Observation-infused simulations of high-speed boundary-layer transition

Buchta, David; Zaki, Tamer A.

doi:10.1017/jfm.2021.172

Cited by 16 publications

(22 citation statements)

References 60 publications

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“…estimated initial conditions, with marked observations. The assimilated trajectory latches onto the truth, reproduces observations, and accurately forecasts the system for some time beyond the observation horizon [18]. Using the preferential weighting of upstream observations, [18] performed an ensemble, rather than adjoint, variational estimation of the initial condition and the results are shown in figure 3c.…”

Section: B Transition To Chaosmentioning

confidence: 97%

“…The assimilated trajectory latches onto the truth, reproduces observations, and accurately forecasts the system for some time beyond the observation horizon [18]. Using the preferential weighting of upstream observations, [18] performed an ensemble, rather than adjoint, variational estimation of the initial condition and the results are shown in figure 3c. While the predicted initial state is visibly displaced relative to the truth, the predicted trajectory quickly latches onto the true one, reproduces all the observations and provides an accurate forecast for the shown duration past the observation horizon.…”

Section: B Transition To Chaosmentioning

confidence: 97%

“…A helpful prototype system to explore the influence of transition and chaos on data assimilation is the Lorenz model of unstable convection in two dimensions [18]. The setup is periodic in the horizontal direction, and both gravity and a temperature difference between the lower and upper boundaries, ∆Θ = Θ(0) − Θ(H), act in the vertical direction.…”

Section: B Transition To Chaosmentioning

confidence: 99%

“…Figure 4 shows that the cost-function landscape is highly oscillatory, laden with local minima and, as a result, difficult to navigate to identify the global minimum. The idea of preferentially weighting early observation was evaluated by Buchta and Zaki [18]. The weighted cost function is 2 , where W is a diagonal matrix with larger elements corresponding to earlier observations.…”

Section: B Transition To Chaosmentioning

confidence: 99%

“…By decoding the observations we reveal the hidden flow physics that is unavailable from forward analysis, including the domain of dependence of an observation site, the critical data resolution for an accurate state estimation, and the robustness of reconstructed flow events to observation noise. This perspective also motivates a new notion of optimal layout and weighting of measurements: Instead of concentrating measurements near a region of interest based on knowledge of the forward problem, sensor placements can be optimized in order to provide the most accurate interpretation, or reconstruction, of the entire flow field using data assimilation [17,18].…”

Section: Introduction a Why Data Assimilation?mentioning

confidence: 99%

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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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Section: B Transition To Chaosmentioning

confidence: 97%

Section: B Transition To Chaosmentioning

confidence: 97%

Section: B Transition To Chaosmentioning

confidence: 99%

Section: B Transition To Chaosmentioning

confidence: 99%

Section: Introduction a Why Data Assimilation?mentioning

confidence: 99%

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