Minimal perturbations approaching the edge of chaos in a Couette flow

Cherubini, Stefania; Palma, P. De

doi:10.1088/0169-5983/46/4/041403

Cited by 11 publications

(9 citation statements)

References 32 publications

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“…In fact, the latter study was able to reduce T down to ≈ 16 D/U before finding any significant structural change in the NLOP. There is also further indirect evidence for this robustness to the choice T in that similar optimals are reported across a variety of flows: in plane Couette flow (Cherubini & De Palma 2013, 2014a; the Blasius boundary layer (Cherubini et al 2010(Cherubini et al , 2011(Cherubini et al , 2012; the asymptotic suction boundary layer (Cherubini et al 2015) and plane Poiseuille flow (Farano et al 2015(Farano et al , 2016). If T is too small, transients can obscure the situation (Rabin et al 2012) or new optimals become preferred (Pringle et al 2015, Farano 2015.…”

Section: Switching Basins Of Attraction: Minimal Seeds For Transitionmentioning

confidence: 63%

Nonlinear Nonmodal Stability Theory

Kerswell

2018

Annu. Rev. Fluid Mech.

133

103

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This review discusses a recently developed optimization technique for analyzing the nonlinear stability of a flow state. It is based on a nonlinear extension of nonmodal analysis and, in its simplest form, consists of finding the disturbance to the flow state of a given amplitude that experiences the largest energy growth at a certain time later. When coupled with a search over the disturbance amplitude, this can reveal the disturbance of least amplitude—called the minimal seed—for transition to another state such as turbulence. The approach bridges the theoretical gap between (linear) nonmodal theory and the (nonlinear) dynamical systems approach to fluid flows by allowing one to explore phase space at a finite distance from the reference flow state. Various ongoing and potential applications of the technique are discussed.

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Section: Switching Basins Of Attraction: Minimal Seeds For Transitionmentioning

confidence: 63%

Nonlinear Nonmodal Stability Theory

Kerswell

2018

Annu. Rev. Fluid Mech.

133

103

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“…However, these methods are impractical at finding the smallest possible solution capable of just kicking the system away from the laminar state, as they require a large number of simulations/experiments. Recent developments have been achieved using variational methods to construct fully nonlinear optimisation problems that seek the minimal seed (Pringle & Kerswell 2010;Pringle et al 2012;Cherubini et al 2012;Duguet et al 2013;Cherubini & Palma 2014); see Kerswell (2018) for a review. From a dynamical-systems point of view, the minimal seed represents the closest (in a chosen norm) point of approach of the laminar-turbulent boundary, or 'edge', to the basic state in phase space, as shown in figure 1.…”

Section: Transition In Pipe Flows and Calculation Of The Minimal Seedmentioning

confidence: 99%

Stabilisation and drag reduction of pipe flows by flattening the base profile

2019

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Recent experimental observations (Kühnen et al., Nat. Phys., 2018) have shown that flattening a turbulent streamwise velocity profile in pipe flow destabilises the turbulence so that the flow relaminarises. We show that a similar phenomenon exists for laminar pipe flow profiles in the sense that the nonlinear stability of the laminar state is enhanced as the profile becomes more flattened. Significant drag reduction is also observed for the turbulent flow when triggered by sufficiently large disturbances. The flattening of the laminar base profile is produced by an artificial localised body force designed to mimic an obstacle used in the experiments of Kühnen et al. (Flow Turbul. Combust., 2018) and the nonlinear stability measured by the size of the energy of the initial perturbations needed to trigger transition. In order to make the latter computation more efficient, we examine how indicative the minimal seed − the disturbance of smallest energy for transition − is in measuring transition thresholds. We first show that the minimal seed is relatively robust to base profile changes and spectral filtering. We then compare the (unforced) transition behaviour of the minimal seed with several forms of randomised initial conditions in the range of Reynolds numbers Re = 2400 to 10000 and find that the energy of the minimal seed after the Orr and oblique phases of its evolution is close to that of a localised random disturbance. In this sense, the minimal seed at the end of the oblique phase can be regarded as a good proxy for typical disturbances (here taken to be the localised random ones) and is thus used as initial condition in the simulations with the body force. The enhanced nonlinear stability and drag reduction predicted in the present study are an encouraging first step in modelling the experiments of Kühnen et al. and should motivate future developments to fully exploit the benefits of this promising direction for flow control.

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“…Edge states are useful from a fundamental point of view because they arise in subcritical bifurcations that are key to the turbulence transition, as discussed in depth in [4,5]. They can also be used to find minimal disturbances that quickly become turbulent [6,7].As an invariant state within the LTB, the edge state can come in many forms. In small computational domains in plane Couette it is a fixed point of the Navier-Stokes equation [8] and for narrow domains in PPF it is either a periodic orbit or a travelling wave, depending on the domain length [9,10].…”

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confidence: 99%