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We propose a high-order stochastic–statistical moment closure model for efficient ensemble prediction of leading-order statistical moments and probability density functions in multiscale complex turbulent systems. The statistical moment equations are closed by a precise calibration of the high-order feedbacks using ensemble solutions of the consistent stochastic equations, suitable for modeling complex phenomena including non-Gaussian statistics and extreme events. To address challenges associated with closely coupled spatiotemporal scales in turbulent states and expensive large ensemble simulation for high-dimensional systems, we introduce efficient computational strategies using the random batch method (RBM). This approach significantly reduces the required ensemble size while accurately capturing essential high-order structures. Only a small batch of small-scale fluctuation modes is used for each time update of the samples, and exact convergence to the full model statistics is ensured through frequent resampling of the batches during time evolution. Furthermore, we develop a reduced-order model to handle systems with really high dimensions by linking the large number of small-scale fluctuation modes to ensemble samples of dominant leading modes. The effectiveness of the proposed models is validated by numerical experiments on the one-layer and two-layer Lorenz ‘96 systems, which exhibit representative chaotic features and various statistical regimes. The full and reduced-order RBM models demonstrate uniformly high skill in capturing the time evolution of crucial leading-order statistics, non-Gaussian probability distributions, while achieving significantly lower computational cost compared to direct Monte-Carlo approaches. The models provide effective tools for a wide range of real-world applications in prediction, uncertainty quantification, and data assimilation.
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PREDICTION OF BOUNDARY LAYER THICKNESS AND FRICTION VELOCITY BY SYMMETRY ARGUMENTS
We derive analytically for the first time the downstream evolution of the boundary layer thickness and the friction ve- locity of the zero-pressure-gradient turbulent boundary layer (ZPGTBL). Lie groups were used to derive the downstream evolution and to obtain the full set of the similarity variables and the leading-order similarity equations. An approximate leading-order solution was obtained using matched asymp- totic expansions. The similarities and differences between ZPGTBL and turbulent channel flows in terms of the similarity equations are discussed to support the notion of leading-order universality of the near-wall layer.
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- Award ID(s):
- 2054983
- PAR ID:
- 10611359
- Editor(s):
- Tavoularis, Stavros; Ganapathisubramani, Bharathram; McKeon, Beverley; Oberlack, Martin; Sung, Hyung Jin; Mydlarski, Laurent
- Publisher / Repository:
- Begell House (International Symposium on Turbulence and Shear Flow Phenomena)
- Date Published:
- Edition / Version:
- 1
- Volume:
- 1
- Issue:
- 1
- ISSN:
- 2642-0554
- ISBN:
- 1-56700-135-1
- Page Range / eLocation ID:
- 1-6
- Subject(s) / Keyword(s):
- Turbulent boundary layer
- Format(s):
- Medium: X Size: 110KB Other: pdf
- Size(s):
- 110KB
- Location:
- Danbury, CT 06810
- Sponsoring Org:
- National Science Foundation
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