Statistics of Extreme Events in Fluid Flows and Waves

Sapsis, Themistoklis P.

doi:10.1146/annurev-fluid-030420-032810

Cited by 73 publications

(42 citation statements)

References 103 publications

(120 reference statements)

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“…Single-phase turbulence at high Reynolds number exhibits fluctuations in space and time of its small-scale quantities that are orders of magnitude larger than the average values, a phenomenon referred to as small-scale intermittency (Frisch 1995; Sreenivasan & Antonia 1997). Such extreme fluctuations are critical for many processes in both nature and engineering (Sapsis 2021), and their investigation continues to be an area of active research (Yeung, Zhai & Sreenivasan 2015; Buaria et al. 2019).…”

Section: Extreme Fluctuations In the Flowmentioning

confidence: 99%

An experimental study on the multiscale properties of turbulence in bubble-laden flows

Hessenkemper

Lucas

et al. 2022

J. Fluid Mech.

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The properties of bubble-laden turbulent flows at different scales are investigated experimentally, focusing on the flow kinetic energy, energy transfer and extreme events. The experiments employed particle shadow velocimetry measurements to measure the flow in a column generated by a homogeneous bubble swarm rising in water, for two different bubble diameters ( $2.7$ mm and $3.9$ mm) and moderate gas volume fractions ( $0.26\,\%\sim 1.31\,\%$ ). The two velocity components were measured at high resolution, and used to construct structure functions up to twelfth order for separations spanning the small to large scales in the flow. Concerning the flow anisotropy, the velocity structure functions are found to differ for separations in the vertical and horizontal directions of the flow, and the cases with smaller bubbles are the most anisotropic, with a dependence on void fraction. The degree of anisotropy is shown to increase as the order of the structure functions is increased, showing that extreme events in the flow are the most anisotropic. Our results show that the average energy transfer with the horizontal velocity component is downscale, just as for the three-dimensional single-phase turbulence. However, the energy transfer associated with the vertical component of the fluid velocity is upscale. The probability density functions of the velocity increments reveal that extreme values become more probable with decreasing Reynolds number, the opposite of the behaviour in single-phase turbulence. We visualize those extreme events and find that regions of intense small-scale velocity increments occur near the turbulent/non-turbulent interface at the boundary of the bubble wake.

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Section: Extreme Fluctuations In the Flowmentioning

confidence: 99%

An experimental study on the multiscale properties of turbulence in bubble-laden flows

Hessenkemper

Lucas

et al. 2022

J. Fluid Mech.

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“…extreme events, panel (a) in Fig. 1, which generate the heavy tail of the distribution [10], panel (b). In the figure, time is expressed in Lyapunov Times (LT), where a LT is the inverse of the Lyapunov exponent, Λ 0.0163.…”

Section: A Low-dimensional Model For Turbulent Shear Flowmentioning

confidence: 99%

“…The prediction of the PDF improves with the size of the datasets, and values of the tail up to laminarization are observed only after 100 time series. The unresolved tail due to lack of data is a signature problem of data-driven analysis of extreme events [10]. Panels (b)-(c) show the Kantorovich metric and the MLE of the training sets and networks as a function of the training set size.…”

Section: Statistical Prediction Of Extreme Eventsmentioning

confidence: 99%

“…Because extreme events are typically rare, information about the heavy tail of the distribution that describes the events is seldom available. This hinders the performance of data-driven methods, which struggle to predict the events when extrapolating from imperfect datasets [10]. In this work, we assess the capability of a form of reservoir computing, the Echo State Network [7], to predict the statistics of extreme events in a turbulent flow [8].…”

Section: Introductionmentioning

confidence: 99%

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Statistical prediction of extreme events from small datasets

Racca¹,

Magri²

2022

Preprint

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We propose Echo State Networks (ESNs) to predict the statistics of extreme events in a turbulent flow. We train the ESNs on small datasets that lack information about the extreme events. We asses whether the networks are able to extrapolate from the small imperfect datasets and predict the heavy-tail statistics that describe the events. We find that the networks correctly predict the events and improve the statistics of the system with respect to the training data in almost all cases analysed. This opens up new possibilities for the statistical prediction of extreme events in turbulence.

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“…The present analysis, thus, encourages further investigation into the emergence of extreme events in the TBL with increasing Re τ . Such events are responsible for the non-Gaussian tails in the probability distribution function of the flux signal, and hence are of significance to the meteorological community interested in predicting ABL turbulence [20,52]. The population density for a specific Re τ case is calculated by considering the statistically significant events from all four quadrants as a reference.…”

mentioning

confidence: 99%

Characterising Momentum Flux Events in High Reynolds Number Turbulent Boundary Layers

Deshpande

Marušić

2021

Fluids

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The momentum flux in a canonical turbulent boundary layer is known to have a time-series signature that is characterised by a highly intermittent variation, which includes very short periods of intense flux activity. Here, we study the variation in these flux signal characteristics across almost a decade of flow Reynolds number (Reτ) by analysing datasets acquired using miniature cross-wire probes with matched spatial resolution. The analysis is facilitated by conditionally sampling the signal based on the quadrant (Qi; i = 1–4) and magnitude of the flux, revealing fractional cumulative contribution from Q4 to increase at a much faster rate than from Q2 with Reτ. An episodic description of the flux signal is subsequently undertaken, which associates this rapid increase in Q4 contributions with the emergence of extreme and rare flux events with Reτ. The same dataset is also used to test Townsend’s hypothesis on the active and inactive components of the momentum flux, which are obtained for the first time by implementing a spectral linear stochastic estimation-based decomposition methodology. While the active component is found to be the dominant contributor to the mean momentum flux consistent with Townsend’s hypothesis, the inactive component is found to be small but non-zero, owing to the non-linear interactions associated with the modulation phenomenon. Finally, an episodic description of the active and inactive momentum flux signal is undertaken to highlight the starkly different time series characteristics of the two flux components. The inactive flux signal is found to comprise individual statistically significant events associated with all four quadrants, leading to a small net contribution to the total flux.

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Statistics of Extreme Events in Fluid Flows and Waves

Cited by 73 publications

References 103 publications

An experimental study on the multiscale properties of turbulence in bubble-laden flows

An experimental study on the multiscale properties of turbulence in bubble-laden flows

Statistical prediction of extreme events from small datasets

Characterising Momentum Flux Events in High Reynolds Number Turbulent Boundary Layers

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