arXiv subjects

Benoît-Joseph Gréa

Publications and source records attributed to Benoît-Joseph Gréa.

5 recordsLinked to original sources

arXiv2026

Linear and Nonlinear Latent-Space Reduced-Order Models for the Rayleigh--Taylor Instability

We use a large database of direct numerical simulations to investigate the transition of the Rayleigh--Taylor instability to turbulence and its evolution toward a late-time self-similar regime. In addition to tracking the growth of the mixing layer through the mean heavy-fluid concentration profile, we analyze one-dimensional profiles of turbulent kinetic energy and dissipation, two key quantities in classical turbulent-mixing models. We consider two reduced-order modeling strategies that differ in where nonlinearity is introduced: either in the construction of the latent space or in the description of its temporal evolution. The first method uses a linear encoder--decoder obtained using Proper Orthogonal Decomposition (POD), with nonlinear reduced dynamics learned by a physics-informed neural network (PINN). The second uses a nonlinear encoder--decoder learned by an autoencoder, while constraining the latent dynamics to remain linear and satisfy physical constraints. Both approaches achieve satisfactory performance in reconstructing, interpolating, and extrapolating the dynamics of the Rayleigh--Taylor instability.

physics.flu-dyn↗

arXiv2026

Mixing induced by Faraday surface waves

We investigate how surface waves enhance mixing across the interface between two miscible fluids with a small density contrast. Imposing a vertical, time-periodic acceleration, we excite Faraday waves both experimentally and numerically. In systems with a shallow density gradient, these standing waves advect the interface and can trigger secondary instabilities. When driven beyond the linear regime, large Faraday crests collapse to form cavities, injecting bubbles and lighter fluid deep into the heavier layer. Together, these mechanisms gradually homogenize the upper layer, diminish the interfacial density jump, and drive the interface downward until it decouples from surface forcing. We report a non-monotonic mixing rate -- first increasing as the interfacial energy barrier lowers, then decreasing as less energy is injected into the weakened surface -- revealing a balance between barrier reduction and energy input. Based on these observations, we introduce a one-dimensional model incorporating a turbulent diffusivity coefficient that depends on depth and the internal Richardson number, which captures the qualitative evolution of the system.

physics.flu-dyn↗

arXiv2026

Learning Turbulence Closures with Physics-Informed Neural Networks for the Rayleigh-Taylor Transition to Turbulence

Reynolds-averaged Navier-Stokes (RANS) turbulence models are known to perform poorly in predicting the dynamics of Rayleigh-Taylor mixing when turbulence is not fully developed, particularly during the transition from an initially perturbed interface. In this work, we investigate the use of data-driven strategies to enhance a simple $k$-$\varepsilon$-$b$ model for this transitional regime. The turbulence model is first embedded within a surrogate physics-informed neural network (PINN), enabling the calibration of coefficients that account for parametric errors and the identification of corrective terms representing structural errors associated with missing physical processes. The learned corrections are then re-expressed onto the model state variables and relevant flow indicators, leading to explicit analytical modifications of the closure. The resulting fully interpretable corrected model is assessed against an extensive database of direct numerical simulations (DNS) of Rayleigh-Taylor flows. This framework enables improved predictions of the mixing-layer growth during the transition to turbulence.

physics.flu-dyn↗

arXiv2025

Modeling late-time sensitivity to initial conditions in Boussinesq Rayleigh-Taylor turbulence

This article sheds light on the late-time influence of initial conditions in Boussinesq Rayleigh-Taylor turbulence using an approach combining direct numerical simulations, machine learning and theory. The initial conditions are characterized by four non-dimensional numbers describing the statistical properties of random-phase multi-mode perturbations of an initial diffuse interface. Based on high-fidelity data, a surrogate physics-informed neural network is used to extrapolate the dynamics to very late times and unseen initial conditions, beyond the reach of simulations. This enables uncertainty and global sensitivity analyses to be carried out, revealing the influence of initial conditions in the late-time regime. While the results support the idea of a universal self-similar growth rate, the virtual time origin is found to be strongly sensitive to the initial Reynolds, perturbation steepness and bandwidth numbers. An analytical model based on the phenomenology of Rayleigh-Taylor mixing layers explains most of this dependency, and provide accurate predictions for the virtual time origin. It turns out that when the initial perturbation reaches nonlinear saturation earlier, the mixing layer also re-accelerates earlier, while the virtual time origin is larger.

physics.flu-dyn↗

arXiv2019

Permanence of large eddies in variable-density homogeneous turbulence with small Mach numbers

In this work, we study the large-scale structure of homogeneous flows displaying high density contrasts and small turbulent Mach numbers. Following Batchelor & Proudman (PTRSA 258, 1956), we draw an analogy between this configuration and that of a single isolated eddy displaying density non-uniformities. By doing so, we are able to highlight the crucial role played by the solenoidal component of the momentum in the preservation of initial conditions. In particular, we show that the large-scale initial conditions of the spectrum of the solenoidal momentum are preserved provided its infrared exponent is smaller than $4$. This condition is reminiscent of the one usually derived in constant density flow, except that it does not apply to the velocity spectrum. The latter is actually shown to be impermanent for infrared exponents larger or equal to $2$. The consequences of these properties on the self-similar decay of the flow are discussed. Finally, these predictions are verified by performing large eddy simulations of homogeneous isotropic turbulence.

physics.flu-dyn↗