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Publications

2019
Farrell, B. F., & Petros, J. I. (2019). Statistical State Dynamics: A New Perspective on Turbulence in Shear Flow. In E. B. Galpirin & P. L. Read (Ed.), Zonal Jets Phenomenology, Genesis, and Physics (pp. 380-400) . Cambridge University Press. .pdf
F., F. B., & Ioannou, P. J. (2019). Statistical State Dynamics: A New Perspective on Turbulence in Shear Flow. Zonal Jets Phenomenology, Genesis, and Physics. , 380-400. .pdf
Fitzgerald, J. G., & Farrell, B. F. (2019). Statistical state dynamics analysis of buoyancy layer formation via the Phillips mechanism in two-dimensional stratified turbulence. J. Fluid Mech. , 864, R3 1-15. .pdf
Farrell, B. F., & Ioannou, P. J. (2019). Statistical State Dynamics: A New Perspective on Turbulence in Shear Flow. Zonal Jets Phenomenology, Genesis, and Physics. Ed. Boris Galpirin and Peter L. Read. Cambridge University Press 2019. , 380-400. .pdf
2018
Fitzgerald, J. G., & Farrell, B. F. (2018). Vertically Sheared Horizontal Flow-Forming Instability in Stratified Turbulence: Analytical Linear Stability Analysis of Statistical State Dynamics Equilibria. J. Atmos. Sci. , 75, 4201-4227. .pdf
Farrell, B. F., Ioannou, P. J., & Nikolaidis, M. - A. (2018). Statistical State Dynamics Based Study of the Role of Nonlinearity in the Maintenance of Turbulence in Couette Flow. arXiv:1808.07948v1. Publisher's Version .pdf
Farrell, B. F., Ioannou, P. J., & Nikolaidis, M. - A. (2018). Parametric mechanism maintaining Couette flow turbulence verified in DNS. Center for Turbulence Research Proceedings of the Summer Program 2018 , 227-236. .pdf
Nikolaidis, M. - A., Farrell, B. F., & Ioannou, P. J. (2018). The mechanism by which nonlinearity sustains turbulence in plane Couette flow. Journal of Physics , 1001, 012014. .pdf
Fitzgerald, J. G., & Farrell, B. F. (2018). Statistical state dynamics of vertically sheared horizontal flows in two-dimensional Strati fied turbulence. Journal of Fluid Dynamics , 854, 544-590. .pdf
2017
Farrell, B. F., Ioannou, P. J., & Nikolaidis, M. A. (2017). Instability of the roll-streak structure induced by background turbulence in pretransitional Couette flow. Phys. Rev. Fluids , 2, 034607. .pdf
Farrell, B. F., Gayme, D. F., & Ioannou, P. J. (2017). A statistical state dynamics approach to wall turbulence. Phil. Trans. R. Soc. A , 375, 20160081. pdf
Farrell, B. F., & Ioannou, P. J. (2017). A statistical state dynamics based theory for the formation and equilibration of Saturn's North Polar Jet. Phys. Rev. Fluids , 2,073801. .pdf
Farrell, B. F., & Ioannou, P. J. (2017). A statistical state dynamics-based analysis of the physical mechanisms sustaining and regulating turbulence in Couette flow. Phys. Rev. Fluids , 2, 084608. .pdf
2016
Farrell, B. F., Ioannou, P. J., Jimenez, J., Constantinou, N. C., Lozano-Duran, A., & Nikolaidis, M. - A. (2016). A statistical state dynamics-based study of the structure and mechanism of large-scale motions in plane Poiseuille flow. J. Fluid Mech. , 809, 290-315. .pdf
Nikolaidis, M. - A., Farrell, B. F., Ioannou, P. J., Gayme, D. F., Lozano-Duran, A., & Jimenez, J. (2016). A POD-based analysis of turbulence in the reduced nonlinear dynamics system. Journal of Physics: Conference Series , 708 (1), 012002. .pdf
Farrell, B. F., Ioannou, P. J., Jimenez, J., Constantinou, N. C., LozanoDuran, A., & Nikolaidis, M. - A. (2016). Structure and mechanism of turbulence under dynamical restriction in plane Poiseuille flow. pages_from_vlsm-poiseulle.pdf
Constantinou, N. C., Farrell, B. F., & Ioannou, P. J. (2016). Statistical state dynamics of jet/wave coexistence in beta-plane turbulence. J. Atmos. Sci. , 73 (1), 2229-2253. pdf
2015
Farrell, B. F., Ioannou, P. J., Jimenez, J., Constantinou, N. C., Lozano-Duran, A., & Nikolaidis, M. A. (2015). Structure and mechanism of turbulence under dynamical restriction in plane Poiseuille flow. arXiv,1512.06018v1. pdf
B.F., F., Ioannou, P. J., Jimenez, J., Constantinou, N. C., Lozano-Duran, A., & Nikolaidis, M. A. (2015). Structure and mechanism of turbulence under dynamical restriction in plane Poiseuille flow. ArXiv , 1512.06018v1.Abstract

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 example
application of SSD is that of the second order closure, referred to as stochastic structural
stability theory (S3T), which has provided insight into the dynamics of wall turbulence
and specically the emergence and maintenance of the roll/streak structure. When
implemented as a coupled set of equations for the streamwise mean and perturbations, this
closure eliminates nonlinear interactions among the perturbations restricting nonlinearity
in the dynamics to that of the mean equation and interaction between the mean and
perturbations. Simulations at modest Reynolds numbers reveal that the essential features
of wall-turbulence dynamics are retained with the dynamics restricted in this manner.
Here this restriction of the dynamics is used to obtain a closely related dynamical system,
referred to as the restricted non-linear (RNL) system, which is used to study the structure
and dynamics of turbulence in plane Poiseuille
ow at moderately high Reynolds numbers.
Remarkably, the RNL system spontaneously limits the support of its turbulence to a small
set of streamwise Fourier components giving rise to a natural minimal representation
of its turbulence dynamics. Although greatly simplied, this RNL turbulence exhibits
natural-looking structures and statistics. Surprisingly, even when a further truncation of
the perturbation support to a single streamwise component is imposed the RNL system
continues to produce self-sustaining turbulent structure and dynamics. The turbulent

ow in RNL simulations at the Reynolds numbers studied is dominated by the roll/streak
structure in the buer layer and 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
buer and logarithmic layer is essentially similar in RNL and DNS.

1512.06018v1.pdf
Thomas, V. L., Farrell, B. F., Ioannou, P. J., & Gayme, D. F. (2015). A Minimal Model of Self-Sustaining Turbulence. Physics of Fluids , 27, 105104. pdf

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