Wave–current interactions (WCIs) are investigated. The study area is located at the northern margin of the Ebro shelf (northwestern Mediterranean Sea), where episodes of strong cross-shelf wind (wind jets) occur. The aim of this study is to validate the implemented coupled system and investigate the impact of WCIs on the hydrodynamics of a wind-jet region. The Coupled Ocean–Atmosphere–Wave–Sediment Transport (COAWST) modeling system, which uses the Regional Ocean Model System (ROMS) and Simulating WAves Nearshore (SWAN) models, is used in a high-resolution domain (350 m). Results from uncoupled numerical models are compared with a two-way coupling simulation. The results do not show substantial differences in the water current field between the coupled and the uncoupled runs. The main effect observed when the models are coupled is in the water column stratification, due to the turbulent kinetic energy injection and the enhanced surface stress, leading to a larger mixed-layer depth. Regarding the effects on the wave fields, the comparison between the coupled and the uncoupled runs shows that, when the models are coupled, the agreement of the modeled wave period significantly improves and the wave energy (and thus the significant wave height) decreases when the current flows in the same direction as the waves propagate.

The works published in this journal are distributed under the Creative Commons Attribution 4.0 License. This licence does not affect the Crown copyright work, which is re-usable under the Open Government Licence (OGL). The Creative Commons Attribution 4.0 License and the OGL are interoperable and do not conflict with, reduce or limit each other.

During the last decade, several water circulation models have
been developed, including the wind–wave-induced currents. There are two
different formulations to include the so-called wave effects on currents
(WECs) in the three-dimensional primitive equations: by means of the
radiation-stress gradient

From a modeling perspective, several circulation and wave models have been
coupled in order to consider the wave–current interactions (WCIs). For
instance,

Previous studies have analyzed the physical processes involved in the WCIs
and the relevance of the coupling effects can vary depending, mainly, on the
water depth and the energy of the studied event. The WCIs have demonstrated
to be important in coastal regions

The north Ebro shelf (northwestern Mediterranean Sea) is a region characterized by
northwestern (NW) winds that are channeled through the Ebro Valley and which
result in cross-shelf wind jets when they reach the sea. This region is very
interesting from a meteo-oceanographic point of view because multiple
processes take place, such as bimodal wave spectra and the development of a
two-layer cross-shelf flow. Some authors have investigated the circulation
patterns

This work is organized as follows. In Sect.

The north Ebro shelf is located at the southern part of the Catalan coast, at
40.4–41.1

The most characteristic wind of the region is the northwesterly wind
(mistral), which is channeled through the Ebro Valley resulting in a
cross-shelf wind jet when it reaches the sea. This wind jet is related to the
presence of a high-pressure area over the Iberian Peninsula and a
low-pressure area over the Mediterranean Sea. Thus, it is more common during
autumn and winter

Study area.

For validation purposes, oceanographic and coastal meteorological
measurements from Puertos del Estado (

The coastal wave buoy (CB) is a TRIAXYS buoy located at 41.07

The HF radar system used in this work is a CODAR SeaSonde standard-range
system composed of three remote shelf-based sites that became operational in
December 2013. Each site comprises a transmitter–receiver antenna that
operates at a nominal frequency of 13.5 MHz with a 90 kHz bandwidth. The
system provides hourly measurements of the current velocities in the top
meter of the water column with a horizontal resolution of 3 km and a cutoff
filter of 100 cm s

The COAWST Modeling System

The SWAN model is a third-generation numerical wave model that computes
random, short-crested waves in coastal regions with shallow water and ambient
currents

The ROMS model is a split-explicit, free-surface, terrain-following,
primitive equation oceanic model that solves the 3-D Reynolds-averaged
Navier–Stokes equations using the hydrostatic and Boussinesq assumptions

The Model Coupling Toolkit

Three different runs have been performed in this work (see
Fig.

Configuration of setup run. In red is the name given to each configuration.

The numerical domain has a horizontal resolution of 350 m and, in the ROMS
case, a vertical resolution of

In order to generate the boundary conditions for the SWAN model, a
downscaling technique has been used. The entire system consists of three
nested domains (see Fig.

In the SWAN model, non-stationary conditions, spherical coordinates and
nautical convention have been selected. The wave growth by wind is computed
with a sum of a linear term and an exponential term. For the linear growth,
the expression from

The initial and boundary conditions for the ROMS model are taken from the
Iberian Biscay Irish – Monitoring and Forecasting Centre (IBI-MFC) product.
This product (

The ROMS model implementation includes a generic length-scale turbulent
vertical mixing scheme with the

In the two-way coupled run, the WCIs are implemented exchanging instantaneous
values of coupling fields every 20 min. The wave model provides wave
direction (

The first mechanism consists of computing enhanced bottom stresses due
to the effect of turbulence in the wave boundary layer by means of the SSW
(Sherwood–Signell–Warner) implementation of

The seconds mechanism involves computing enhanced surface stresses (SStr) due to changes in the surface roughness

The third mechanism is to inject turbulent kinetic energy (TKE) at the surface due to breaking waves. It is introduced as a surface flux of
turbulence kinetic energy in the generic length scale method

The fourth mechanism is to include the wave forces using the VF formalism

The wave model receives currents (

The cross-shelf momentum balance is used to analyze the
coupling effects on the circulation over the continental shelf. The
simplified equations for the VF approach can be obtained after removing the
curvilinear terms, body forces and horizontal and vertical mixing, and then
using Cartesian coordinates

The pressure gradient term includes

The non-conservative wave forcing term

In order to assess the model behavior, the estimation of bias, the root mean
square deviation (RMSD), the Pearson correlation (Pearson's

For circular data, e.g., wave direction, the metrics are computed as follows:

The ROMS and SWAN models for the same study period and the same model
configurations have been validated thoroughly in previous studies

The first step in the numerical skill assessment is to examine the quality of
the wind field, which is used to force the numerical models.
Table

Statistics comparing the 3 m wind and the modeled wave parameters with the DB data.

Comparison between the wind measured by the DB buoy (black) and the
one modeled by the WRF model and used as input for the SWAN and ROMS models
(green); see statistics in Table

Table

Table

Statistics comparing the modeled wave parameters with the CB data.

In Table

Statistics comparing the modeled water currents at P3 with data from the HF radar.

Figure

Wind intensity, along- and cross-shelf subinertial surface currents
and

With the aim of visualizing the differences in the current patterns and the
spatial variability between the different runs, in Fig.

Results for the wind-jet E3 event.

Figure

The evolution of the buoyancy or Brunt–Väisälä frequency
(

Comparison of the Brunt–Väisälä frequency at the start
(solid line) and the end (dashed line) of each wind-jet event obtained from
the results of the

Analyzing the results from

Time series comparison of the TKE

In order to evaluate how the waves' effects are taken into account in the
momentum balance, the terms of Eq. (

The irregular nature of wind causes irregular wind waves of different
heights, periods and directions. For this reason, wind waves are usually
described using spectral techniques, where the random motion of the sea
surface is treated as a summation of harmonic wave components. In
Fig.

Spectra evolution during the E3 event at P2.

In Figs.

In order to analyze the

The Tm

Comparison of the Tm

Regarding the mean wave direction, no relevant differences are observed
between the

The main differences between the

The results presented above show that including the wave effects does not
produce a relevant difference to the water current velocity during a wind-jet
event and has a weak impact on the water circulation patterns. Similar
results were presented by

The numerical results presented an improvement in the Tm

During a wind-jet event, a decrease of the

The differences in mean wave direction found in shallow waters could be due
to the current-induced refraction

Finally, considering the currents causes wave spectral reshaping. During a
cross-shelf wind-jet event, the presence of currents induces a shoaling-like
process. In general, a reduction of the energy peak and a slight increase of
the energy at the tail of the spectrum are observed. This is consistent with
the results presented in

The wave–current interactions have been investigated using numerical models.
Three different runs have been performed: an uncoupled ROMS run, an uncoupled
SWAN run and a two-way coupled run. The comparison among these runs shows
that at the continental shelf the surface water current presents similar
results in the coupled and the uncoupled configurations, and the momentum
balance analysis reveals that the non-conservative WF term
plays an important role in shallow waters. The results show that coupling the
models results in a major mixing of the water column (the SML increase),
mainly due to the TKE injection and the enhanced surface stress.
Additionally, wave spectral reshaping occurs, the Tm

Overall, the numerical results are physically reasonable, as they reproduce the well known coupling effects. The results have enabled the WCIs to be investigated but more measurements would be needed in order to perform a more quantitative analysis. Thus, in the future, it would be interesting to perform some measurement campaigns to enable more accurate model validation and more exhaustive analysis of the dynamics of the region. In addition, it would be interesting to investigate the role of the sea surface roughness coupling the ROMS and SWAN models with the WRF model.

HF radar data and buoy measurements used in this contribution can be found in

The logarithmic wind profile used to extrapolate the modeled wind from 10 to 3 m is as follows:

The roughness length is estimated by means of the Charnock relation:

The friction velocity is related to the known wind speed at 10 m elevation
(

All the authors conceived and designed the experiments and contributed ideas in the writing process. LR performed the experiments, analyzed the data and wrote the paper.

The authors declare that they have no conflict of interest.

The development of this research was partially funded by the Doctorats Industrials 2013 PhD program of the Catalan Government. The authors also acknowledge Puertos del Estado for the data set provided. This work received funding from the EU H2020 program under grant agreement no. 730030 (CEASELESS project). Edited by: John M. Huthnance Reviewed by: two anonymous referees