in Section 2, which forms buoyancy layers, our previous work has shown that these buoyancy layers do not emerge in homogeneous turbulence but instead form nonlinearly once a finite-amplitude VSHF has emerged (Fitzgerald and Farrell 2016).…”

Section: A Isotropic Ring Excitation (Ire)contrasting

confidence: 62%

“…This transition in behavior coincides with the emergence of a coherent VSHF. The abrupt emergence of the VSHF as the excitation strength is increased results from a bifurcation associated with the growth rate of the VSHF-forming instability crossing zero toward positive values at a critical excitation strength (Fitzgerald and Farrell 2016). This bifurcation is predicted by SSD and is reflected in the NL system as shown in Figure 3…”

Section: A Nl Systemmentioning

confidence: 91%

“…Here we carry out an S3T analysis of VSHF emergence in 2D stratified turbulence that complements our previous work by taking advantage of the differential linearized approach to analyzing S3T instabilities first developed by Srinivasan and Young (2012) in the context of the zonostrophic instability. Our previous work primarily addressed the structure and maintenance mechanism of finite amplitude VSHFs (Fitzgerald and Farrell 2016), and used the traditional matrix implementation of S3T appropriate for this purpose (Farrell and Ioannou 2003). This analysis expands on that of our previous work in several ways.…”

Section: Introductionmentioning

confidence: 92%

“…The matrix approach is required when performing S3T analysis of the finite-amplitude structure and equilibration dynamics of the VSHF following its initial emergence. A derivation of the S3T system following the matrix approach can be found in Fitzgerald and Farrell (2016). The light grey curves in Figure 3 show the behavior of the matrix S3T system.…”

Section: S3t Systemmentioning

confidence: 99%

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Vertically Sheared Horizontal Flow-Forming Instability in Stratified Turbulence: Analytical Linear Stability Analysis of Statistical State Dynamics Equilibria

Fitzgerald

Farrell

2018

Journal of the Atmospheric Sciences

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Vertically banded zonal jets are frequently observed in weakly or non-rotating stratified turbulence, with the quasi-biennial oscillation in the equatorial stratosphere and the ocean's equatorial deep jets being two examples. Explaining the formation of jets in stratified turbulence is a fundamental problem in geophysical fluid dynamics. Statistical state dynamics (SSD) provides powerful methods for analyzing turbulent systems exhibiting emergent organization, such as banded jets. In SSD, dynamical equations are written directly for the evolution of the turbulence statistics, enabling direct analysis of the statistical interactions between the incoherent component of the turbulence and the coherent large-scale structure component that underlie jet formation. A second-order closure of SSD, known as S3T, has previously been applied to show that meridionally banded jets emerge in barotropic β -plane turbulence via a statistical instability referred to as the zonostrophic instability. Two-dimensional Boussinesq turbulence provides a simple model of non-rotating stratified turbulence analogous to the β -plane model of planetary turbulence. Jets known as vertically sheared horizontal flows (VSHFs) often emerge in simulations of Boussinesq turbulence, but their dynamics is not yet clearly understood. In this work S3T analysis of the zonostrophic instability is extended to study VSHF emergence in two-dimensional Boussinesq turbulence using an analytical formulation of S3T amenable to perturbation stability analysis. VSHFs are shown to form via an instability that is analogous in stratified turbulence to the zonostrophic instability in β -plane turbulence. This instability is shown to be strikingly similar to the zonostrophic instability, suggesting that jet emergence in both geostrophic and non-rotating stratified turbulence may be understood as instances of the same generic phenomenon. ABSTRACTTest. ABSTRACTTest. ABSTRACTTest.

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Section: Stability Boundaries a Iresupporting

confidence: 71%

Section: A Isotropic Ring Excitation (Ire)contrasting

confidence: 62%

Section: A Nl Systemmentioning

confidence: 91%

Section: Introductionmentioning

confidence: 92%

Section: S3t Systemmentioning

confidence: 99%

See 3 more Smart Citations

Vertically Sheared Horizontal Flow-Forming Instability in Stratified Turbulence: Analytical Linear Stability Analysis of Statistical State Dynamics Equilibria

Fitzgerald

Farrell

2018

Journal of the Atmospheric Sciences

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Structure formation in turbulence as an instability of effective quantum plasma

2020

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Structure formation in turbulence is effectively an instability of "plasma" formed by fluctuations serving as particles. These "particles" are quantumlike; namely, their wavelengths are non-negligible compared to the sizes of background coherent structures. The corresponding "kinetic equation" describes the Wigner matrix of the turbulent field, and the coherent structures serve as collective fields. This formalism is usually applied to manifestly quantumlike or scalar waves. Here, we extend it to compressible Navier-Stokes turbulence, where the fluctuation Hamiltonian is a five-dimensional matrix operator and diverse modulational modes are present. As an example, we calculate these modes for a sinusoidal shear flow and find two modulational instabilities. One of them is specific to supersonic flows, and the other one is a Kelvin-Helmholtz-type instability that is a generalization of the known zonostrophic instability. This work serves as a stepping stone toward improving the understanding of magnetohydrodynamic turbulence, which can be approached similarly.

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

Cited by 13 publications

References 80 publications

Vertically Sheared Horizontal Flow-Forming Instability in Stratified Turbulence: Analytical Linear Stability Analysis of Statistical State Dynamics Equilibria

Vertically Sheared Horizontal Flow-Forming Instability in Stratified Turbulence: Analytical Linear Stability Analysis of Statistical State Dynamics Equilibria

Structure formation in turbulence as an instability of effective quantum plasma

Is spontaneous generation of coherent baroclinic flows possible?

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