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Reexamining the framework for intermittency in Lagrangian stochastic models for turbulent flows: a way to an original and versatile numerical approach

Letournel, Roxane and Goudenège, Ludovic and Zamansky, Rémi and Vié, Aymeric and Massot, Marc Reexamining the framework for intermittency in Lagrangian stochastic models for turbulent flows: a way to an original and versatile numerical approach. (2021) Physical Review E, 104 (1). 015104. ISSN 2470-0045

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Official URL: https://doi.org/10.1103/PhysRevE.104.015104

Abstract

The characterization of intermittency in turbulence has its roots in the refined similarity hypotheses of Kolmogorov, and if no proper definition is to be found in the literature, statistical properties of intermittency were studied and models were developed in an attempt to reproduce it. The first contribution of this work is to propose a requirement list to be satisfied by models designed within the Lagrangian framework. Multifractal stochastic processes are a natural choice to retrieve multifractal properties of the dissipation. Among them, we investigate the Gaussian multiplicative chaos formalism, which requires the construction of a log-correlated stochastic process Xt. The fractional Gaussian noise of Hurst parameter H=0 is of great interest because it leads to a log correlation for the logarithm of the process. Inspired by the approximation of fractional Brownian motion by an infinite weighted sum of correlated Ornstein-Uhlenbeck processes, our second contribution is to propose a stochastic model: Xt=∫∞0Yxtk(x)dx, where Yxt is an Ornstein-Uhlenbeck process with speed of mean reversion x and k is a kernel. A regularization of k(x) is required to ensure stationarity, finite variance, and logarithmic autocorrelation. A variety of regularizations are conceivable, and we show that they lead to the aforementioned multifractal models. To simulate the process, we eventually design a new approach relying on a limited number of modes for approximating the integral through a quadrature XNt=∑Ni=1ωiYxit, using a conventional quadrature method. This method can retrieve the expected behavior with only one mode per decade, making this strategy versatile and computationally attractive for simulating such processes, while remaining within the proposed framework for a proper description of intermittency.

Item Type:Article
Additional Information:Thanks to the editor American Physical Society. The article is available at the adresse : https://doi.org/10.1103/PhysRevE.104.015104. Publisher copyright and source must be acknowledged with citation.
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
Other partners > Université Paris-Saclay (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Other partners > CentraleSupélec (FRANCE)
Other partners > Ecole Polytechnique (FRANCE)
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Deposited On:04 Oct 2021 09:35

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