# A Stochastic description of eddy-mean flow interactions

Mattéo Nex, Quentin Jamet, Etienne Mémin, Florian Sévellec

► To cite this version:

Mattéo Nex, Quentin Jamet, Etienne Mémin, Florian Sévellec. A Stochastic description of eddy-mean flow interactions. 2025 - EGU General Assembly, Apr 2025, Vienne, Austria. 10.5194/egusphere-egu25-17449. hal-05468203

HAL Id: hal-05468203

https://hal.science/hal-05468203v1

Submitted on 20 Jan 2026

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# A Stochastic description of eddy-mean flow interactions

Mattéo Nex<fnref n="1" />, Quentin Jamet<fnref n="2" />, Etienne Mémin<fnref n="3" />, and Florian Sévellec<fnref n="4" />

When studying large tuburlent regions of the ocean, interactions between the mean flow and eddies plays a

central role in shaping large-scale circulation patterns by redistributing heat, momentum, and energy across the

ocean. Accurately representing these interactions in General Circulation Models (GCMs) remains a challenge,

particularly due to the subgrid-scale modelling issues and the limitations of traditional parameterization methods.

In this study we highlight the limitations of the diagnostics that can be performed with a too small in size en-

semble of simulations for capturing the Reynolds stress tensor as well as accurately diagnosing the work of such

tensor. In the context of studying energy exchange between the mean flow and eddies, the work of the Reynolds

stress is associated with the mean-to-eddy energy conversion rate MEC (Jamet et al. 2022).

To address the above issues, we explore the capabilities of the Location Uncertainty (LU) framework (Mémin

2014) to provide a better representation of eddy-mean flow energy transfer. By introducing stochastic variability

directly into the governing equations of fluid motion, LU provides an approach to model the unresolved turbulent

effects. A rederivation of the equation for the energy transfers is then possible through a stochastic version of

the Reynolds Transport Theorem (Bauer et al. 2020) and leads to an alternative representation of the interactions

between mean flow and eddies.

Based on 48-member ensemble simulation of the North Atlantic under realistic forcing, we provide a robust

comparison between deterministic and stochastic estimates of the work of Reynolds stress (MEC).

<footnote n="1">¹Centre Inria de l'Université de Rennes, France (matteo.nex@inria.fr)</footnote>

<footnote n="2">²SHOM, Brest, France (quentinjamett@gmail.com)</footnote>

<footnote n="3">³Centre Inria de l'Université de Rennes, France (etienne.memin@inria.fr)</footnote>

<footnote n="4">⁴LOPS, CNRS, Plouzané, France (florian.sevellec1@univ-brest.fr)</footnote>
By comparing

deterministic and stochastic estimates of MEC, we show that LU can effectively address the issues
of stastistical

convergence by inflating intrinsic variability leading to a more robust representation of these non-
linear terms. In

addition, statistical moments are shown to be more stable than from the deterministic
formulation of the eddy-mean

flow interactions. Key results of this study include a detailed formulation of kinetic energy
evolution equations

under the LU framework, which reveals significant improvements compared to the deterministic
formulation of

the work of the Reynolds stress in terms of statistical moments. The noise definition relies, in this
study, on the

snapshot proper orthogonal decomposition (POD) in the ensemble dimension, offering a time
varying orthogonal

eigenfunctions basis. These diagnostics provide usefull tools to observe moving patterns and
stability regions,

leading to physical interpretation of the eddy-mean flow interactions in the Gulf Stream.