Diurnal Warm Layers in the ocean: Energetics, non-dimensional scaling, and parameterization

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 modelling, 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 non-dimensional parameters for DWL evolution and find that the scaling relations of Price et al. (1986) 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 15:00-16:30 for a broad range of parameters.