Stochastic Lagrangian dynamics of vorticity. Part 1. General theory for viscous, incompressible fluids

Eyink, Gregory L.; Gupta, Akshat; Zaki, Tamer A.

doi:10.1017/jfm.2020.491

Cited by 19 publications

(18 citation statements)

References 70 publications

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“…In practice, control of wall-bounded turbulence may rely on sensing and actuation at the wall, and effective strategies are often predicated on decoding the wall signature of outer turbulence structures. It has been demonstrated both mathematically (Lighthill 1963; Constantin & Iyer 2011) and numerically (Eyink, Gupta & Zaki 2020 a , b ) that all the interior vorticity is generated at the wall. The converse problem, specifically to what extent the initial flow state can be predicted from wall observations, has not been addressed as comprehensively.…”

Section: State Estimation Resultsmentioning

confidence: 99%

“…From a theoretical perspective, it is known that all the vorticity in the field can be traced back in time to its origin at the wall (Lighthill 1963; Constantin & Iyer 2011; Eyink et al. 2020 a , b ); here the converse problem is examined, where the wall vorticity is traced back to the initial state of the flow. From a practical perspective, the capacity to control wall turbulence is often reliant on our ability to predict its state from wall measurements.…”

Section: Discussionmentioning

confidence: 99%

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State estimation in turbulent channel flow from limited observations

Wang

Zaki

2021

J. Fluid Mech.

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Section: State Estimation Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

State estimation in turbulent channel flow from limited observations

Wang

Zaki

2021

J. Fluid Mech.

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“…In particular, Wu & Wu (1993, 1996, 1998) assert that Lyman's proposal is not correct and that Lighthill's original definition must be used. On the other hand, Kolár (2003) appears to accept that either definition may be used, while Eyink (2008) and Eyink, Gupta & Zaki (2020) prefer Lyman's definition. It remains unclear, then, whether it is appropriate to use Lyman's definition of the boundary vorticity flux.…”

Section: Introductionmentioning

confidence: 99%

The generation and diffusion of vorticity in three-dimensional flows: Lyman's flux

2021

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“…We will focus the application of the above formulation on wall observations in turbulent channel flow due to their theoretical significance. The generation of all the interior vorticity in the channel can be traced back to the wall [40,41]. The converse problem, specifically whether the entire initial turbulent state can be decoded from wall signals, has not been addressed comprehensively.…”

Section: Domain Of Dependence and Hessian Matrixmentioning

confidence: 99%

From limited observations to the state of turbulence: Fundamental difficulties of flow reconstruction

Zaki¹,

Wang²

2021

Preprint

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Numerical simulations of turbulence provide non-intrusive access to all the resolved scales and any quantity of interest, although they often invoke idealizations and assumptions that can compromise realism. In contrast, experimental measurements probe the true flow with lesser idealizations, but they continually contend with spatio-temporal sensor resolution. Assimilating observations directly in simulations can combine the benefits of both approaches and mitigate their respective deficiencies. The problem is expressed in variational form, where we seek the flow field that satisfies the Navier-Stokes equations and minimizes a cost function defined in terms of the deviation of the computational predictions and available observations. In this framework, measurements are no longer a mere record of the instantaneous, local quantity, but rather an encoding of the antecedent flow events that we aim to decode using the governing equations. Chaos plays a central role in obfuscating the interpretation of the data: observations that are infinitesimally close may be due to entirely different earlier conditions. We examine a number of state estimation problems: In circular Couette flow, starting from observations of the wall stress, we accurately reconstruct the wavy Taylor vortices that interact nonlinear to maintain a saturated state. Through a discussion of transition to chaos in a Lorenz system, we highlight the challenge of navigating the landscape of the cost function, and how the landscape can favorably be modified by sensor weighting and placement. In turbulent channel flow, the Taylor microscale and Lyapunov timescale place restrictions on the resolution of observations for which we can accurately reconstruct all the missing scales. The notion of domain of dependence of an observation is introduced and related to the Hessian of the cost function. For measurements of wall shear stress, the eigenspectrum of the Hessian demonstrates the sensitivity of short-time observations to the fine near-wall turbulent scales and to the large scales only in the outer flow. At long times, backward chaos obfuscates the interpretation of the data: observations that are infinitesimally close may be traced back to entirely different earlier flow states-a dual to the more common butterfly effect for forward trajectories.

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Stochastic Lagrangian dynamics of vorticity. Part 1. General theory for viscous, incompressible fluids

Abstract: Abstract

Cited by 19 publications

References 70 publications

State estimation in turbulent channel flow from limited observations

State estimation in turbulent channel flow from limited observations

The generation and diffusion of vorticity in three-dimensional flows: Lyman's flux

From limited observations to the state of turbulence: Fundamental difficulties of flow reconstruction

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