arXiv subjects

Pierre Augier

Publications and source records attributed to Pierre Augier.

14 recordsLinked to original sources

arXiv2026

Aliasing and phase shifting in pseudo-spectral simulations of the incompressible Navier-Stokes equations

Pseudo-spectral methods are widely used for direct numerical simulations of turbulence, but the standard 2/3 truncation rule for dealiasing is computationally expensive -- accounting for up to 80% of the total cost in three dimensions. Phase shifting methods provide a more efficient alternative by canceling aliasing errors the combination of nonlinear terms evaluated on shifted grids, allowing the same physical resolution to be achieved on a coarser numerical grid. Despite their use in high-resolution turbulence codes, these methods remain poorly documented in the literature and no open-source implementation exists. This paper presents a comprehensive analysis of phase-shifting dealiasing for pseudo-spectral simulations of the incompressible Navier-Stokes equations. We derive the aliasing mechanism from quadratic nonlinearities in discrete Fourier space and explain how phase-shifting cancels aliasing contributions exactly or approximately depending on the time-stepping scheme. We describe and compare several algorithms -- including the exact and approximate RK2 phase-shifting schemes of Patterson Jr and Orszag (1971) and Rogallo (1981), and an extension to forced flows -- and discuss their interaction with different truncation geometries in three dimensions. All algorithms are implemented in the open-source framework Fluidsim, providing the first publicly available implementation of phase-shifting dealiasing for pseudo spectral Navier-Stokes solvers. We evaluate the methods on two test cases: the transition to turbulence of Taylor-Green vortices and forced homogeneous isotropic turbulence at $Re_\lambda = 200$. Phase-shifting methods achieve speedups of up to a factor of 3 compared to RK4 with 2/3 truncation at the same maximum wavenumber, with small accuracy loss.

physics.flu-dyn↗

arXiv2026

Lagrangian dispersion in experimental stratified turbulence

Lagrangian measurements of tracer particle dispersion in stratified turbulence are presented from a large-scale experiment achieving both high buoyancy Reynolds numbers and low Froude numbers -- a regime characteristic of oceanic conditions. Stratification has a pronounced effect on the vertical particle dispersion, which is observed to be constrained to distances on the order of the buoyancy scale $w_{\mathrm{std}}/N$, where $w_{\mathrm{std}}$ is the standard deviation of the vertical velocity and $N$ is the Brunt-V\"ais\"al\"a frequency. As expected in strongly nonlinear, stratified turbulence, the frequency spectrum of the Lagrangian velocity becomes isotropic at frequencies higher than $N$. The spectral decay follows a $1/f^3$ scaling, which contrasts with the $1/f^2$ behavior typical of homogeneous isotropic turbulence. At time scales corresponding to internal waves, the statistics of velocity increments remain Gaussian, consistent with the weakly nonlinear regime of wave turbulence. At smaller scales, however, the flow exhibits strongly non-Gaussian statistics, indicative of fully nonlinear turbulent dynamics driven by wave breaking.

physics.flu-dyn↗

arXiv2023

From internal waves to turbulence in a stably stratified fluid

We report on the statistical analysis of stratified turbulence forced by large-scale waves. The setup mimics some features of the tidal forcing of turbulence in the ocean interior at submesoscales. Our experiments are performed in the large-scale Coriolis facility in Grenoble which is 13 m in diameter and 1 m deep. Four wavemakers excite large scale waves of moderate amplitude. In addition to weak internal wave turbulence at large scales, we observe strongly nonlinear waves, the breaking of which triggers intermittently strong turbulence at small scales. A transition to strongly nonlinear turbulence is observed at smaller scales. Our measurements are reminiscent of oceanic observations. Despite similarities with the empirical Garrett & Munk spectrum that assumes weak wave turbulence, our observed energy spectra are rather be attributed to strongly nonlinear internal waves.

physics.flu-dyn↗

arXiv2023

Vertical convection regimes in a two-dimensional rectangular cavity: Prandtl and aspect ratio dependance

Vertical convection is the fluid motion that is induced by the heating and cooling of two opposed vertical boundaries of a rectangular cavity (see e.g. Wang et al. 2021). We consider the linear stability of the steady two-dimensional flow reached at Rayleigh numbers of O($10^8$). As a function of the Prandtl number, $Pr$, and the height-to-width aspect ratio of the domain, $A$, the base flow of each case is computed numerically and linear simulations are used to obtain the properties of the leading linear instability mode. Flow regimes depend on the presence of a circulation in the entire cavity, detachment of the thermal layer from the boundary or the corner regions, and on the oscillation frequency relative to the natural frequency of oscillation in the stably temperature-stratified interior, allowing for the presence of internal waves or not. Accordingly the regime is called slow or fast, respectively. Either the global circulation or internal waves in the interior may couple the top and bottom buoyancy currents, while their absence implies asymmetry in their perturbation amplitude. Six flow regimes are found in the range of $0.1 \leq Pr \leq 4$ and $0.5 \leq A \leq 2$. For $Pr \lessapprox 0.4 $ and $A>1$ the base flow is driven by a large circulation in the entire cavity. For $Pr \gtrapprox 0.7$ the thermal boundary layers are thin and the instability is driven by the motion along the wall and the detached boundary layer. A transition between these regimes is marked by a dramatic change in oscillation frequency at $Pr = 0.55 \pm0.15$ and $A <2$.

physics.flu-dyn↗

arXiv2023

Internal gravity waves in stratified flows with and without vortical modes

The comprehension of stratified flows is important for geophysical and astrophysical applications. The Weak Wave Turbulence theory aims to provide a statistical description of internal gravity waves propagating in the bulk of such flows. However, internal gravity waves are usually perturbed by other structures present in stratified flow, namely the shear modes and the vortical modes. In order to check whether a weak internal gravity wave turbulence regime can occur, we perform direct numerical simulations of stratified turbulence without shear modes, and with or without vortical modes at various Froude and buoyancy Reynolds numbers. We observe that removing vortical modes naturally helps to have a better overall balance between poloidal kinetic energy, involved in internal gravity waves, and potential energy. However, conversion between kinetic energy and potential energy does not necessarily show fluctuations around zero in our simulations, as we would expect for a system of weak waves. A spatiotemporal analysis reveals that removing vortical modes helps to concentrate the energy around the wave frequency, but it is not enough to observe a weak wave turbulence regime. Yet, we observe that internal gravity waves whose frequency are large compared to the eddy turnover time are present, and we also find evidences for slow internal gravity waves interacting by Triadic Resonance Instabilities in our strongly stratified flows simulations. Finally, we propose conditions that should be fulfilled in order to observe a weak internal gravity waves turbulence regime in real flows.

physics.flu-dyn↗

arXiv2022

Numerical study of experimentally inspired stratified turbulence forced by waves

Stratified flows forced by internal waves similar to those obtained in the Coriolis platform (LEGI, Grenoble, France) \cite{Savaro2020} are studied by pseudospectral triply-periodic simulations. The experimental forcing mechanism consisting in large oscillating vertical panels is mimicked by a penalization method. The analysis of temporal and spatiotemporal spectra reveals that the flow for the strongest forcing in the experiments is composed of two superposed large and quasi-steady horizontal vortices, of internal waves in box modes and of much weaker waves outside the modes. Spatial spectra and spectral energy budget confirm that the flow is in an intermediate regime for very small horizontal Froude number $F_h$ and buoyancy Reynolds number $R$ close to unity. Since the forcing frequency $\omega_f$ is just slightly smaller than the Brunt-V\"ais\"al\"a frequency $N$, there are energy transfers towards slower waves and large vortices, which correspond to an upscale energy flux over the horizontal. Two other experimentally feasible sets of parameters are investigated. A larger amplitude forcing shows that it would indeed be possible to produce in huge apparatus like the Coriolis platform stratified turbulence forced by waves for small $F_h$ and buoyancy Reynolds number $R$ of order 10. Forcing slower waves for $\omega_f = 0.40 N$ leaves space between $\omega_f$ and $N$ for "down-time-scale" transfers through weakly nonlinear interactions with temporal spectra consistent with $\omega^{-2}$ slope. However, for this set of parameters, the large scales of the flow are strongly dissipative and there is no downscale energy cascade.

physics.flu-dyn↗

arXiv2022

Experimental observations of internal wave turbulence transition in a stratified fluid

Recent developments of the weak turbulence theory applied to internal waves exhibit a power-law solution of the kinetic energy equation close to the oceanic Garrett \& Munk spectrum, confirming weakly nonlinear wave interactions as a likely explanation of the observed oceanic spectra. However, finite-size effects can hinder wave interactions in bounded domains, and observations often differ from theoretical predictions. This article studies the dynamical regimes experimentally developing in a stratified fluid forced by internal gravity waves in a pentagonal domain. We find that by changing the shape and increasing the dimensions of the domain, finite-size effects diminish and wave turbulence is observed. In this regime, the temporal spectra decay with a slope compatible with the Garrett-Munk spectra. Different regimes appear by changing the forcing conditions, namely discrete wave turbulence, weak wave turbulence, and strongly stratified turbulence. The buoyancy Reynolds number $Re_b$ marks well the transitions between the regimes, with weak wave turbulence occurring for $1\lesssim Re_b\lesssim 3.5$ and strongly non-linear stratified turbulence for higher $Re_b$.

physics.flu-dyn↗

arXiv2020

Generation of weakly nonlinear turbulence of internal gravity waves in the Coriolis facility

We investigate experimentally stratified turbulence forced by waves. Stratified turbulence is present in oceans and it is expected to be dominated by nonlinear interaction of internal gravity waves as described by the Garrett & Munk spectrum. In order to reach turbulent regimes dominated by stratification we use the Coriolis facility in Grenoble (France) which large size enables us to reach regimes with both low Froude number and large Reynolds number. Stratification is obtained by using vertically linearly varying salt concentration and we force large scale waves in a $6\times6\times 1$ m$^3$ domain. We perform time-resolved PIV to probe the space-time structure of the velocity field. We observe a wide band spectrum which is made of waves. Discrete modes are observed due to the square shape of the flow container as well as a continuum part which appears consistent with an axisymmetric superposition of random weakly nonlinear waves. Our observations support the interpretation of turbulence of a strongly stratified fluid as wave turbulence of internal waves although our spectrum is quite different from the Garrett & Munk spectrum. Weak turbulence proceeds down to a small cutoff length scale (the buoyancy wavelength) at which a transition to more strongly nonlinear turbulence is expected.

physics.flu-dyn↗

arXiv2019

Comparative terrestrial atmospheric circulation regimes in simplified global circulation models: II. energy budgets and spectral transfers

The energetics of possible global atmospheric circulation patterns in an Earth-like atmosphere are explored using a simplified GCM based on the University of Hamburg's Portable University Model for the Atmosphere. Results from a series of simulations, obtained by varying planetary rotation rate {\Omega} with an imposed equator-to-pole temperature difference, were analysed to determine the heat transport and other contributions to the energy budget for the time-averaged, equilibrated flow. These show clear trends with {\Omega}, with the most intense Lorenz energy cycle for an Earth-sized planet occurring with a rotation rate around half that of the present day Earth. KE and APE spectra, E_K(n) and E_A(n) (where n is total spherical wavenumber), also show clear trends with \Omega, with n^{-3} enstrophy-dominated spectra around \Omega* = \Omega/\Omega_E = 1, where \Omega_E is the rotation rate of the Earth) and steeper (\sim n^{-5}) slopes in the zonal mean flow with little evidence for the n^{-5/3} spectrum anticipated for an inverse KE cascade. Instead, both KE and APE spectra become almost flat at scales larger than the internal Rossby radius, L_d, and exhibit near-equipartition at high wavenumbers. At \Omega* << 1, the spectrum becomes dominated by KE with E_K(n) \sim 2-3 E_A(n) at most wavenumbers and a slope \sim n^{-5/3} across most of the spectrum. Spectral flux calculations show that enstrophy and APE are almost always cascaded downscale, regardless of {\Omega}. KE cascades are more complicated, however, with downscale transfers across almost all wavenumbers, dominated by horizontally divergent modes, for \Omega* \lesssim 1/4. At higher rotation rates, transfers of KE become increasingly dominated by rotational components with strong upscale transfers (dominated by eddy-zonal flow interactions) for scales larger than L_d and weaker downscale transfers for scales smaller than L_d.

astro-ph.EP↗

arXiv2018

FluidDyn: a Python open-source framework for research and teaching in fluid dynamics

FluidDyn is a project to foster open-science and open-source in the fluid dynamics community. It is thought of as a research project to channel open-source dynamics, methods and tools to do science. We propose a set of Python packages forming a framework to study fluid dynamics with different methods, in particular laboratory experiments (package fluidlab), simulations (packages fluidfft, fluidsim and fluidfoam) and data processing (package fluidimage). In the present article, we give an overview of the specialized packages of the project and then focus on the base package called fluiddyn, which contains common code used in the specialized packages. Packages fluidfft and fluidsim are described with greater detail in two companion papers, Mohanan et al. (2018a,b). With the project FluidDyn, we demonstrate that specialized scientific code can be written with methods and good practices of the open-source community. The Mercurial repositories are available in Bitbucket (https://bitbucket.org/fluiddyn/). All codes are documented using Sphinx and Read the Docs, and tested with continuous integration run on Bitbucket, Pipelines and Travis. To improve the reuse potential, the codes are as modular as possible, leveraging the simple object-oriented programming model of Python. All codes are also written to be highly efficient, using C++, Cython and Pythran to speedup the performance of critical functions.

cs.OH↗

arXiv2018

FluidFFT: common API (C++ and Python) for Fast Fourier Transform HPC libraries

The Python package fluidfft provides a common Python API for performing Fast Fourier Transforms (FFT) in sequential, in parallel and on GPU with different FFT libraries (FFTW, P3DFFT, PFFT, cuFFT). fluidfft is a comprehensive FFT framework which allows Python users to easily and efficiently perform FFT and the associated tasks, such as as computing linear operators and energy spectra. We describe the architecture of the package composed of C++ and Cython FFT classes, Python "operator" classes and Pythran functions. The package supplies utilities to easily test itself and benchmark the different FFT solutions for a particular case and on a particular machine. We present a performance scaling analysis on three different computing clusters and a microbenchmark showing that fluidfft is an interesting solution to write efficient Python applications using FFT.

cs.MS↗

arXiv2018

FluidSim: modular, object-oriented Python package for high-performance CFD simulations

The Python package fluidsim is introduced in this article as an extensible framework for Computational Fluid Mechanics (CFD) solvers. It is developed as a part of FluidDyn project (Augier et al., 2018), an effort to promote open-source and open-science collaboration within fluid mechanics community and intended for both educational as well as research purposes. Solvers in fluidsim are scalable, High-Performance Computing (HPC) codes which are powered under the hood by the rich, scientific Python ecosystem and the Application Programming Interfaces (API) provided by fluiddyn and fluidfft packages (Mohanan et al., 2018). The present article describes the design aspects of fluidsim, viz. use of Python as the main language; focus on the ease of use, reuse and maintenance of the code without compromising performance. The implementation details including optimization methods, modular organization of features and object-oriented approach of using classes to implement solvers are also briefly explained. Currently, fluidsim includes solvers for a variety of physical problems using different numerical methods (including finite-difference methods). However, this metapaper shall dwell only on the implementation and performance of its pseudo-spectral solvers, in particular the two- and three-dimensional Navier-Stokes solvers. We investigate the performance and scalability of fluidsim in a state of the art HPC cluster. Three similar pseudo-spectral CFD codes based on Python (Dedalus, SpectralDNS) and Fortran (NS3D) are presented and qualitatively and quantitatively compared to fluidsim. The source code is hosted at Bitbucket as a Mercurial repository bitbucket.org/fluiddyn/fluidsim and the documentation generated using Sphinx can be read online at fluidsim.readthedocs.io.

cs.CE↗

arXiv2016

Nonlinear waves in stratified Taylor--Couette flow. Part 1. Layer formation

This paper is the first part of a two-fold study of mixing, i.e. the formation of layers and upwelling of buoyancy, in axially stratified Taylor--Couette flow, with fixed outer cylinder. Using linear analysis and direct numerical simulation, we show the critical role played by non-axisymmetric instability modes, despite the fact that the flow is centrifugally unstable in the sense of Rayleigh's criterion. Interactions between helical modes of opposite handedness leads to the formation of nonlinear coherent structures: (mixed)-ribbons and (mixed)-cross-spirals. These give birth to complex density interface patterns, seemingly appearing and disappearing periodically as the coherent structure slowly rotates around the annulus. These coherent structures seem to be responsible for the formation of layers reported in a recent experiment by Oglethorpe et al. (2013). We distinguish `dynamic layering', instantaneous, localized and caused by the vortical motions, from `static layering' corresponding to the formation of a `staircase profile' in the adiabatically sorted background density. The latter only occurs at large enough Schmidt number, revealing the significant impact of the Schmidt number in the layering process.

physics.flu-dyn↗

arXiv2012

A new formulation of the atmospheric spectral energy budget, with application to two high-resolution general circulation models

A new formulation of the spectral energy budget of kinetic and available potential energies of the atmosphere is derived, with spherical harmonics as base functions. Compared to previous formulations, there are three main improvements: (i) the topography is taken into account, (ii) the exact three-dimensional advection terms are considered and (iii) the vertical flux is separated from the energy transfer between different spherical harmonics. Using this formulation, results from two different high resolution GCMs are analyzed: the AFES T639L24 and the ECMWF IFS T1279L91. The spectral fluxes show that the AFES, which reproduces realistic horizontal spectra with a k^{-5/3} inertial range at the mesoscales, simulates a strong downscale energy cascade. In contrast, neither the k^{-5/3} vertically integrated spectra nor the downscale energy cascade are produced by the ECMWF IFS.

physics.ao-ph↗