**1. Introduction**

Wave–currents interaction has recently gained interest in the field of coastal and ocean forecasting [1,2]. Wind-wave-current processes control the momentum and energy exchange between the atmosphere and the ocean and must be better understood and resolved. The physics of wave-currents interaction depend on the kinematics and dynamics of the wave field. These include processes such as wind-wave growth, nonlinear wavewave interactions, wave-currents interaction and wave dissipation, all of which can only be accurately represented using wave models. Reducing the uncertainties in the nowadays forecasting models that result from the non-linear feedback between the currents [3], water level variations [4,5] and wind waves [6] is therefore essential. Over the past 40 years, a considerable amount of research has been devoted to investigating the role of ocean waves in the air-sea interaction. An accurate representation of ocean surface waves has been recognised as essential in various applications, ranging from marine meteorology to ocean and coastal engineering to operational forecasting [7,8].

Important contributions to the field of wave-currents interaction include the pioneering work of [9] on what is now referred to as the Stokes–Coriolis force, the work of [10] on wave-driven ocean circulation and of [11] on upper ocean mixing by wave breaking. The impact of the oceanic wave field on upper-ocean mixing and mean properties has

**Citation:** Causio, S.; Ciliberti, S.A.; Clementi, E.; Coppini, G.; Lionello, P. A Modelling Approach for the Assessment of Wave-Currents Interaction in the Black Sea. *J. Mar. Sci. Eng.* **2021**, *9*, 893. https:// doi.org/10.3390/jmse9080893

Academic Editor: Eugen Rusu

Received: 5 July 2021 Accepted: 17 August 2021 Published: 19 August 2021

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been examined using various model experiments [11–17]. Most find that waves appear to have a profound impact on the upper part of the ocean, but there is still considerable disagreement about which processes are more important. Waves define the mixing in the oceanic surface boundary layer (OSBL) via breaking and Langmuir turbulence. For example, ref. [18] identified Langmuir turbulence over wide areas of the global ocean and particularly in the Southern Ocean. In this region, they showed that the inclusion of the effect of surface waves on upper-ocean mixing during summertime led to a reduction in systematic bias in the OSBL depth. Jansen et al. 2013 [17] showed the positive impact of wave breaking on the daily cycle of the sea surface temperature. Babanin et al. 2012 [19] investigated the mixing process related to the orbital motion of non-breaking waves.

All of these wave-driven processes influence the vertical structure of the temperature and current fields in the mixed layer in general, and in the upper few meters in particular. This has implications for coupled models as these processes will affect the feedback between the ocean and the atmosphere [17]. However, on shorter time scales and at higher spatial resolution these processes will influence the drift of objects and pollutants on the sea surface or that are partially or wholly submerged. This has practical implications for oil spill modelling [20] and search and rescue [21–23]. Studies focusing on the Baltic Sea [24] and the North Sea [25] apply the coupling approach previously implemented by [26,27], which consists of coupling the wave model with the circulation model. Staneva et al. 2021 [28] in particular demonstrated how the Eulerian currents provided by a coupled NEMO-WAM model in the North Sea can improve the representation of particle transports, dealing with a number of possible impacts on downstream services for marine litter, oil spill and environmental water properties. This was then adapted to include the Stokes–Coriolis effect, the sea-state-dependent momentum and energy fluxes. These studies show that coupling the models has a pronounced effect on vertical temperature distribution and mesoscale events, and improves predictions of sea level and currents during storm events. In the Mediterranean Sea, Ref. [29] presents an approach based on the assumption that the currents are driven by surface wind stresses that in turn are a function of the sea state, while the sea state depends on the wind speed and the currents. These complex feedback mechanisms can be modelled by coupling hydrodynamic and wave models, which to date have been developed separately. Examples are provided by [8,30] for the North-West European Shelf system. In particular by understanding the role of ocean-wave coupling in an eddy-resolving operational configuration to improve the predictability of sea surface temperature, surface and sea bed salinity, sea surface height and currents.

The active literature production on this topic and the interest in regional modelling in particular for marginal seas induced our attention in understanding the complex mechanisms of wave-currents interaction in the Black Sea. This basin acts as a small-scale laboratory for investigating processes that are common to numerous areas of the world's oceans. Considering that the water and salt balances can be controlled, and the scales are smaller than in the global ocean, the basin is a useful test region for developing models, which can then be applied at larger scales [31].

From the physical point of view, the Black Sea is an inland sea, one of the largest and deepest basins in the world and the farthest to the east among the seas of the Atlantic Ocean. It works with a complex straits system—the Kerch Strait connects the Black Sea with the Azov Sea; the Bosphorus Strait makes the connection with the Marmara Sea which is connected in turn to the Mediterranean Sea through the Dardanelles Strait [32]. Straits system and limited water exchange with the open ocean play an important role in the water balance, influencing the ventilation, stratification and water mass formation [31,33]. Rivers are one of the strongest contributors of freshwater with impact to the general circulation in the Black Sea together with wind stress and bathymetric peculiarities: in particular, the North-West shelf region is dominated by the Danube River floodplain and outflow. The Danube, together with the Dniepr and the Dniester and the dense distribution of rivers along the overall coastline contribute to a positive water budget (~5.4 × 105 km3), making the Black Sea a typical estuarine basin [34–36]. The Black Sea

circulation is structured usually in two connected gyre systems encompassing the basin (the Rim Current) and quasi-stationary anticyclonic eddies in the coastal zone, such as Batumi, Sevastopol, Caucasian, Sakarya, Sinop ones [30,37,38]. Some scientific works focused attention on reconstructing the past ocean state in the Black Sea [39] with reference to mesoscale circulation and water mass properties [40–42]. The wind is the main driving force in creating a cyclonic general circulation. Simulation [43] and observations [44] showed that there are three major regions with different regimes of currents: (a) coastal zone of very variable flow, with currents speeds of up to 20–30 cm/s; (b) the main Black Sea currents zone, which has jet-stream character, with a width of 40–80 km and speed of 40–50 cm/s, reaching values of 1–1.5 m/s; (c) the open sea area, where the velocity of the current decreases gradually from the periphery to the centre, not exceeding 5–15 cm/s.

Another important feature of the Black Sea, strictly related to convective processes due to the thermohaline inertia in the upper layer and impact of air-sea fluxes, is the Cold Intermediate Layer (CIL) [45]. CIL is a sub-surface water mass that results from the Winter convective mixing in the centres of cyclonic gyres and shelf areas [32]. CIL formation in the Black Sea depends on the fact that Winter convection is limited by the shallow depth of halocline (such as in the Baltic Sea, the Sea of Okhotsk, the Gulf of St. Lawrence). A consequence of the vertical stratification is that the surface layer (about 0 to 50 m) is well oxygenated while the deep layer (100 m to 2000 m) is anoxic and contains high sulphide concentrations [46].

The wind regime over the Black Sea results from the cyclonic and anticyclonic activity over Europe. The Island cyclone and the Azores anticyclone acts throughout the year, while the Mediterranean cyclones and Siberian anticyclone are more effective in Winter [47]. The Black Sea is dominated by Northerly winds in the West and the North of the sea; Eastern and South-Easterly winds are typical for the East and South-East of the sea. In Spring and Summer, in the Western part of the sea, under the influence of the Azores High, the frequency of Western, South-Western and Southern winds increases [48–51]. South-eastern and Southern coasts of the sea are characterised by weak winds (average annual wind speed < 3 m/s); in the Western and Northwestern parts of the sea, as well as in the Kerch Strait area, stronger winds are observed (average annual wind speed > 4 m/s, at some stations > 5 m/s) [32].

Wind waves in the Black Sea have been widely studied by many researchers from the surrounding regions [52–56]. Brief information about Black Sea wave average climate based on long simulation (1949–2010) is here provided from one of the more recent works [57]. They showed that the average wave parameters are at a maximum in Winter, with maximal values of average Hs exceeding 0.95 m. Areas of most expressed storminess in terms of all average values correspond to the central part of the basin. The same spatial pattern is also observed in the distribution of Springtime averaged wave parameters, but their values are significantly lower (maximal average Hs 0.65 m). The calmest wave field corresponds to Summertime, where Hs > 0.5 m occurred only in small areas of the basin.

From a technical point of view, there are two ways to investigate the impact of oceanwave interactions: offline or online. Offline coupling e.g., [27,58] implies that the model which provides the fields (sender) runs independently and before the receiving model (receiver). The output from the sender is subsequently used, as the other forcing, by the receiver. This methodology has computational and timing benefits but does not consider the mutual interaction between the two components of the forced system. In the online coupling e.g., [7,28] both the cores are integrated simultaneously, allowing feedback at a predefined exchange time. This methodology more intimately reflects the wave-currents interaction, but it requires an external coupler to drive the models' communication, and the overall running time is almost the sum of both the models running times.

The aim of this work is the assessment, for the first time, of the effects due to the reciprocal interaction between hydrodynamics and waves in the Black Sea through a forced system based on NEMO v4.0 for the hydrodynamics and Wave Watch III for the waves. The main scope is then to improve the representation of the physical processes and dynamics in the Black Sea region by accounting for the role of waves. To complete the overall investigation, this work presents also some numerical results on the impact of improved hydrodynamics on the sea-state.

The coupling strategy here proposed is based on the exchange of surface Stokes drift, wave energy to the ocean, sea-state dependent momentum flux, currents and the air-sea temperature difference, with the main purpose to improve firstly the mixing process in the hydrodynamical core model. The effects have been evaluated via comparison with a standalone run (without forcing) for both waves and hydrodynamics.

This paper is organised as follows. In Section 2 we present the model system and the coupling strategy. Section 3 illustrates the numerical experiment and validation strategy. Section 4 gives the numerical model results and a comparison with observations, and Section 5 provides conclusions and future works.

#### **2. The Modelling System**

The numerical system presented in this work is a reciprocal forced hydrodynamic circulation model with a third-generation spectral wind-wave model, implemented in the Black Sea basin. This section presents information about the horizontal numerical grid, which is common to the implementation of both wave and hydrodynamical models. The specific features of this grid, such as spectral discretization for waves and vertical discretization for hydrodynamics, are detailed in the related subsections.

#### *2.1. Atmospheric Forcing, Numerical Grid and Bathymetry*

Both hydrodynamics and waves are forced by the high-resolution atmospheric model at a horizontal resolution of 0.125◦ × 0.125◦ and 6-h frequency, as produced by the European Centre for Medium-range Weather Forecasts (ECMWF, [59]). The system uses Zonal and Meridional Components of the 10 m wind (m/s), Total Cloud Cover (%), 2 m Air Temperature (K), 2 m Dew Point Temperature (K) and mean sea-level pressure (Pa). Precipitation (Kg/m2/s) data are provided as monthly climatologies from GPCP [60,61].

The Black Sea region has been discretised in horizontal space using a regular mesh of 395 × 215 grid points, at 0.037◦ (longitude) × 0.0278◦ (latitude) spatial resolution in spherical coordinates (Figure 1).

**Figure 1.** The Black Sea domain and bathymetry.

The bathymetric dataset used in this work is the GEBCO\_14 [62] at 30" grid resolution. The GEBCO\_14 in the Black Sea basin was merged with a high-resolution dataset for the Bosphorus Strait, as described in [63].
