publications

2025

1. Energetically Consistent Eddy-Diffusivity Mass-Flux Convective Schemes: 1. Theory and Models

   M. Perrot, F. Lemarié, and T. Dubos

   Journal of Advances in Modeling Earth Systems, 2025

   Abs DOI

   This paper presents a self-contained derivation, from first principles, of a convective vertical mixing scheme based on the Eddy-Diffusivity Mass-Flux (EDMF) approach. This type of closure separates vertical turbulent fluxes into two components: an eddy-diffusivity (ED) which accounts for local small-scale mixing in a nearly isotropic environment, and a mass-flux (MF) transport term, which represents the non-local transport driven by vertically coherent plumes. Using the multi-fluid averaging underlying the MF concept, we review consistent energy budgets between resolved and subgrid scales for seawater and dry atmosphere, in anelastic and Boussinesq frameworks. We demonstrate that when using an EDMF scheme, closed energy budgets can be recovered if: (a) bulk production terms of turbulent kinetic energy (TKE) by shear buoyancy include MF contributions; (b) boundary conditions are consistent with EDMF, to avoid spurious energy fluxes at the boundary. Furthermore, we show that lateral mixing, due to either entrainment or detrainment induces a net production of TKE via the shear term, with enhanced production under increased horizontal drag. We also provide constraints on boundary conditions to ensure mathematical consistency. Throughout the theoretical development, we maintain transparency regarding underlying assumptions. In a companion paper (Perrot and Lemarié (2024, https://hal.science/hal-04666049); hereafter Part II) we assess the validity of these hypotheses, and analyze the sensitivity of the scheme to modeling choices against Large Eddy Simulations (LES) and observational data on oceanic convection. Part II also details an energy-conserving discretization and quantifies energy biases in inconsistent formulations.

2. Energetically Consistent Eddy-Diffusivity Mass-Flux Convective Schemes: 2. Implementation and Evaluation in an Oceanic Context

   M. Perrot and F. Lemarié

   Journal of Advances in Modeling Earth Systems, 2025

   Abs DOI

   A convective vertical mixing scheme rooted in the Eddy-Diffusivity Mass-Flux (EDMF) approach is carefully derived from first principles in Part I. In addition, consistent energy budgets between resolved and subgrid scales when using an EDMF scheme are presented for seawater and dry atmosphere. In this second part, we focus on oceanic convection with the following objectives: (a) justify in the oceanic context the assumptions made in Part I for the derivation of an EDMF scheme and a new Turbulent Kinetic Energy (TKE) turbulent transport term (b) show how continuous energy budgets can guide an energetically consistent discretization (c) quantify energy biases of inconsistent formulations, including double-counting errors due to inconsistent boundary conditions. The performance of the proposed energetically consistent EDMF scheme is evaluated against Large Eddy Simulations (LES) and observational data of oceanic convection. We systematically evaluate the sensitivity of numerical solutions to different aspects of the new formulation: energetic consistency, flux of TKE, flux of horizontal momentum and plume fractional area. Notably, when compared to LES data, energetic consistency is key to obtaining accurate TKE and turbulent transport of TKE profiles. To further illustrate that the EDMF concept is a credible alternative to the traditional approaches used in the oceanic context (using an enhanced vertical diffusion or a counter gradient term) the proposed scheme is validated in a single-column configuration against observational data of oceanic convection from the LION buoy.

3. Modeling Oceanic and Atmospheric Convection : Energy, Uncertainties and Rotation

   Manolis Perrot

   Apr 2025

   Abs HTML

   Numerical models of the ocean and atmosphere are essential tools for operational weather and ocean forecasting, as well as for studying past and future climate dynamics. Due to computational constraints, these models cannot explicitly resolve small-scale or fast-evolving phenomena. However, to enhance the realism of simulations, the effects of some unresolved processes must be accounted for through subgrid parameterization. Convection is an important unresolved process, since it produces vertical mixing of fluid. It arises from buoyancy differences between fluid parcels and their environment, typically occurring in the atmosphere when the Sun heats up the Earth’s surface or in the ocean when cold air cools the sea surface. This thesis focuses on a specific class of parameterizations for convective processes: the Eddy-Diffusivity Mass-Flux (EDMF) approach. While EDMF has been widely employed in atmospheric models, its application in ocean models is more recent.In the first part of this thesis, we demonstrate that existing EDMF implementations do not always conserve energy. Through theoretical analysis and numerical experiments, we develop a new EDMF formulation that ensures energy conservation at both continuous and discrete levels.The EDMF model contains several unconstrained parameters that require calibration. In the second part, we analyze the model’s sensitivity to these parameters then perform a Bayesian estimation, using high-resolution turbulence simulations as synthetic reference data. In certain regimes, Earth rotation is known to inhibit oceanic free convection. In the third part, we incorporate the effects of rotation into the EDMF parameterization to better capture their impacts on convective dynamics.

2024

1. Eulerian and Lagrangian Stability in Zeitlin’s Model of Hydrodynamics

   Klas Modin and Manolis Perrot

   Communications in Mathematical Physics, Jul 2024

   Abs DOI

   The two-dimensional (2-D) Euler equations of a perfect fluid possess a beautiful geometric description: they are reduced geodesic equations on the infinite-dimensional Lie group of symplectomorphims with respect to a right-invariant Riemannian metric. This structure enables insights to Eulerian and Lagrangian stability via sectional curvature and Jacobi equations. The Zeitlin model is a finite-dimensional analogue of the 2-D Euler equations; the only known discretization that preserves the rich geometric structure. Theoretical and numerical studies indicate that Zeitlin’s model provides consistent long-time behaviour on large scales, but to which extent it truly reflects the Euler equations is mainly open. Towards progress, we give here two results. First, convergence of the sectional curvature in the Euler–Zeitlin equations on the Lie algebra \\\mathfrak \textbraceleft su\textbraceright (N)\\to that of the Euler equations on the sphere. Second, \Ł^2\\-convergence of the corresponding Jacobi equations for Lagrangian and Eulerian stability. The results allow geometric conclusions about Zeitlin’s model to be transferred to Euler’s equations and vice versa, which could expedite the ultimate aim: to characterize the generic long-time behaviour of perfect 2-D fluids.

2019

1. Topological Transition in Stratified Fluids

   Manolis Perrot, Pierre Delplace, and Antoine Venaille

   Nature Physics, Aug 2019

   Abs DOI arXiv

   Lamb waves are trapped acoustic-gravity waves that propagate energy over great distances along a solid boundary in density stratified, compressible fluids. They constitute useful indicators of explosions in planetary atmospheres. When the density stratification exceeds a threshold, or when the impermeability condition at the boundary is relaxed, atmospheric Lamb waves suddenly disappear. Here we use topological arguments to predict the possible existence of new trapped Lamb-like waves in the absence of a solid boundary, depending on the stratification profile. The topological origin of the Lamb-like waves is emphasized by relating their existence to two-band crossing points carrying opposite Chern numbers. The existence of these band crossings coincides with a restoration of the vertical mirror symmetry that is in general broken by gravity. From this perspective, Lamb-like waves also bear strong similarities with boundary modes encountered in quantum valley Hall effect. Our study shows that the presence of Lamb-like waves encode essential information on the underlying stratification profile in astrophysical and geophysical flows, which is often poorly constrained by observations.