abstract = {Here, the effects of surface waves on submesoscale instabilities are studied through analytical and linear analyses as well as nonlinear large-eddy simulations of the wave-averaged Boussinesq equations. The wave averaging yields a surface-intensified current (Stokes drift) that advects momentum, adds to the total Coriolis force, and induces a Stokes shear force. The Stokes–Coriolis force alters the geostrophically balanced flow by reducing the burden on the Eulerian–Coriolis force to prop up the front, thereby potentially inciting an anti- Stokes Eulerian shear, while maintaining the Lagrangian (Eulerian plus Stokes) shear. Since the Lagrangian shear is maintained, the Charney–Stern–Pedlosky criteria for quasigeostrophic (QG) baroclinic instability are unchanged with the appropriate Lagrangian interpretation of the shear and QG potential vorticity. While the Stokes drift does not directly affect vorticity, the anti-Stokes Eulerian shear contributes to the Ertel potential vorticity (PV). When the Stokes shear and geostrophic shear are aligned (antialigned), the PV is more (less) cyclonic. If the Stokes-modified PV is anticyclonic, the flow is unstable to symmetric instabilities (SI). Stokes drift also weakly impacts SI through the Stokes shear force. When the Stokes and Eulerian shears are the same (opposite) sign, the Stokes shear force does positive (negative) work on the flow associated with SI. Stokes drift also allows SI to extract more potential energy from the front, providing an indirect mechanism for Stokes-induced restratification.},
  author = {Haney, Sean and Fox-Kemper, Baylor and Julien, Keith and Webb, Adrean},
  doi = {10.1175/JPO-D-15-0044.1},
  isbn = {10.1175/JPO-D-15-0044.1},
  issn = {0022-3670},
  journal = {Journal of Physical Oceanography},
  keywords = {Baroclinic flows,Circ,[Ageostrophic circulations},
  number = {12},
  pages = {3033--3056},
  title = {{Symmetric and Geostrophic Instabilities in the Wave-Forced Ocean Mixed Layer}},
  volume = {45},
  year = {2015}
  abstract = {The effects of Langmuir mixing on the surface ocean mixing may be parameterized by applying an enhancement factor which depends on wave, wind, and ocean state to the turbulent velocity scale in the K-Profile Parameterization. Diagnosing the appropriate enhancement factor online in global climate simulations is readily achieved by coupling with a prognostic wave model, but with significant computational and code development expenses. In this paper, two alternatives that do not require a prognostic wave model, (i) a monthly mean enhancement factor climatology, and (ii) an approximation to the enhancement factor based on the empirical wave spectra, are explored and tested in a global climate model. Both appear to reproduce the Langmuir mixing effects as estimated using a prognostic wave model, with nearly identical and substantial improvements in the simulated mixed layer depth and intermediate water ventilation over control simulations, but significantly less computational cost. Simpler approaches, such as ignoring Langmuir mixing altogether or setting a globally constant Langmuir number, are found to be deficient. Thus, the consequences of Stokes depth and misaligned wind and waves are important.},
  author = {Li, Qing and Fox-Kemper, Baylor and Breivik, {\O}yvind and Webb, Adrean},
  doi = {10.1016/j.ocemod.2017.03.016},
  isbn = {1463-5003},
  issn = {14635003},
  journal = {Ocean Modelling},
  keywords = {Climate model,KPP,Langmuir mixing,Statistical modeling},
  pages = {95--114},
  title = {{Statistical models of global Langmuir mixing}},
  volume = {113},
  year = {2017}
  abstract = {Large-Eddy Simulations (LES) have shown the effects of ocean surface gravity waves in enhancing the ocean boundary layer mixing through Langmuir turbulence. Neglecting this Langmuir mixing process may contribute to the common shallow bias in mixed layer depth in regions of the Southern Ocean and the Northern Atlantic in most state-of-the-art climate models. In this study, a third generation wave model, WAVEWATCH III, has been incorporated as a component of the Community Earth System Model, version 1.2 (CESM1.2). In particular, the wave model is now coupled with the ocean model through a modified version of the K-Profile Parameterization (KPP) to approximate the influence of Langmuir mixing. Unlike past studies, the wind-wave misalignment and the effects of Stokes drift penetration depth are considered through empirical scalings based on the rate of mixing in LES. Wave-Ocean only experiments show substantial improvements in the shallow biases of mixed layer depth in the Southern Ocean. Ventilation is enhanced and low concentration biases of pCFC-11 are reduced in the Southern Hemisphere. A majority of the improvements persist in the presence of other climate feedbacks in the fully coupled experiments. In addition, warming of the subsurface water over the majority of global ocean is observed in the fully coupled experiments with waves, and the cold subsurface ocean temperature biases are reduced.},
  author = {Li, Qing and Webb, Adrean and Fox-Kemper, Baylor and Craig, Anthony and Danabasoglu, Gokhan and Large, William G. and Vertenstein, Mariana},
  doi = {10.1016/j.ocemod.2015.07.020},
  isbn = {1463-5003},
  issn = {14635003},
  journal = {Ocean Modelling},
  keywords = {Climate model,KPP,Langmuir mixing,Mixed layer},
  pages = {145--160},
  title = {{Langmuir mixing effects on global climate: WAVEWATCH III in CESM}},
  volume = {103},
  year = {2016}
  abstract = {The relationships between the moments of wave spectra and Stokes drift velocity are calculated for empirical spectral shapes and a third-generation wave model. From an assumed spectral shape and only an estimate of wave period and significant wave height, one may determine: the leading-order Stokes drift, other wave period estimates, and all spectral moments. The conversion factors are tabulated for quick reference for the common empirical spectral shapes. The different spectral shapes considered are shown to exhibit similar spectral moment relationships. Using these relationships, uncertainty in Stokes drift may be decomposed into the uncertainty in spectral shape and a much greater uncertainty due to significant wave height and wave period discrepancies among ERA40/WAM, satellite altimetry, and CORE2 reanalysis-forced WAVEWATCH III simulations. Furthermore, using ERA40 or CORE2 winds and assuming fully-developed waves results in discrepancies that are unable to explain the discrepancies in modeled Stokes drift; the assumption of fully-developed waves is likely the culprit.},
  author = {Webb, Adrean and Fox-Kemper, Baylor},
  doi = {10.1016/j.ocemod.2011.08.007},
  issn = {14635003},
  journal = {Ocean Modelling},
  keywords = {Significant wave height,Stokes drift,Wave period,Wave spectra},
  number = {3-4},
  pages = {273--288},
  title = {{Wave spectral moments and Stokes drift estimation}},
  volume = {40},
  year = {2011}
  author = {Webb, Adrean},
  school = {University of Colorado Boulder},
  title = {{Stokes Drift and Meshless Wave Modeling}},
  url = {},
  year = {2013}
  abstract = {The Stokes drift, and its leading-order approximation, for a random sea depend upon the interaction of different wave groups and the process of wave spreading. Here Stokes drift direction and magnitude from prescribed spectra, local observational buoy data, and global model WAVEWATCH III output are used to analyze approximations of Stokes drift for directional random seas in deep water. To facilitate analysis, a new approximation is defined to incorporate the systematic effects of wave spreading. Stokes drift is typically overestimated by ignoring these effects or by ignoring directional differences in swell and wind seas. These two errors are differentiated and found to be largely uncorrelated. These errors depend strongly on depth, with deeper Stokes drift favoring narrow-banded swell and shallower Stokes drift favoring wind seas. Results are consistent among the data examined. Mean Stokes drift magnitude reductions from wave spreading and multidirectional wave effects alone are 14-20{\%} and 7-23{\%} respectively, giving a combined reduction of 20-40{\%} versus unidirectional waves, depending on wave age and depth. Approximations that do not include these reductions however, will on average overestimate Stokes drift by 16-26{\%}, 26-43{\%}, and 45-71{\%} respectively. In addition to magnitude, the direction of Stokes drift is also affected and multidirectional waves generate a directional veer with depth: the 30/60/90{\%} confidence intervals are bounded (approximately) by ± 0.12/0.28/0.84 radians ( ± 7/16/48. deg) at the surface, with smaller intervals at depth. Complementary depth-integrated approximations are also investigated and directional effects are similar with depth-dependent subsurface results. Furthermore, an optimized directional spread correction for the surface is nearly identical for global simulations and a buoy located at Ocean Weather Station P (50°N 145°W), and does not require directional wave spectrum data.},
  author = {Webb, Adrean and Fox-Kemper, Baylor},
  doi = {10.1016/j.ocemod.2014.12.007},
  issn = {14635003},
  journal = {Ocean Modelling},
  keywords = {Stokes drift,Unidirectional waves,Wave spreading},
  pages = {49--64},
  title = {{Impacts of wave spreading and multidirectional waves on estimating Stokes drift}},
  volume = {96},
  year = {2015}
  author = {A. Webb, T. Waseda, W. Fujimoto, K. Horiuchi, K. Kiyomatsu, K. Matsuda, Y. Miyazawa, S. Varlamov, and J. Yoshikawa},
  archivePrefix = "arXiv",
  eprint = {1607.02251},
  primaryClass = "",
  title={A High-Resolution, Wave and Current Resource Assessment of {Japan}: {The} Web {GIS} Dataset},
  year = {2016},