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Mathematical analysis of a spectral hyperviscosity LES model for the simulation of turbulent flows

Jean-Luc Guermond, Serge Prudhomme (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

This paper presents a model based on spectral hyperviscosity for the simulation of 3D turbulent incompressible flows. One particularity of this model is that the hyperviscosity is active only at the short velocity scales, a feature which is reminiscent of Large Eddy Simulation models. We propose a Fourier–Galerkin approximation of the perturbed Navier–Stokes equations and we show that, as the cutoff wavenumber goes to infinity, the solution of the model converges (up to subsequences) to a weak solution...

Mathematical analysis of a spectral hyperviscosity LES model for the simulation of turbulent flows

Jean-Luc Guermond, Serge Prudhomme (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper presents a model based on spectral hyperviscosity for the simulation of 3D turbulent incompressible flows. One particularity of this model is that the hyperviscosity is active only at the short velocity scales, a feature which is reminiscent of Large Eddy Simulation models. We propose a Fourier–Galerkin approximation of the perturbed Navier–Stokes equations and we show that, as the cutoff wavenumber goes to infinity, the solution of the model converges (up to subsequences) to a weak...

Mathematical and numerical analysis of an alternative well-posed two-layer turbulence model

Bijan Mohammadi, Guillaume Puigt (2001)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this article, we wish to investigate the behavior of a two-layer k - ε turbulence model from the mathematical point of view, as this model is useful for the near-wall treatment in numerical simulations. First, we explain the difficulties inherent in the model. Then, we present a new variable θ that enables the mathematical study. Due to a problem of definition of the turbulent viscosity on the wall boundary, we consider an alternative version of the original equation. We show that some physical aspects...

Mathematical and Numerical Analysis of an Alternative Well-Posed Two-Layer Turbulence Model

Bijan Mohammadi, Guillaume Puigt (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this article, we wish to investigate the behavior of a two-layer k - ε turbulence model from the mathematical point of view, as this model is useful for the near-wall treatment in numerical simulations. First, we explain the difficulties inherent in the model. Then, we present a new variable θ that enables the mathematical study. Due to a problem of definition of the turbulent viscosity on the wall boundary, we consider an alternative version of the original equation. We show that some physical...

Microscale Complexity in the Ocean: Turbulence, Intermittency and Plankton Life

L. Seuront (2008)

Mathematical Modelling of Natural Phenomena

This contribution reviews the nonlinear stochastic properties of turbulent velocity and passive scalar intermittent fluctuations in Eulerian and Lagrangian turbulence. These properties are illustrated with original data sets of (i) velocity fluctuations collected in the field and in the laboratory, and (ii) temperature, salinity and in vivo fluorescence (a proxy of phytoplankton biomass, i.e. unicelled vegetals passively advected by turbulence) sampled from highly turbulent coastal waters. The strength...

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