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1. Diurnal Warm Layers in the Ocean: Energetics, Nondimensional Scaling, and Parameterization

   https://doi.org/10.1175/JPO-D-23-0129.1  

   Schmitt, M; Pham, H T; Sarkar, S; Klingbeil, K; Umlauf, L (April 2024, Journal of Physical Oceanography)

   Abstract Diurnal warm layers (DWLs) form near the surface of the ocean on days with strong solar radiation, weak to moderate winds, and small surface-wave effects. Here, we use idealized second-moment turbulence modeling, validated with large-eddy simulations (LES), to study the properties, dynamics, and energetics of DWLs across the entire physically relevant parameter space. Both types of models include representations of Langmuir turbulence (LT). We find that LT only slightly modifies DWL thicknesses and other bulk parameters under equilibrium wave conditions, but leads to a strong reduction in surface temperature and velocity with possible implications for air–sea coupling. Comparing tropical and the less frequently studied high-latitude DWLs, we find that LT has a strong impact on the energy budget and that rotation at high latitudes strongly modifies the DWL energetics, suppressing net energy turnover and entrainment. We identify the key nondimensional parameters for DWL evolution and find that the scaling relations of Price et al. provide a reliable representation of the DWL bulk properties across a wide parameter space, including high-latitude DWLs. We present different sets of revised model coefficients that include the deepening of the DWL due to LT and other aspects of our more advanced turbulence model to describe DWL properties at midday and during the DWL temperature peak in the afternoon, which we find to occur around 1500–1630 local time for a broad range of parameters. 

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2. Assessing a Turbulent Mixing Scheme in Diurnal Warm Layers considering Langmuir Turbulence

   https://doi.org/10.1175/JPO-D-24-0164.1  

   Wang, Xingchi; Kukulka, Tobias (July 2025, Journal of Physical Oceanography)

   Abstract This study investigates how Langmuir turbulence (LT) driven by Stokes drift shear affects the heated ocean surface boundary layer (OSBL) based on turbulence-resolving large-eddy simulations (LES) and assesses an analytic vertical mixing parameterization based on a simplified second-moment closure (SMC) approach. Diurnal solar heating forces OSBL shoaling to generate a diurnal warm layer (DWL) in which heat and momentum are trapped. Without LT, relatively weak turbulent mixing results in a near-surface jet that is associated with enhanced turbulent kinetic energy (TKE) production of shear-driven turbulence (ST), which approximately balances TKE dissipation rates. Conversely, LT maintains strong mixing, delaying the DWL formation and preventing the TKE dissipation enhancement by generating a less sheared jet. However, sufficiently strong heating destroys TKE to ultimately reduce mixing and to create more sheared jets, which effectively shifts the LT to an ST-dominated regime. A second-moment turbulence budget analysis suggests that 1) the near-surface OSBL responds rapidly to the surface forcing, 2) Stokes drift impacts heat and momentum budgets in profoundly different ways, and 3) buoyancy terms are to leading order negligible. Building on these findings and introducing a physics-based mixing length, we develop a simplified SMC model that can be solved for near-surface expressions for key turbulent variables and mixing coefficients in terms of known variables. For ST, these expressions are consistent with the Monin–Obukhov similarity theory. For LT, these expressions reveal a fundamental dependence of turbulent variables on Stokes drift shear. 

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3. Ocean Surface Boundary Layer Response to Abruptly Turning Winds

   https://doi.org/10.1175/JPO-D-20-0198.1  

   Wang, Xingchi; Kukulka, Tobias (March 2021, Journal of Physical Oceanography)

   null (Ed.)

   Abstract Turbulence driven by wind and waves controls the transport of heat, momentum, and matter in the ocean surface boundary layer (OSBL). For realistic ocean conditions, winds and waves are often neither aligned nor constant, for example, when winds turn rapidly. Based on a Large Eddy Simulation (LES) method, which captures shear-driven turbulence (ST) and Langmuir turbulence (LT) driven by the Craik-Leibovich vortex force, we investigate the OSBL response to abruptly turning winds. We design idealized LES experiments, whose winds are initially constant to equilibrate OSBL turbulence before abruptly turning 90° either cyclonically or anticyclonically. The transient Stokes drift for LT is estimated from a spectral wave model. The OSBL response includes three successive stages that follow the change in direction. During stage 1, turbulent kinetic energy (TKE) decreases due to reduced TKE production. Stage 2 is characterized by TKE increasing with TKE shear production recovering and exceeding TKE dissipation. Transient TKE levels may exceed their stationary values due to inertial resonance and non-equilibrium turbulence. Turbulence relaxes to its equilibrium state at stage 3, but LT still adjusts due to slowly developing waves. During stages 1 and 2, greatly misaligned wind and waves lead to Eulerian TKE production exceeding Stokes TKE production. A Reynolds stress budget analysis and Reynolds-averaged Navier-Stokes equation models indicate that Stokes production furthermore drives the OSBL response. The Coriolis effects result in asymmetrical OSBL responses to wind turning directions. Our results suggest that transient wind conditions play a key role in understanding realistic OSBL dynamics. 

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4. Wind–Wave Misalignment Effects on Langmuir Turbulence in Tropical Cyclone Conditions

   https://doi.org/10.1175/JPO-D-19-0093.1  

   Wang, Dong; Kukulka, Tobias; Reichl, Brandon G.; Hara, Tetsu; Ginis, Isaac (December 2019, Journal of Physical Oceanography)

   This study utilizes a large-eddy simulation (LES) approach to systematically assess the directional variability of wave-driven Langmuir turbulence (LT) in the ocean surface boundary layer (OSBL) under tropical cyclones (TCs). The Stokes drift vector, which drives LT through the Craik–Leibovich vortex force, is obtained through spectral wave simulations. LT’s direction is identified by horizontally elongated turbulent structures and objectively determined from horizontal autocorrelations of vertical velocities. In spite of a TC’s complex forcing with great wind and wave misalignments, this study finds that LT is approximately aligned with the wind. This is because the Reynolds stress and the depth-averaged Lagrangian shear (Eulerian plus Stokes drift shear) that are key in determining the LT intensity (determined by normalized depth-averaged vertical velocity variances) and direction are also approximately aligned with the wind relatively close to the surface. A scaling analysis of the momentum budget suggests that the Reynolds stress is approximately constant over a near-surface layer with predominant production of turbulent kinetic energy by Stokes drift shear, which is confirmed from the LES results. In this layer, Stokes drift shear, which dominates the Lagrangian shear, is aligned with the wind because of relatively short, wind-driven waves. On the contrary, Stokes drift exhibits considerable amount of misalignments with the wind. This wind–wave misalignment reduces LT intensity, consistent with a simple turbulent kinetic energy model. Our analysis shows that both the Reynolds stress and LT are aligned with the wind for different reasons: the former is dictated by the momentum budget, while the latter is controlled by wind-forced waves. 

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5. An Eulerian two-phase model investigation on wave-induced scour around a vertical circular cylinder

   Benjamin Tsai, Antoine Mathieu (September 2023, International Conference on Scour and Erosion)

   A three-dimensional Eulerian two-phase flow solver, SedFoam, has been developed for various sediment transport applications. The solver has demonstrated success in modeling sheet flow and bedforms driven by oscillatory flows using a Reynolds-averaged Navier–Stokes (RANS) formulation. However, the accuracy of the RANS formulation for more complex flows, such as scour around structures, requires further evaluation. SedFoam has recently been enhanced to incorporate two-phase large-eddy simulation (LES) capability. In this study, RANS and LES approaches are tested via a three-dimensional case of wave-induced local scour around a single vertical circular pile. Two laboratory experiments, one with an erodible bed and the other with a rigid bed, were chosen for simulation, with both experiments having a Keulegan-Carpenter (KC) number of 10. The k-ω turbulence closure was selected for the RANS simulation, and the dynamic Lagrangian subgrid closure was chosen for the LES simulation. Numerical results reveal that both RANS and LES simulations can resolve lee-wake vortices, although the vortices are significantly weaker in the RANS simulation. In comparison with the LES results, the RANS approach fails to predict horseshoe vortex with sufficient intensity, leading to an underestimation of scour hole depth development. Although the scour depths develop at a very similar rate in the early stage, the scour depth predicted by the RANS simulation quickly reaches equilibrium, while the LES simulation follows the measured trend. These findings indicate that a turbulence-resolving methodology, i.e. LES, is necessary for accurate scour simulations. 

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