A stochastic method to account for the ambient turbulence in Lagrangian Vortex computations

Type Article
Date 2020-12
Language English
Author(s) Choma Bex Camille1, 2, Carlier Clement1, 2, Fur Arnaud1, 2, Pinon Gregory1, Germain GregoryORCID2, Rivoalen Elie3
Affiliation(s) 1 : Normandie Univ, UNILEHAVRE, CNRS, LOMC, F-76600 Le Havre, France.
2 : IFREMER, Inst Francais Rech & Exploitat Mer Boulogne Sur M, Boulogne Sur Mer, France.
3 : Normandie Univ, INSA Rouen, LMN, F-76000 Rouen, France.
Source Applied Mathematical Modelling (0307-904X) (Elsevier Science Inc), 2020-12 , Vol. 88 , P. 38-54
DOI 10.1016/j.apm.2020.05.025
Keyword(s) Ambient turbulence, Synthetic Eddy Method, Lagrangian method, Turbulence, Vortex method, Wake

This paper describes a detailed implementation of the Synthetic Eddy Method (SEM) initially presented in Jarrin et al. (2006) applied to the Lagrangian Vortex simulation. While the treatment of turbulent diffusion is already extensively covered in scientific literature, this is one of the first attempts to represent ambient turbulence in a fully Lagrangian framework. This implementation is well suited to the integration of PSE (Particle Strength Exchange) or DVM (Diffusion Velocity Method), often used to account for molecular and turbulent diffusion in Lagrangian simulations. The adaptation and implementation of the SEM into a Lagrangian method using the PSE diffusion model is presented, and the turbulent velocity fields produced by this method are then analysed. In this adaptation, SEM turbulent structures are simply advected, without stretching or diffusion of their own, over the flow domain. This implementation proves its ability to produce turbulent velocity fields in accordance with any desired turbulent flow parameters. As the SEM is a purely mathematical and stochastic model, turbulent spectra and turbulent length scales are also investigated. With the addition of variation in the turbulent structures sizes, a satisfying representation of turbulent spectra is recovered, and a linear relation is obtained between the turbulent structures sizes and the Taylor macroscale. Lastly, the model is applied to the computation of a tidal turbine wake for different ambient turbulence levels, demonstrating the ability of this new implementation to emulate experimentally observed tendencies.

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