1. Introduction
Wind–wave interaction has been a topic of continuous research for almost a century: from Jeffreys’s sheltering hypothesis (Jeffreys 1925) to the most recent high-fidelity, wave-phase-resolved, and turbulence-resolving numerical simulations (Hao and Shen 2019) and large-scale field campaigns (Black et al. 2007; Edson et al. 2007). As many physical processes rely on accurately quantifying the heat, mass, and momentum exchanges that take place at the air–sea interface, wind–wave interaction dynamics have been cardinal to many scientific and engineering disciplines: from climate and weather prediction to plankton generation models (Sullivan and McWilliams 2010; Cavaleri et al. 2012). A relatively new field that is expected to also be affected by wind–wave interaction is offshore wind energy. Currently, the total installed offshore wind energy capacity of the United States amounts to 30 MW and is expected to increase drastically over the next decade, with up to 14 GW of capacity planned to be installed off the U.S. East Coast by 2030 (Musial et al. 2019). The installation and operation of offshore large-scale wind farms have raised numerous questions about the predictability of wind and wave resources in offshore environments, including our ability to predict the mean wind speed and turbulence levels that future wind turbines will experience as well as the wave field relevant to floating offshore wind turbine dynamics. To this end, wind–wave interaction lies in the epicenter of offshore wind energy. First, wind–wave interaction together with other prevalent marine boundary layer phenomena (e.g., low-level jets) can draw a completely different picture for the dynamics of atmospheric turbulence than its land-based counterpart. For instance, a recent study by Bodini et al. (2019) showed that the turbulence levels experienced by offshore wind turbines in the U.S. East Coast can be considerably lower than those found onshore. Second, the combined aerodynamic and hydrodynamic loading on floating offshore wind turbines introduces the need to also simulate both effects simultaneously for either operational (Butterfield et al. 2007) or extreme, nonoperational event scenarios (Kim et al. 2016). In any case, better models for wind–wave interaction are key to reducing uncertainty in the simulation of offshore wind energy systems and therefore further contribute to their financial viability (Veers et al. 2019).
In recent years, wind–wave interaction research has enjoyed the renewed interest from both the engineering and scientific communities. This is evident by the increasing number of large-scale field campaigns (Black et al. 2007; Edson et al. 2007) and the development of novel numerical models capable of resolving and incorporating wave motions in atmospheric turbulence simulations (Yang and Shen 2011a,b; Sullivan et al. 2014). Wave-resolving simulations are relevant to turbulence-resolving atmospheric modeling via large-eddy simulation (LES) of the airflow over regular and irregular waves. It should be noted here that large-eddy simulations of the planetary boundary layer have been performed for almost five decades and are known to yield high-fidelity data for canonical cases (e.g., flow over a horizontally homogeneous flat terrain) including the daytime buoyancy-driven boundary layer (Deardorff 1972; Moeng 1984; Mason 1988; Moeng and Sullivan 1994), the neutrally stratified atmospheric boundary layer (ABL) (Mason and Thomson 1987; Andren et al. 1994; Pedersen et al. 2014), and the nocturnal stable boundary layer (Kosović and Curry 2000; Mason and Derbyshire 1990; Basu and Porté-Agel 2006). The high accuracy of LES is because of to the fact that the larger flow structures are sufficiently resolved at the computational grid scale while smaller subgrid-scale structures can be accurately modeled (Meneveau and Katz 2000). LES has also been successfully employed to study atmospheric turbulence over complex terrain (Fedorovich 1986; Smith and Skyllingstad 2005; Chow et al. 2006). More recently, however, wave-phase-resolved simulations of the marine atmospheric boundary layer (MABL) have been undertaken (Sullivan et al. 2008, 2014, 2018b; Hao et al. 2018; Hao and Shen 2019), which have enhanced our understanding of the offshore turbulence characteristics. Wave-phase-resolved simulations require the use of more sophisticated numerical algorithms often comprising two separate but loosely coupled subsolvers, one to predict the temporal/spatial evolution of the free-surface waves and another to simulate the atmospheric turbulence or alternatively a two-phase (i.e., air/water) solver with an advanced interface-tracking algorithm (Prosperetti and Tryggvason 2009). The latter approach has not been used in large-eddy simulation of the MABL and only a handful of direct-numerical simulation (DNS) studies exist to this day (Lin et al. 2008; Yang et al. 2018). However, the former approach that employs the two subsolvers loosely coupled together at the air–sea interface is considered to be a state-of-the-art model for large-eddy simulations of the MABL. Its use in marine boundary layer simulations has helped us gain insight into the complex wind–wave interaction processes and to that extent it has also challenged the validity of the widely used Monin–Obukhov similarity theory (MOST; Monin and Obukhov 1954) in wave-driven wind cases (Sullivan and McWilliams 2010; Jiang et al. 2016). We note here that MOST provides an analytical expression for the mean velocity and temperature profiles in the lower part of the ABL also known as the “surface layer” (see section 2) and therefore is germane to wind energy applications. Considering the importance of wind–wave interactions in predicting the ambient atmospheric turbulence as well as the impact they may have on predicting turbine loads and power output, as it was recently demonstrated by Yang et al. (2014a,b), AlSam et al. (2015), and Calderer et al. (2018), we argue that wind–wave coupling models remain a key aspect of offshore wind energy modeling and therefore need to be thoroughly studied.
In this article, we present a comprehensive review of wind–wave coupling models that can be adopted to perform large-eddy simulations of the MABL within the context of turbulence-resolving simulations at grid scales of magnitude O(1–15 m) and used in offshore wind energy applications at similar or finer resolution. We shall refer to such scale-resolving simulations within domain sizes of O(1–50 km3) as “microscale” simulations. This article complements many existing reviews on the fluid dynamics of wind over waves and the marine boundary layer (Belcher and Hunt 1998; Sullivan and McWilliams 2010) and textbooks and proceedings on wind–wave interaction (Csanady and Gibson 2001; Jones and Toba 2001; Hunt and Sajjadi 2003; Janssen 2004). However, in this review, we emphasize the modeling aspects by laying out all of the crucial algorithmic components. Thereby, the remainder of this review article starts with section 2, where we introduce the main geophysical processes present in the MABL together with the governing equations used within a three-dimensional, unsteady LES framework. Next, we present the wave-phase-averaged and phase-resolved modeling techniques in sections 3 and 4, respectively. These are followed in section 5 by a brief introduction of the most recent field databases collected in offshore regions of high relevance to offshore wind energy. In section 6, we summarize the physical insights gained from performing large-eddy simulations of the MABL as well as the remaining knowledge gaps and modeling limitations of the reviewed models.
2. The marine atmospheric boundary layer structure and governing equations
The MABL is a special type of the ABL that occurs over oceans or large lakes. As such, it shares many of its features with the well-studied, land-based ABL, including a similar vertical structure. On the other hand, the physical processes of the MABL are more complex as they involve additional processes at the air–sea interface that span multiple time and length scales. Nonetheless, for the sake of simplicity, we define the vertical structure of the MABL in analogy with the land-based ABL (Stull 1988; Kaimal and Finnigan 1994; Wyngaard 2010) by splitting it into two distinct regions: the “surface” or “constant-flux” layer and a free-atmosphere-topped “mixed” layer, as shown in Fig. 1. The former is about 1–100 m high, and the vertical variations of the turbulent fluxes therein are not expected to exceed 10% of their surface values. This region can be further split into the “wave boundary layer,” which is the region immediately adjacent to, and directly impacted by, the motion of the waves, and the “inertial sublayer,” where the bulk exchange of mass, momentum, heat, and moisture between the wind and waves takes place. The wave boundary layer is considered to be only a few meters high [O(1 m)] for wind-driven waves and it is believed to reach higher altitudes only in cases when light winds blow over faster-moving swells (Grachev and Fairall 2001; Grachev et al. 2003). The inertial sublayer, together with the wave boundary layer, make up approximately 10%–20% of the overall boundary thickness. Above the surface layer lies the mixed layer, which, depending on the thermal stratification, can extend to altitudes of 200–700 m. Last, the free atmosphere, a stably stratified nonturbulent region above the atmospheric boundary layer, lies atop the mixed layer and its onset defines the overall MABL thickness. For completeness, we should also mention that a thin layer above the air–sea interface exists, called the surface or viscous sublayer, where viscous fluid forces are important. Thanks to the very-high-Reynolds-number nature of the MABL, Re > 107, this region is only a few millimeters thick and therefore ignored in most numerical models.

Schematic representation of the atmospheric vertical structure over ocean waves.
Citation: Journal of the Atmospheric Sciences 78, 10; 10.1175/JAS-D-21-0003.1

Schematic representation of the atmospheric vertical structure over ocean waves.
Citation: Journal of the Atmospheric Sciences 78, 10; 10.1175/JAS-D-21-0003.1
Schematic representation of the atmospheric vertical structure over ocean waves.
Citation: Journal of the Atmospheric Sciences 78, 10; 10.1175/JAS-D-21-0003.1
3. Wave-phase-averaged, wall-modeled LES
a. Wave-age and wave-steepness dependence of the sea surface roughness
Table of models for the sea surface roughness length scale.



Compilation of models for sea surface roughness as a function of the nondimensional angular peak frequency.
Citation: Journal of the Atmospheric Sciences 78, 10; 10.1175/JAS-D-21-0003.1

Compilation of models for sea surface roughness as a function of the nondimensional angular peak frequency.
Citation: Journal of the Atmospheric Sciences 78, 10; 10.1175/JAS-D-21-0003.1
Compilation of models for sea surface roughness as a function of the nondimensional angular peak frequency.
Citation: Journal of the Atmospheric Sciences 78, 10; 10.1175/JAS-D-21-0003.1
b. Wave-spectra-informed sea surface
4. Wave-phase-resolved LES
The sea surface–roughness approach provides a static representation of the wind–wave interaction and can be interpreted as a wave-informed drag model that only accounts for a downward momentum transfer (from wind to waves). However, recent studies have shown that this is not the case under swell-dominated seas where long waves propagate into light or moderate winds and where momentum can also be transferred upward (Grachev and Fairall 2001; Sullivan et al. 2008). In such a scenario, a dynamic coupling between the airflow and the propagating waves is needed. Such approaches have been pursued for airflow over monochromatic or broadband waves in either the context of direct-numerical simulations (Sullivan et al. 2000; Sullivan and McWilliams 2002; Shen et al. 2003; Kihara et al. 2007; Yang and Shen 2009, 2010; Druzhinin et al. 2012; Åkervik and Vartdal 2019; Wang et al. 2020), wall-resolved large-eddy simulations (Zhang et al. 2019; Cao et al. 2020), or wall-modeled LES (Sullivan et al. 2008; Yang et al. 2013a; Sullivan et al. 2014; Hara and Sullivan 2015; Sullivan et al. 2018a,b; Hao et al. 2018; Hao and Shen 2019). The latter approach is appropriate for the dynamic coupling between wind and ocean waves in the context of the MABL and requires the use of two separate models: a wall-model-equipped LES solver to resolve the atmospheric turbulent flow and a potential-flow solver to advance the free-surface. The dynamic coupling between the two models is achieved by an exchange of information at the air–sea interface. In particular, the potential-flow wave model provides information about the free-surface vertical displacement η(x, y, t) and local orbital velocity (uo, υo, wo), which in turn enters the LES solver through a waving boundary condition. The updated sea surface elevation distorts the LES mesh by moving the mesh nodes vertically to remap the computational domain. On the other hand, the LES model passes the surface atmospheric pressure fluctuations,