Submesoscales are a significant turbulence source in global ocean surface boundary layer

The ocean surface boundary layer (OSBL) mediates air–sea exchanges of momentum, heat, gases, and nutrients, influencing climate variability from days to centuries. Classical OSBL turbulence frameworks emphasize one-dimensional sources from wind-driven shear, surface waves (Langmuir turbulence), and surface buoyancy loss (convection). However, observations and high-resolution models demonstrate that submesoscale fronts (0.1–10 km) with strong horizontal buoyancy gradients and vertical geostrophic shear can substantially energize turbulence, particularly away from the surface. This study asks how important geostrophic shear production (GSP) associated with submesoscale fronts is relative to Langmuir shear production (LSP), ageostrophic wind-driven shear (AGSP), and vertical buoyancy production (VBP) in the global OSBL, and assesses its seasonal, spatial, and depth dependence using a non-dimensional turbulent kinetic energy (TKE) budget.

Previous global assessments of OSBL turbulence emphasized wave- and wind-driven processes and convection (e.g., Belcher et al. 2012; Li et al. 2019), often neglecting horizontal inhomogeneities. Observations and theory indicate that fronts can enhance turbulence and energy dissipation (e.g., D’Asaro et al. 2011; Thomas et al. 2013; Yu et al. 2019), and that classical OSBL scalings are deficient in frontal regions. Parameterizations widely used in climate models typically omit GSP associated with submesoscale fronts, despite evidence of significant shear and mixing at these features and calls for energetically consistent boundary layer schemes. Prior studies also documented seasonality in submesoscale activity and the prevalence of log-skew-normal turbulence statistics, motivating a reassessment that includes frontal processes within a unified TKE budget framework.

Data and setup: The analysis uses the submesoscale-permitting global model LLC4320 (MITgcm on LLC grid) at 1/48° horizontal resolution with 90 vertical levels, forced by ECMWF fluxes (6-hourly, 0.14°) and tides, run Sep 2011–Nov 2012. Stokes drift is from ECMWF ERA5 (0.5°). Two months are analyzed: February (winter) and August (summer), subsampled to 4° spacing. The K-Profile Parameterization (KPP) determines OSBL properties; an offline KPP is used for consistent OSBL thickness h. Model performance is assessed using SST structure-function comparisons with VIIRS L2 and mixed layer depth comparisons with Argo-derived products. Non-dimensional TKE budget: Assuming steady state and negligible vertical TKE transport at OSBL mid-depth, dissipation ε balances production by four sources: LSP (Stokes drift shear), GSP (geostrophic shear at fronts under down-front winds), AGSP (ageostrophic wind-driven shear), and VBP (vertical buoyancy production from surface buoyancy loss). The non-dimensional form used is ε/(z^2/h^3) = A_L L_a + A_g L_g + A_s L_s + A_c L_a − L_a/h, with parameters: A_L = 0.22, A_g = 0.5, A_s = 2[1 − exp(−0.5 L_a)], A_c = 0.3. Key non-dimensional groups: La (turbulent Langmuir number), h/L1 (ratio of OSBL depth to Langmuir stability length), and h/Lg (ratio to geostrophic shear stability length). The analysis focuses on destabilizing surface buoyancy flux and down-front wind components, providing a conservative GSP estimate. Buoyancy gradient estimation and rescaling: GSP depends on horizontal buoyancy gradient magnitude M^2. Because resolved M^2 is resolution-dependent, gradients are rescaled assuming fronts are arrested by Turbulent Thermal Wind (TTW) balance. The arrested frontal width L_cf is estimated using an energetics-based PBL closure (ePBL) scaling: L_cf = C1[(m u_*^3 + n w_c^3)^(2/3)]/(f^2 h), with C1 = 1 (chosen from comparison with OSMOSIS observations), mechanical efficiency m derived from ePBL relations, convective efficiency n = 0.066, convective velocity w_c = (B0 h)^(1/3), f the Coriolis parameter, and h the OSBL thickness. The amplification factor (L_eff/L_f)^(1/2) rescales model M to approximate unresolved frontal gradients; where fronts are resolved (low latitudes), no amplification is applied. Sensitivity tests consider (i) uncorrected raw gradients (lower bound) and (ii) a no-slope white spectrum assumption (upper bound). Validation and sensitivity: The TKE production model is validated with OSMOSIS observations (northeast Atlantic moorings and gliders; Jan–Apr 2013), computing La, Lg, Ls, ε at OSBL mid-depth (OSBL thickness defined where observed ε falls to 1×10^-8 W kg^-1). Including GSP improves agreement with observed dissipation PDFs and time series, especially for moderate dissipation events, and reduces PDF skewness and kurtosis biases. Cross-model comparison with eNATL60 (NEMO, 1/60°, North Atlantic, Feb 2010) shows similar non-dimensional dissipation PDFs for all sources, indicating robustness to model choice. Regime analysis: Global parameter-space PDFs in La–h/L1–h/Lg space are used to map regimes where each source dominates (dominance defined as >75% of total dissipation; mixed regimes defined by >25% for multiple sources). Seasonal distributions of parameters highlight shifts in dominance across wind, wave, buoyancy, and geostrophic shear forcings.

• GSP is a significant, highly intermittent source of OSBL turbulence away from the surface: it contributes on average 34% of total dissipation in winter and 17% in summer at OSBL mid-depth globally.
• LSP has the largest mean and median absolute dissipation in both seasons, consistent with earlier studies, but GSP often exceeds VBP and AGSP and rivals LSP in winter, especially in western boundary currents and the Southern Ocean.
• PDFs of dissipation for all sources are nearly log-skew-normal; GSP exhibits the widest distribution (highest intermittency), implying rare, sharp fronts strongly influence mean dissipation.
• Spatial prevalence (winter): LSP is the first-ranked source at 44% of locations, GSP at 37%, VBP at 16%. Considering the top two sources, GSP provides a leading contribution in 71% of locations (vs 70% for LSP and 51% for VBP). Dominance varies with latitude; the leading source typically contributes <50% at low latitudes, rising to >75% at high latitudes.
• Spatial prevalence (summer): LSP dominates 84% of locations; GSP 11%; VBP 4%. LSP likely accounts for >50% of turbulence production outside the tropics in summer; GSP is often the secondary source at high latitudes and VBP at low latitudes.
• Regime mapping in La–h/L1–h/Lg space shows that as geostrophic shear increases, GSP and mixed GSP regimes expand while LSP/AGSP weaken; under strong buoyancy loss, LSP is suppressed and GSP/VBP dominate.
• Uncertainty bounds from gradient estimation methods: mean GSP contributions are 34% [27%, 37%] in winter and 17% [16%, 18%] in summer. Even using uncorrected gradients, GSP remains a major source.
• GSP conditions (down-front winds and destabilizing buoyancy) occur ~31% of the time in winter and ~21% in summer; under assumptions extending to up-front winds (A_g unchanged), estimated GSP contributions would be ~35% [28%, 38%] in 65% of winter and ~18% [17%, 19%] in 40% of summer.
• The sum of the top two sources explains most (>55%) of total dissipation at each location.

The analysis demonstrates that submesoscale frontal geostrophic shear (GSP) is a leading-order source of OSBL turbulence at mid-depth over large oceanic regions, particularly in winter, challenging classic horizontally uniform boundary layer concepts focused solely on wind, waves, and convection. The strong intermittency and spatially localized yet energetically potent nature of GSP implies that observational sampling and model resolution must capture submesoscale fronts to accurately estimate global OSBL energy budgets. Including GSP in parameterizations can reduce OSBL biases in regional and climate models and improve projections of air–sea exchange, mixed layer depth, and associated biogeochemical processes. While LSP remains dominant near the surface and in summer, the relative role of GSP increases with depth within the OSBL, highlighting its importance for interior exchanges. Interactions among sources (e.g., restratification by fronts reducing VBP, or destabilizing fluxes enhancing GSP) likely modulate the simple linear superposition used here and warrant further study. The robustness across gradient-scaling choices, independent observations (OSMOSIS), and models (LLC4320 vs eNATL60) supports the main conclusion that fronts are a globally significant OSBL turbulence source.

This work extends a global OSBL TKE budget to include geostrophic shear production (GSP) from submesoscale fronts and shows that GSP contributes substantially to OSBL turbulence at mid-depth (34% in winter, 17% in summer), often rivaling or exceeding traditional sources (VBP, AGSP) and approaching LSP in winter. The findings call for reappraisal of observational sampling scales, higher model resolution or improved parameterizations, and energetically consistent inclusion of GSP in ocean and climate models to reduce OSBL biases. Future research should refine buoyancy gradient estimation and frontal arrest scaling, incorporate interactions among turbulence sources and up-/down-front wind asymmetries, evaluate depth-varying contributions, and develop and test GSP-aware parameterizations within energetically consistent frameworks.

• GSP estimates restricted to down-front winds and destabilizing surface buoyancy flux; up-front conditions and stabilizing periods are not fully treated.
• Assumes steady-state TKE balance at OSBL mid-depth and neglects vertical TKE transport and horizontal shear production, which may be non-negligible at fronts.
• Buoyancy gradient rescaling relies on TTW frontal arrest theory and spectral assumptions; fronts are not always arrested, and rescaling introduces uncertainty (bounded by uncorrected vs no-slope methods).
• Linear superposition of sources ignores interactions (e.g., restratification reducing VBP, VBP–GSP coupling) that may alter contributions.
• Model-based analysis uses LLC4320 with KPP and subsampling to 4°; only February and August are analyzed; observational validation (OSMOSIS) is regional and limited to depths >50 m.
• Potential biases in mixed layer/OSBL thickness and unresolved processes (e.g., small-scale mixed layer instabilities) may affect quantitative estimates.