A probabilistic protocol for the assessment of transition and control

Pershin, Anton; Beaume, Cédric; Tobias, Steven M.

doi:10.1017/jfm.2020.306

Cited by 4 publications

(31 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This paves the way for their use as generators of earlywarning signals of critical transitions (26). Finally, we take a look at the opposite kind of transition, laminar-to-turbulent transition, and show that ESNs can be used to approximate the transition probability, one of the key statistics associated with this type of instability (27).…”

Section: Resultsmentioning

confidence: 89%

“…To characterize this transition statistically, it is convenient to introduce the laminarization probability P lam (E), which is the probability that a random perturbation to the laminar flow decays as a function of its kinetic energy E (27). The laminarization probability is related to the relative volume of the basin of attraction of the laminar flow and is therefore related to the notion of basin stability (18).…”

Section: B Early Warning Of Turbulent-to-laminar Transitionmentioning

confidence: 99%

See 1 more Smart Citation

Can neural networks predict dynamics they have never seen?

Pershin¹,

Beaume²,

Li³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

Neural networks have proven to be remarkably successful for a wide range of complicated tasks, from image recognition and object detection to speech recognition and machine translation. One of their successes is the skill in prediction of future dynamics given a suitable training set of data. Previous studies have shown how Echo State Networks (ESNs), a subset of Recurrent Neural Networks, can successfully predict even chaotic systems for times longer than the Lyapunov time. This study shows that, remarkably, ESNs can successfully predict dynamical behavior that is qualitatively different from any behavior contained in the training set. Evidence is provided for a fluid dynamics problem where the flow can transition between laminar (ordered) and turbulent (disordered) regimes. Despite being trained on the turbulent regime only, ESNs are found to predict laminar behavior. Moreover, the statistics of turbulent-to-laminar and laminar-to-turbulent transitions are also predicted successfully, and the utility of ESNs in acting as an early-warning system for transition is discussed. These results are expected to be widely applicable to data-driven modelling of temporal behaviour in a range of physical, climate, biological, ecological and finance models characterized by the presence of tipping points and sudden transitions between several competing states.

show abstract

Section: Resultsmentioning

confidence: 89%

Section: B Early Warning Of Turbulent-to-laminar Transitionmentioning

confidence: 99%

Can neural networks predict dynamics they have never seen?

Pershin¹,

Beaume²,

Li³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…The streamwise and spanwise directions are discretized using and Fourier coefficients, and the wall-normal direction is discretized using Chebyshev coefficients (Pershin et al. 2020), yielding approximately degrees of freedom. A third-order semi-implicit backward differentiation scheme with time step is used to advance the flow in time.…”

Section: Plane Couette Flow Under Spanwise Wall Oscillationsmentioning

confidence: 99%

“…Pershin et al. (2020) used it successfully to quantify the nonlinear stability of laminar plane Couette flow at several values of the Reynolds number and under the action of spanwise wall oscillations. However, the calculation of the laminarization probability in Pershin et al.…”

Section: Introductionmentioning

confidence: 99%

“…However, the calculation of the laminarization probability in Pershin et al. (2020) required an extremely large number of simulations to be performed to achieve statistically converged results. Here, we introduce a novel Bayesian approach to calculating the laminarization probability that requires substantially fewer simulations to provide useful results.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Optimizing the control of transition to turbulence using a Bayesian method

et al. 2022

View full text Add to dashboard Cite

The nonlinear robustness of laminar plane Couette flow is considered under the action of in-phase spanwise wall oscillations by computing properties of the edge of chaos, i.e. the boundary of its basins of attraction. Three measures are used to quantify the chosen control strategy on laminar-to-turbulent transition: the kinetic energy of edge states (local attractors on the edge of chaos), the form of the minimal seed (least energetic perturbation on the edge of chaos), and the laminarization probability (the probability that a random perturbation from the laminar flow of given kinetic energy will laminarize). A novel Bayesian approach is introduced to enable the accurate computation of the laminarization probability at a fraction of the cost of previous methods. While the edge state and the minimal seed provide useful information about the dynamics of transition to turbulence, neither measure is particularly useful to judge the effectiveness of the control strategy since they are not representative of the global geometry of the edge. In contrast, the laminarization probability provides global information about the edge and can be used to evaluate the control effectiveness by computing a laminarization score (the expected laminarization probability) and the associated expected dissipation rate of the controlled flow. These two quantities allow for the determination of optimal control parameter values subject to desired constraints. The results discussed in the paper are expected to be applied to a wide range of transitional flows and control strategies aimed at suppressing or triggering transition to turbulence.

show abstract

Improving performances of biomimetic wings with leading-edge tubercles

2022

View full text Add to dashboard Cite

The present study aims investigating experimentally wing/blade geometries in which the leading edge is modified by the presence of artificial bumps, following examples in nature (“biomimetics”). Specifically, the tubercles observed in humpback whales are considered with a special focus on easy manufacturing and performance improvements, trying to overcome the observed lift coefficient reduction before stall in comparison with a standard wing. To this end, different tubercle geometries are tested, by measuring overall forces acting on the wings and by deriving detailed velocity fields using particle image velocimetry. Measurements indicate performance improvements for all trailing edge tubercle geometries here tested. In addition, the detailed analysis of mechanisms underlying the improvement of performances suggests that a triangular shape of the leading edge combines the advantages of easy manufacturing and improvements of pre-stall behaviour. So far, a simple mathematical model, describing tubercles as delta wings, is presented and verified by experimental data. The objective of the present work is focusing on the basic fluid-mechanics phenomena involved, to show that beneficial effects of tubercles are present even when tubercle details are simplified, in order to couple performance improvement and ease of assembly. Graphical Abstract

show abstract

A probabilistic protocol for the assessment of transition and control

Cited by 4 publications

References 40 publications

Can neural networks predict dynamics they have never seen?

Can neural networks predict dynamics they have never seen?

Optimizing the control of transition to turbulence using a Bayesian method

Improving performances of biomimetic wings with leading-edge tubercles

Contact Info

Product

Resources

About