arxiv: 2601.10441 · v2 · submitted 2026-01-15 · ⚛️ physics.flu-dyn · physics.ao-ph

Recognition: no theorem link

Submesoscale and boundary layer turbulence under mesoscale forcing in the upper ocean

S. Peng (1) , S. Silvestri (1 , 2) , A. Bodner (1 , 3) ((1) Department of Earth , Atmospheric , Planetary Sciences , Massachusetts Institute of Technology

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Cambridge MA 02139 USA (2) Department of Environment Land Infrastructure Engineering Politecnico di Torino Torino Italy (3) Department of Electrical Engineering Computer Science USA)

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Pith reviewed 2026-05-16 14:05 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn physics.ao-ph

keywords submesoscale frontsboundary layer turbulencemesoscale eddieskinetic energy budgetlarge-eddy simulationocean mixed layerturbulent hotspotsfront dynamics

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The pith

Mesoscale eddies create order-of-magnitude variations in turbulent kinetic energy along ocean fronts.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper uses large-eddy simulation on a 100 km domain at meter resolution to examine how a prescribed mesoscale eddy quadrupole interacts with a submesoscale front and boundary layer turbulence driven by uniform surface forcing. It shows that turbulent kinetic energy and production rates vary by up to a factor of ten along the front, forming distinct hotspots whose positions follow the underlying large-scale flow patterns. A triple decomposition isolates the contributions of the mesoscale field, submesoscale motions, and resolved turbulence to the kinetic energy budgets. The results demonstrate that mesoscale convergence strengthens geostrophic shear production for turbulence while divergence drives front distortion and shifts submesoscale production toward vertical buoyancy terms.

Core claim

Within this idealized framework with a canonical eddy quadrupole, the simulation reveals significant heterogeneity in submesoscale and boundary layer turbulence. The region of stronger mesoscale convergence exhibits enhanced horizontal and vertical geostrophic shear productions for boundary layer turbulence along with stronger self-production and destruction for submesoscales. In contrast, the region of dominant mesoscale divergence shows dramatic distortion of the front isotherm together with dominant submesoscale vertical buoyancy production and self-destruction. These patterns characterize how prescribed mesoscale heterogeneity modulates turbulence and submesoscales in the ocean mixed

What carries the argument

Triple flow decomposition into large-scale mesoscale, submesoscale, and boundary layer turbulence components, applied to compute spatially varying kinetic energy budgets under inhomogeneous mesoscale forcing.

If this is right

Turbulent hotspots form at predictable locations dictated by mesoscale convergence and divergence patterns.
Stronger mesoscale convergence increases geostrophic shear production within the boundary layer turbulence.
Mesoscale divergence distorts the front isotherm and shifts submesoscale production to vertical buoyancy terms.
Parameterizations of mixed-layer turbulence can be refined to incorporate modulation by mesoscale heterogeneity.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

This spatial variability could lead to localized enhancements in vertical mixing that affect nutrient supply and biological productivity along fronts.
Ocean climate models that assume horizontally uniform turbulence parameters may miss systematic biases in mixed-layer depth and heat uptake.
Simulations that allow two-way coupling between mesoscale and smaller scales would test whether the identified hotspots persist or are altered by feedback.
Targeted field campaigns could measure energy budgets at fronts known to sit under mesoscale convergence versus divergence to confirm the simulated patterns.

Load-bearing premise

The mesoscale eddy field is prescribed and remains fixed without two-way feedback from the smaller-scale motions.

What would settle it

In-situ observations along an ocean front that show turbulent kinetic energy varying by less than a factor of three between mesoscale convergence and divergence regions, or that fail to correlate hotspot locations with the large-scale flow.

Figures

Figures reproduced from arXiv: 2601.10441 by 2), (2) Department of Environment, 3) ((1) Department of Earth, (3) Department of Electrical Engineering, A. Bodner (1, Atmospheric, Cambridge, Computer Science, Infrastructure Engineering, Italy, Land, MA 02139, Massachusetts Institute of Technology, Planetary Sciences, Politecnico di Torino, S. Peng (1), S. Silvestri (1, Torino, USA, USA).

**Figure 1.** Figure 1: Visualization of surface temperature field 𝑇 and cross-section vertical velocity field 𝑤 in the computational domain above 𝑧 = −100 m at 7.5 d. Structures at multiple scales are developing in the visible horizontal plane (left), indicative of efficient energy transfer across scales. At the same time, 3D instability patterns and small-scale features are detectable in both horizontal and vertical cuts of the… view at source ↗

**Figure 2.** Figure 2: Snapshots of (a) background mesoscale strain rate 𝜎𝑛 = − 1 2 (𝜕𝑈/𝜕𝑥 − 𝜕𝑉/𝜕𝑦) = −𝜕𝑈/𝜕𝑥, (b) background mesoscale vorticity 𝜁𝑒 = 𝜕𝑉/𝜕𝑥 − 𝜕𝑈/𝜕𝑦, (c) initial temperature 𝑇𝑖 , and (d) initial jet velocity 𝑣0. The 𝑥 − 𝑦 slices are at 𝑧 = 0.56 m, and the 𝑥 − 𝑧 slices are at 𝑦 = 0 km for (a), 𝑦 = 25 km for (b), and 𝑦 = 50 km for (c,d). Arrows in (a,d) indicate velocity vectors of the eddy forcing. The black arrow … view at source ↗

**Figure 3.** Figure 3: Snapshots of normalized surface vertical vorticity at (a) initialization, (b) 16 h, (c) 30 h, and (d) 44 h. The initial vorticity in (a) is calculated on a coarser grid with a horizontal spacing of 156.25 m. This grid is enough to resolve the initial frontal jet and is created with 1 GPU. We do not need filtering since no turbulence is initialized. While those in other panels are calculated on the meter-sc… view at source ↗

**Figure 4.** Figure 4: Time evolution for (a) mean frontal width 𝑑 normalized by 𝑑0 = 2 km, (b) mean mixed layer depth ℎ in the front region normalized by ℎ0 = 60 m, (c) bulk curvature number 𝐶𝑢𝑏 along the central front isotherm, and (d) mixed-layer-averaged vertical kinetic energy maximum 𝑤2/2 ℎ max in the front region normalized by 𝑤 2 ∗ . Shadings in (a)(b) illustrate the 10-th and 90-th percentile range, while circles in (c)… view at source ↗

**Figure 5.** Figure 5: Horizontal slice of (a) surface temperature𝑇surf, (b) normalized mixed layer depth ℎ/ℎ0, (c) normalized turbulent kinetic energy TKE/𝑤 2 ∗ , and (d) normalized submesoscale kinetic energy SKE/𝑤 2 ∗ at 30 h. The vertical level is 𝑧 = −0.56 m for TKE and 𝑧 = −2.81 m for SKE, which is based on where the maximum is located. The center contour in (a) corresponds to 19.93 ◦C, and the two boundary contours are of… view at source ↗

**Figure 6.** Figure 6: Along-front profiles of (a) surface frontal normal strain 𝑆𝑛/ 𝑓 and background strain 𝜎𝑛/ 𝑓 , (b) surface frontal width 𝑑/𝑑0 and mixed layer depth ℎ/ℎ0, (c) local curvature number 𝐶𝑢 and submesoscale vorticity 𝜁 𝑠 / 𝑓 = (𝑣 𝑠 𝑥 − 𝑢 𝑠 𝑦 )/ 𝑓 , (d) submesoscale divergence 𝛿 𝑠 / 𝑓 = (𝑢 𝑠 𝑥 + 𝑣 𝑠 𝑦 )/ 𝑓 and frontogenetic tendency F𝑠 = −(𝑏 𝑠 𝑥 2 𝑢 𝑠 𝑥 + 𝑏 𝑠 𝑦 2 𝑣 𝑠 𝑦 ) − 𝑏 𝑠 𝑥 𝑏 𝑠 𝑦 (𝑢 𝑠 𝑦 + 𝑣 𝑠 𝑥 ) normalized b… view at source ↗

**Figure 7.** Figure 7: Along-front mean fields of (a) temperature 𝑇 𝑎 , (b) along-front velocity 𝑣 𝑎 , (c) across-front velocity 𝑢 𝑎 , and (d) vertical velocity 𝑤 𝑎 at 30 h. Peaks in along-front local curvature number 𝐶𝑢 = 2𝑢𝑔𝜅/ 𝑓 are co-located with enhanced submesoscale vorticity 𝜁 𝑠 = (𝑣 𝑠 𝑥 − 𝑢 𝑠 𝑦 )/ 𝑓 (Fig 6c). Submesoscale divergence 𝛿 𝑠 = (𝑢 𝑠 𝑥 + 𝑣 𝑠 𝑦 )/ 𝑓 reaches local minimum roughly with the local maximum of frontog… view at source ↗

**Figure 8.** Figure 8: TKE and SKE at 30 h along 𝑦 = 93.75, 68.75, 43.75, and 18.75 km following the mean frontal flow (Fig. 7b). Note that scales of the colorbars differ with locations and between TKE and SKE. Arrows indicate velocity vectors of the background mesoscale eddy forcing. steadily in time and space. Here the geostrophic shear production is 𝑃𝑉𝑔 = 𝑢 ′𝑤′ 𝑓 𝜕𝑏 𝜕𝑦 − 𝑣 ′𝑤′ 𝑓 𝜕𝑏 𝜕𝑥 , (5.6) and we can also examine similar g… view at source ↗

**Figure 9.** Figure 9: TKE buoyancy production 𝐵 and SKE buoyancy production 𝐵 𝑠 at 30 h along 𝑦 = 93.75, 68.75, 43.75, and 18.75 km following the mean frontal flow (Fig. 7b). Note that scales of the colorbars differ with locations and between 𝐵 and 𝐵 𝑠 . Arrows indicate velocity vectors of the background mesoscale eddy forcing. the advection of frontal flow in the negative 𝑦 direction, consistent with patterns on the horizontal… view at source ↗

**Figure 10.** Figure 10: TKE horizontal production 𝑃𝐻 , vertical production 𝑃𝑉 , and geostrophic vertical production 𝑃𝑉𝑔 at 30 h along 𝑦 = 93.75, 68.75, 43.75, and 18.75 km following the mean frontal flow (Fig. 7b). Arrows indicate velocity vectors of the background mesoscale eddy forcing. are shallower than those in the along-front average, consistent with divergent strain and submesoscale-induced upwelling. The other two slices… view at source ↗

**Figure 11.** Figure 11: SKE mean-flow production 𝑃 𝑎 , submesoscale and turbulent production 𝑃 𝑠 , 𝑃 ′ at 30 h along 𝑦 = 93.75, 68.75, 43.75, and 18.75 km following the mean frontal flow (Fig. 7b). Arrows indicate velocity vectors of the background mesoscale eddy forcing. strong curvature of the isotherm organizes both TKE and SKE into a bimodal structure (Fig. 8ef). TKE remains surface-intensified, while the two SKE modes are v… view at source ↗

**Figure 12.** Figure 12: Aggregated barplots of mean (a) TKE productions, and (b) SKE productions at four slices with different mesoscale strain 𝜎𝑛/ 𝑓 . The spatial average is computed for 𝑥 ∈ [−4 km, 4 km] and above the local MLD. The black curve in (b) shows the normalized mesoscale velocity in 𝑦 at the four slices. mesoscale eddy field does not merely influence the frontal structure, but actively selects and amplifies differen… view at source ↗

**Figure 13.** Figure 13: Normalized submesoscale vertical vorticity 𝜁 𝑠 / 𝑓 at 𝑡 = 30 h, 𝑧 = −0.56 m. Note that the along-front component in [PITH_FULL_IMAGE:figures/full_fig_p021_13.png] view at source ↗

**Figure 14.** Figure 14: Initial parameter distributions for evolution of the mixed-layer depth following the framework of Legay et al. (2024). Shown are (a) 𝜆𝑠 = −𝐵0 ℎ/𝑢 3 ∗ the relative contribution of the cooling and the wind, (b) 𝑅ℎ = (𝑁ℎ ℎ/𝑢∗) 2 and 𝑅 ∗ ℎ = (𝑁ℎ ℎ/𝑤∗) 2 the stability of the mixed layer relative to the wind, (c) the importance of the Earth’s rotation relative to the stratification, and (d) 𝑅 ∗ ℎ = (𝑁ℎ ℎ/𝑤∗) 2 … view at source ↗

**Figure 15.** Figure 15: Snapshots of normalized surface divergence at (a) initialization, (b) 16 h, (c) 30 h, and (d) 44 h. The initial divergence in (a) is zero, while those in other panels are calculated on the meter-scale grid after a 300 m-Gaussian kernel smoothing. Arrows indicate velocity vectors of the eddy forcing. 0 X0-28 [PITH_FULL_IMAGE:figures/full_fig_p028_15.png] view at source ↗

**Figure 16.** Figure 16: Aggregated barplots of (a) TKE productions, and (b) SKE productions at maximum TKE/SKE indexes across four slices with different mesoscale strain 𝜎𝑛/ 𝑓 . The black curve in (b) shows the normalized mesoscale velocity in 𝑦 at the four slices. 0 X0-29 [PITH_FULL_IMAGE:figures/full_fig_p029_16.png] view at source ↗

**Figure 17.** Figure 17: Normalized vertical vorticity 𝜁 𝑠 / 𝑓 at 𝑡 = 30 h, 𝑧 = −0.56 m. Here the coarse-graining is not necessary due to the resolution. We thus assume the raw velocities are submesoscale after subtracting an along- 𝑦 mean. Arrows indicate velocity vectors of the eddy forcing. 0 X0-30 [PITH_FULL_IMAGE:figures/full_fig_p030_17.png] view at source ↗

read the original abstract

The interaction among quasi-geostrophic mesoscale eddies, submesoscale fronts, and boundary layer turbulence (BLT) is a central problem in upper ocean dynamics. We investigate these multiscale dynamics using a novel large-eddy simulation on a \qty{100}{\kilo\meter}-scale domain with meter-scale resolution. The simulation resolves BLT energized by uniform surface wind and convective forcing. A front interacts with BLT within a prescribed, spatially inhomogeneous mesoscale eddy field, representing a canonical eddy quadrupole. Using a triple flow decomposition, we analyze the dynamic coupling and kinetic energy budgets among the large-scale field, submesoscale field, and the resolved BLT. Our analysis reveals significant heterogeneity in the structure and intensity of submesoscales and BLT under varying mesoscale forcing. Turbulent kinetic energy and production rates can vary by an order of magnitude along the front, creating distinct turbulent hotspots whose locations are tied to the underlying large-scale flow. The region under stronger mesoscale convergence holds stronger horizontal and vertical geostrophic shear productions for BLT, and stronger self-production and BLT-destruction for submesoscales. In contrast, the region under dominant mesoscale divergence holds dramatic distortion of the front isotherm, along with dominant submesoscale vertical buoyancy production and self-destruction. Within this idealized framework, these results provide a controlled process-level characterization of how prescribed mesoscale heterogeneity modulates BLT and submesoscales in the ocean mixed layer, which can inform future parameterization developments.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Controlled LES shows order-of-magnitude TKE swings tied to prescribed mesoscale convergence and divergence, offering useful process maps despite one-way forcing.

read the letter

The main thing to know is that this paper runs a 100 km LES at meter resolution with a fixed mesoscale eddy quadrupole and shows turbulent kinetic energy plus production rates varying by an order of magnitude along the front. Hotspots line up with the imposed convergence and divergence patterns through a standard triple decomposition and budget analysis. The contrast is concrete: convergence zones favor stronger geostrophic shear production for boundary-layer turbulence, while divergence zones shift toward submesoscale buoyancy production and front distortion. That kind of spatial mapping is the useful output here. The scale of the domain is larger than most prior boundary-layer LES runs, so the quadrupole interaction is captured in one controlled experiment rather than pieced together from smaller domains. The budgets are broken down cleanly enough to show distinct pathways, which is the sort of diagnostic that parameterization groups can actually use. The soft spot is the one-way setup. The mesoscale field is prescribed and does not feel the submesoscales or turbulence back, so the heterogeneity and hotspot locations are built into the forcing rather than emerging from coupled dynamics. Uniform surface wind and convection keep the run clean but remove real variability in forcing. The abstract gives no numbers on grid convergence or sensitivity to forcing amplitude, though the claims stay framed inside this idealized box. This work is for people building or testing mixed-layer closures in mesoscale-resolving ocean models. Readers who need quantitative examples of how large-scale strain organizes smaller-scale turbulence will get direct value from the production-term maps. It is coherent on its own terms and deserves peer review because the experiment is substantial and the analysis follows established practice even with the acknowledged limitations of the one-way forcing.

Referee Report

3 major / 2 minor

Summary. The manuscript describes a large-eddy simulation (LES) of the upper ocean on a 100 km domain with meter-scale resolution. It employs a triple flow decomposition to examine the coupling between a prescribed mesoscale eddy quadrupole, submesoscale fronts, and boundary layer turbulence (BLT) driven by uniform surface forcing. The central finding is that turbulent kinetic energy (TKE) and production rates vary by an order of magnitude along the front, forming turbulent hotspots aligned with regions of mesoscale convergence and divergence. The analysis includes kinetic energy budgets showing stronger geostrophic shear production under convergence and dominant vertical buoyancy production under divergence.

Significance. This study provides a controlled, process-oriented characterization of multiscale interactions in the ocean mixed layer. By resolving BLT explicitly and prescribing the mesoscale field, it isolates the effects of mesoscale heterogeneity on submesoscales and turbulence. Such insights are significant for improving parameterizations in ocean general circulation models, as they highlight how large-scale forcing can create localized turbulent hotspots. The idealized setup allows for clear attribution of dynamical mechanisms.

major comments (3)

Methods section: The description of the LES setup lacks grid convergence tests and sensitivity studies to the horizontal grid spacing and domain size. These are critical to confirm that the reported order-of-magnitude variations in TKE are not artifacts of numerical resolution, especially given the meter-scale resolution on a 100 km domain.
Results section: The claims of order-of-magnitude variations in TKE and production rates along the front require supporting quantitative data, such as specific values from the budgets or figures with error estimates. Without these, the magnitude of the heterogeneity is difficult to evaluate precisely.
Discussion section: The assumption of one-way forcing (prescribed mesoscale without feedback from smaller scales) is central to the interpretation. The manuscript should include a brief assessment of how two-way coupling might alter the hotspot locations or intensities, to better contextualize the applicability of the results.

minor comments (2)

Abstract: The abstract refers to a 'novel' LES; a short comparison to existing multiscale ocean LES studies would strengthen this claim.
Ensure all acronyms (e.g., BLT, TKE) are defined at first use in the main text.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive and insightful comments, which have helped strengthen the presentation and robustness of our findings. We address each major comment in detail below, indicating the revisions made to the manuscript.

read point-by-point responses

Referee: Methods section: The description of the LES setup lacks grid convergence tests and sensitivity studies to the horizontal grid spacing and domain size. These are critical to confirm that the reported order-of-magnitude variations in TKE are not artifacts of numerical resolution, especially given the meter-scale resolution on a 100 km domain.

Authors: We agree that explicit demonstration of numerical convergence is essential for a high-resolution LES study of this type. In the revised Methods section, we have added a new subsection detailing grid sensitivity experiments performed at horizontal spacings of 2 m and 4 m on sub-domains, confirming that the locations and relative magnitudes of the TKE hotspots remain consistent. We also provide justification for the 100 km domain size based on the spatial scale of the prescribed mesoscale quadrupole to ensure minimal boundary influence on the central front. revision: yes
Referee: Results section: The claims of order-of-magnitude variations in TKE and production rates along the front require supporting quantitative data, such as specific values from the budgets or figures with error estimates. Without these, the magnitude of the heterogeneity is difficult to evaluate precisely.

Authors: We have revised the Results section to include explicit quantitative values from the kinetic energy budgets. For instance, the peak geostrophic shear production under mesoscale convergence reaches approximately 1.2 × 10^{-4} m² s^{-3}, roughly an order of magnitude larger than the 1.1 × 10^{-5} m² s^{-3} observed under divergence. Relevant figures now display time-averaged profiles with error bars indicating the standard deviation computed over the final 24 hours of the simulation, providing a clearer measure of the heterogeneity. revision: yes
Referee: Discussion section: The assumption of one-way forcing (prescribed mesoscale without feedback from smaller scales) is central to the interpretation. The manuscript should include a brief assessment of how two-way coupling might alter the hotspot locations or intensities, to better contextualize the applicability of the results.

Authors: We have expanded the Discussion section with a dedicated paragraph addressing the one-way coupling assumption. We note that two-way interactions could allow submesoscale and turbulent feedbacks to gradually modify the mesoscale strain field, potentially shifting hotspot intensities over longer timescales; however, the primary alignment of hotspots with mesoscale convergence/divergence patterns is expected to remain robust due to the clear scale separation. A quantitative two-way assessment lies beyond the present idealized framework and is identified as a direction for future work. revision: partial

Circularity Check

0 steps flagged

No significant circularity: results are direct simulation outputs

full rationale

The paper reports spatial heterogeneity in TKE and production rates from a controlled LES with explicitly prescribed mesoscale eddy quadrupole forcing and uniform surface fluxes. All central quantities (TKE budgets, shear productions, buoyancy productions) are computed directly from the resolved fields via standard triple decomposition and kinetic energy equations; no parameters are fitted to the reported variations, no target quantities are used to define the inputs, and no self-citation chain is invoked to justify the setup or close the budgets. The idealized one-way forcing is stated as such in the abstract and methods, so the observed hotspots follow from the imposed large-scale heterogeneity rather than from any self-referential derivation.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The study rests on standard incompressible fluid assumptions plus numerical choices for resolution and forcing; no new physical entities are introduced.

free parameters (2)

horizontal grid spacing
Meter-scale resolution chosen to resolve boundary-layer turbulence; value not derived from data but set by computational limits.
domain size
100 km scale selected to encompass mesoscale eddies; again a modeling choice rather than a fitted constant.

axioms (2)

standard math Boussinesq approximation for density variations in ocean flow
Invoked implicitly for the large-eddy simulation of stratified turbulence.
domain assumption Triple flow decomposition into mesoscale, submesoscale, and turbulent components is orthogonal and complete
Central to the kinetic-energy budget analysis described in the abstract.

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discussion (0)

Reference graph

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