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

TL;DR

This work addresses how mesoscale heterogeneity organizes submesoscale fronts and boundary-layer turbulence in the upper ocean. It introduces a novel 100 km by 100 km LES with meter-scale resolution and a nonuniform, stationary mesoscale background, enabling a triple flow decomposition to separate mesoscale, submesoscale, and BLT energetics. The results reveal spatially localized turbulent hotspots and distinct energy-budget pathways along the front that depend on local strain and Ekman forcing, underscoring the inadequacy of uniform-strain parameterizations. The findings have implications for improving vertical transport and subgrid-scale representations in climate models, highlighting the need for scale- and location-aware parameterizations that capture mesoscale–submesoscale–BLT coupling. The study demonstrates the power of high-resolution, nonhydrostatic LES in bridging scales and guiding development of more accurate upper-ocean models.

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 100km-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. These results provide a direct characterization of BLT and submesoscales in the ocean mixed layer modulated by a mesoscale eddy field, which can better inform future parameterization developments.

Figures (17)

• Figure 1: Visualization of surface temperature field $T$ and cross-section vertical velocity field $w$ in the computational domain above $z=\qty{-100}{\meter}$ at 7.5. 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 zoomed-in simulation domain (right), suggesting a forward turbulent cascade.
• Figure 2: Snapshots of (a) background mesoscale strain rate $\sigma_n=-\frac{1}{2}(\partial U/\partial x-\partial V/\partial y)=-\partial U/\partial x$, (b) background mesoscale vorticity $\zeta_e=\partial V/\partial x-\partial U/\partial y$, (c) initial temperature $T_i$, and (d) initial jet velocity $v_0$. The $x-y$ slices are at $z=\qty{0.56}{\meter}$, and the $x-z$ slices are at $y=\qty{0}{\kilo\meter}$ for (a), $y=\qty{25}{\kilo\meter}$ for (b), and $y=\qty{50}{\kilo\meter}$ for (c,d). Arrows in (a,d) indicate velocity vectors of the eddy forcing. The black arrow in (a) indicates the wind direction. White lines in (a) show the initial mixed layer depth. Light rings in (b) that are roughly at a half radius point implies merged effects due to compactly positioned eddy quadruple.
• 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. 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-scale grid after a 300-Gaussian kernel smoothing. Arrows indicate velocity vectors of the eddy forcing.
• Figure 4: Time evolution for (a) mean frontal width $d$ normalized by $d_0=\qty{2}{\kilo\meter}$, (b) mean mixed layer depth $h$ in the front region normalized by $h_0=\qty{60}{\meter}$, (c) bulk curvature number $Cu_b$ along the central front isotherm, and (d) mixed-layer-averaged vertical kinetic energy maximum $\overline{w^2/2}^h_{\max}$ 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)(d) local peaks. Black and red curves in (a) are predictions from uniform strain frontogenesis theory shakespeare_generalized_2013, with $\sigma_n=\pm 0.03 f$ for black and red, respectively. The bulk curvature number is the maximum along-front local curvature number $Cu\equiv 2u_g \kappa/f$, with $u_g=\alpha g \varDelta T h/fd$ the geostrophic velocity scale and $\kappa$ the geometric curvature. Only solid lines of $d$ and $h$ are averaged over the whole frontal domain.
• Figure 5: Horizontal slice of (a) surface temperature $T_{\text{surf}}$, (b) normalized mixed layer depth $h/h_0$, (c) normalized turbulent kinetic energy $\text{TKE}/w_*^2$, and (d) normalized submesoscale kinetic energy $\text{SKE}/w_*^2$ at 30 h. The vertical level is $z=\qty{-0.56}{\meter}$ for TKE and $z=\qty{-2.81}{\meter}$ for SKE, which is based on where the maximum is located. The center contour in (a) corresponds to 19.93, and the two boundary contours are offset by 0.194 which gives an initial frontal width of 2. Arrows in (b)-(d) shows the velocity vector field that induces the strain, while white and black stars the maximum of $h$-averaged vertical kinetic energy, near-surface TKE ($z>\qty{-4.5}{\meter}$), and near-surface SKE ($z>\qty{-4.5}{\meter}$), respectively. Four dashed lines in (c,d) show slice locations along $y=\qtylist{93.75;68.75;43.75;18.75}{\kilo\meter}$ to be discussed in §\ref{['subsec:budgets']}.