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Selfsustaining turbulence in a restricted nonlinear model of plane Couette flow
, 2014
"... This paper demonstrates the maintenance of selfsustaining turbulence in a restricted nonlinear (RNL) model of plane Couette flow. The RNL system is derived directly from the Navier Stokes equations and permits computationally tractable studies of the dynamical system obtained using stochastic struc ..."
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This paper demonstrates the maintenance of selfsustaining turbulence in a restricted nonlinear (RNL) model of plane Couette flow. The RNL system is derived directly from the Navier Stokes equations and permits computationally tractable studies of the dynamical system obtained using stochastic structural stability theory (S3T), which is a second order approximation of the statistical state dynamics of the flow. The RNL model shares the dynamical restrictions of the S3T model but can be easily implemented through reducing a DNS code to the equations governing the RNL system. Comparisons of turbulence arising from DNS and RNL simulations demonstrate that the RNL system supports selfsustaining turbulence with a mean flow as well as structural and dynamical features that are consistent with DNS. These results demonstrate that the simplified RNL/S3T system captures fundamental aspects of fully developed turbulence in wallbounded shear flows and motivates use of the RNL/S3T system for further study of wall turbulence. 1 ar
SUBCRITICAL TRANSISTION TO TURBULENCE IN TAYLORCOUETTE FLOW Approved by:
, 2014
"... chispas... iii ACKNOWLEDGEMENTS The work presented here would not have been possible without the support of many people. First, and foremost, I would like to thank my advisor, Mike Schatz, without whose patience and optimism this work would have never come to be. Mike was always a great sounding boa ..."
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chispas... iii ACKNOWLEDGEMENTS The work presented here would not have been possible without the support of many people. First, and foremost, I would like to thank my advisor, Mike Schatz, without whose patience and optimism this work would have never come to be. Mike was always a great sounding board for ideas and somehow managed to find the funds to try out any crazy idea that I came up with, always egging me on with a cheeful, “Onward and upward! ” Mike was a constant source of support through the ups and downs of research and was incredibly generous with providing me with many opportunities for professional development. Mike’s passion for teaching has also been a great inspiration. Predrag Cvitanovic ́ has been a persistence presence, always pushing me and the rest of the Center for Nonlinear Science to dream big and attack the hard problems. Ever quotable, his dry sense of humor is always good for a chuckle. Roman Grigoriev has been the ying to Predrag’s yang. Ever patient and willing to answer even the most basic questions, Roman
Invariant tori Parallel algorithms Continuation methods Generalized Poincaré maps
, 2013
"... ih i g h l i g h t s • A parallel algorithm to compute invariant tori of largescale systems is presented. • The new method is compared with a previous serial algorithm. • The two methods are applied to the thermal convection of a binary mixture. • Speedups around the number of processors employed ..."
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ih i g h l i g h t s • A parallel algorithm to compute invariant tori of largescale systems is presented. • The new method is compared with a previous serial algorithm. • The two methods are applied to the thermal convection of a binary mixture. • Speedups around the number of processors employed are achieved for the new method. • The comparison with the old method shows speedups above the number of processors. a r t i c l e i n f o Article history:
Exact Coherent States
, 2011
"... Shear enhanced dissipation, R1/3 scaling in shear flows. Critical layer in lower branch exact coherent states. SSP model modified to include critical layers. Construction of exact coherent states in full NavierStokes. Optimum traveling wave and nearwall coherent structures, 100+ streak spacing. Ph ..."
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Shear enhanced dissipation, R1/3 scaling in shear flows. Critical layer in lower branch exact coherent states. SSP model modified to include critical layers. Construction of exact coherent states in full NavierStokes. Optimum traveling wave and nearwall coherent structures, 100+ streak spacing. Physical space structures of turbulence. State space structure of turbulence. 1 Shear enhanced dissipation In the (quick) overview of the SSP model, we discussed how the shearing of xdependent modes by the mean shear leads to a positive feedback on the mean flow. In the SSP model these are the W 2 term in the M equation and the −MW term in the W equation. Although this interaction is not necessary for the selfsustaining process itself, it is the key effect that leads to the R −1 scaling of the transition threshold, and of the V and W components of the lower branch steady state (while U and 1 − M are O(1), see lectures 1 and 5). Advection by a shear flow leads to enhanced dissipation and an R −1/3 scaling characteristic of linear perturbations about shear flows, or evolution of a passive scalar. The R −1/3 enhanced damping, instead of R −1, was included by Chapman for the xdependent modes
Accepted for publication in J. Fluid Mech. Rapids 1 A doublylocalized equilibrium solution of plane
"... We present an equilibrium solution of plane Couette flow that is exponentially localized in both the spanwise and streamwise directions. The solution is similar in size and structure to previously computed turbulent spots and localized, chaotically wandering edge states of plane Couette flow. A lin ..."
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We present an equilibrium solution of plane Couette flow that is exponentially localized in both the spanwise and streamwise directions. The solution is similar in size and structure to previously computed turbulent spots and localized, chaotically wandering edge states of plane Couette flow. A linear analysis of dominant terms in the NavierStokes equations shows how the exponential decay rate and the wallnormal overhang profile of the streamwise tails are governed by the Reynolds number and the dominant spanwise wavenumber. Perturbations of the solution along its leading eigenfunctions cause rapid disruption of the interior rollstreak structure and formation of a turbulent spot, whose growth or decay depends on the Reynolds number and the choice of perturbation. 1.
and plane Couette
"... the transition to turbulence of wallbounded flows in general, ..."
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unknown title
, 2014
"... Under consideration for publication in J. Fluid Mech. 1 Edge states for the turbulence transition in the asymptotic suction boundary layer ..."
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Under consideration for publication in J. Fluid Mech. 1 Edge states for the turbulence transition in the asymptotic suction boundary layer