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Modelling the effect of wave current
interaction at the mouth of the
Danube river
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979Developments in Maritime T ransportation and Exploitation of Sea Resources –
Guedes Soares & López Peña (eds)
© 2014 T aylor & Francis Group, London, ISBN 978-1-138-00124-4
Modelling the effect of wave current interaction at the mouth
of the Danube river
Eugen Rusu & C. Guedes Soares
Centre for Marine Technology and Engineering (CENTEC), Instituto Superior Técnico,
Technical University of Lisbon, Lisbon, Portugal
ABSTRACT: The objective of the present work is to evaluate the effects of the wave-current interactions
at the mouths of the Danube river in the Black Sea, area usually subjected to intense navigation. A SW AN
based modelling system is applied to the target area and numerical simulations are performed in a high resolution computational domain for the main environmental patterns characteristic to this part of the sea, considering the situations without and with the current fields included. A field experiment was also
carried out and its results confirm in general the output provided by the model simulations. The results
show that the currents induce relevant enhancements in terms of significant wave heights. Moreover, the higher values of the Benjamin Feir Index, resulted in the case when the current fields are considered in the modelling process, indicate also an elevated risk of rogue wave occurrences in the target area.
This is because here high energetic wave conditions are usual and the currents induced by the Danube outflow make this coastal area representative from the point of view of the relevance of the wave–current interaction process. A visual representa-tion that gives a first idea on the impact of these interactions between waves and opposite currents 1 INTRODUCTION
The coastal sector at the mouths of the Danube River can be considered as very significant for coastal navigation because it is the main south-ern gate for the Rhine–Main–Danube Canal that is part of a trans-European waterway from
Rotterdam on the North Sea to Sulina on the
Black Sea (3500 km). Hence the navigation in this
area represents a key issue in the development of the logistic chain related to the inland navigation in Europe and the links of the harbors from the Black and the Mediterranean seas with those from the northern part of Europe.
Since the Sulina channel represents the main
entrance to the seventh Pan European transport
corridor, this coastal area is usually subjected to
high navigation traffic. On the other hand, the environmental conditions, which are often quite hard in this part of the sea, especially in winter time, raise elevated risks to the navigation in this coastal sector.
For this reason, several accidents and incidents
took place in the last years close to Sulina channel and as an illustrative example only in December
2009, two sea ships, under Georgian flag, JUPITER
and TURGUT’S, grounded at the entrance on the
Sulina channel, due to the bad weather conditions.
Images from these two accidents, which fortunately had not very important negative consequences, are shown in Figure 1.
Moreover, the most sensitive problems occur
exactly at the entrance of the Sulina channel.
Figure 1. Recent accidents close to the Danube mouths
(December 2009): a) Jupiter ship, which grounded south
of Sulina beach; b) Turgut S ship, which grounded north of Sulina Channel.

980in this area is illustrated in Figure 2. This figure
presents a satellite view of the Danube river out-
flow in the Black Sea at Sulina channel.
In this context, the objective of the present work
is to evaluate the wave-current interaction effects,
which can influence the navigation risks at the
mouths of the Danube river considering in a first approach the results of a modelling system SW AN based (Booij et al. 1999) that is focused on the tar –
get area. Numerical simulations are performed in a high resolution computational domain for the main environmental patterns characteristic to this part of the sea, considering the situations with-out and with the current fields included as model
input. Moreover in order to validate the results of
the numerical simulations, a field experiment was also carried out and its results confirm in gen-eral the output provided by the modelling system developed.
2 FOCUSING OF THE W AvE PREDICTION
SySTEM TOW ARDS THE DANUBE
DELTA
A multilevel wave prediction system based on the
SW AN spectral phase-averaged model was imple-
mented in the Black Sea basin. The system focuses on the Danube delta considering three subsequent computational domains with increasing resolution in the geographical space. The characteristics of these computational domains considered in the first approach for the system focusing towards the Danube delta are presented in Table 1, while
Figure 3 illustrates the geographical spaces of
each computational level defined. Thus, these first three levels considered are: the global level that covers the entire basin of the Black Sea, the trans-formation level that corresponds to the Romanian nearshore and the local level which is represented by the coastal area at the mouths of the Danube River.validations against measured data were per –
formed for each computational level. Thus for the global level validations against buoy data have been performed as presented by Guedes Soares & Rusu
(2005), Rusu (2009 and 2011) For the coastal and
local levels, both the measurements at the Gloria
drilling unit and satellite data have been consid-
ered for the system validation (Rusu & Ivan 2010 and Rusu 2010).
Designing of a such a wave prediction system,
SW AN based, has the advantage that one single wave model (SW AN) is used for the entire mod-elling process, from the generation level to the
high resolution coastal areas, although the physics
might be rather different from one computational level to another. For the present application the current field was considered only at the local level (level III). Such approach that is more convenient in sea environment cannot be applied for the wave prediction systems at ocean level, where the wave generation process is better represented by large scale models as W AM (W Ave Model, W AMDI
Group 1988) or WW3 (Tolman 1991).
Figure 4 illustrates the wave conditions in the
three computational levels considered for a repre-
sentative high energetic non storm situation that corresponds to the time frame 2002/02/04/h18.
In order to assess the influence of the currents on
the waves at the third computational level simula-tions were performed without and with the current field included as input in the model simulations.
Modeling the wave-currents interactions in the
spectral models is based on the fact that if the medium is moving with a velocity

U
, the frequency
of wave passing a field point is shifted due to the Doppler Effect:
ωσ=+⋅= ()+ 
kU gk kh kU tanh12
(1)
where g is the acceleration of gravity and h is
the water depth. Usually the quantity ω is called
observed or absolute frequency while σ is the
relative or intrinsic frequency whose functional
dependence on k (the wave number in absolute
value) is known as the classical dispersion relation-ship. In the spectral approach the variation of the frequency spectrum due to the presence of currents is given by the relationship:
Exk
kC
CkUEg
gωθω
ωωθ ,, ,
()=



−()
00
0
(2)
where: Cg0, k0 and
E0(, )ωθ are the group veloc-
ity, the wave number and two dimensional spectral
density in deep water in absence of the currents, respectively.
Figure 2. Satellite view of the Danube River outflow in
the Black Sea at Sulina channel (image processed from
Google Earth).

981Table 1. The computational grids considered in the modelling system SW AN based
towards the Danube Delta.
Level Δx × Δy Δt (min) nf nθ ngx × ngy = np
Global 0.08ș × 0.08ș 10 non-stat 35 24 176 × 76 = 13376
Coast 0.02ș × 0.02ș 10 non-stat 35 36 141 × 141 = 19881
Local 0.005ș × 0.005ș 10 non-stat
180 stat35 36 141 × 121 = 17061
Figure 3. Focusing of the wave prediction system
towards the Danube Delta: a) Level I—area of genera-
tion, b) Level II—coastal transformation, c) Level III—simulation of the local effects (currents induced by the river Danube outflow). In the background are the bathy-metric maps of the areas, in the foreground for the levels I and II the wind vectors are represented corresponding to the conditions from 2002/02/04/h18 (white arrows), and for level III the currents induced by the Danube. The maximum values of the currents and their locations in
the computational domain are marked with circles.
Figure 4. System focusing towards the Danube Delta,
conditions for the time frame 2002/02/04/h18, a) Level I,
b) Level II, c) Level (without currents), d) Level III—(with currents). In the background the significant height fields are represented and in the foreground the wave vectors (black arrows), the maximum Hs values are also indicated.
In relationship with the approach considered for
modelling the wave-current interactions, it has to
be highlighted that in the currently operating third generation spectral wave models the action balance equation is considered as governing equation (see
for example Holthuijsen 2007). This means that
the action density spectrum (N) stands instead of the energy density spectrum mainly because in the presence of currents action density is conserved whereas energy density is not. The action density is equal to the energy density (E) divided by the relative frequency (
σ
).If ambient currents are present, an iteration
process for the spectral propagation (current-induced refraction and frequency shift) is carried out in the SW AN model. The fluxes in the spectral space are not approximated with the first-order upwind scheme, since this turns out to be very dif-fusive for frequencies near the blocking frequency (when the waves are blocked by the currents). It has to be observed also that in the absence of a mean current there are no shifts in the frequency.
On the other hand, wave induced currents are not
computed by the model. Hence if they are relevant they should be included as a component in the input current field.
As a limitation of the modelling process, it has
to be highlighted that SW AN cannot handle wave propagation on supercritical current flow, i.e., when the flow velocity is larger than the local group wave velocity. If such flow is encountered during SW AN
computations, the current is locally reduced to
subcritical flow. Nevertheless, it is obvious that this

982limitation does not affect the results of the present
work when the effect of the opposite currents on the incoming waves is studied.
Another effect related to the supercritical flow
that might affect the results of the present work,
since the model simulations are performed in finite
water depth, would be that the currents may mis-match with a given water depth in the sense that the Froude number
FrUg d=
(where d repre-
sents the water depth) might become larger than 1, a situation in which the flow becomes supercritical. From this reason, in SW AN a parameter denoted as froudmax (having as default value 0.8) is used
(SW AN team 2013). Thus, if the current velocity
is relatively large, i.e., the Froude number is larger than froudmax, it will be reduced such that the Froude number is set equal to froudmax. The value of 0.9 for the parameter froudmax was considered in the present work.
The experimental results performed by Rusu &
Gudes Soares (2011) showed that the SW AN model is able to represent quite accurately the effect of
the opposite currents on the waves. Moreover, a
similar wave prediction system SW AN based was applied successful by Rusu et al. (2011) to assess
the wave-current interaction in the coastal environ-ment of the Tagus Estuary, close to Lisbon.
3 HIGH RESOLUTION MODEL
SIMULATIONS
In order to model in a more appropriate way the interactions between waves and currents in front of the navigation gate represented by the Sulina chan-nel, a forth computational domain with higher spa-tial resolution (50 m × 50 m) was implemented and
coupled to the three-level wave modelling system
SW AN based. Unlike the three levels before that
used the spherical coordinates, this time the simu-lations were carried out considering the Cartesian coordinates. This is mainly because some physical processes as diffraction and wave induced set up are better represented when such coordinates are used. A high resolution and accurate bathymetry provided by the National Romanian Authority for the Danube river was used and the main physical
processes specific to shallow water, as triad wave-
wave nonlinear interactions, bottom friction, dif-fraction and wave induced set up were activated together with the standard processes considered in deep water wave modelling (generation by wind, whitecapping dissipation and quadruplet wave-wave nonlinear interactions).
Figure 5 presents the bathymetric map of this
high resolution area and one of the current fields considered, which correspond to the most rel-evant circulation patterns. This field includes the currents induced by the Danube river outflow and the background current evaluated with POM simulations (Princeton Ocean Model, Blumberg & Mellor 1987) performed by the National Institute for Marine Research and Development “Grigore Antipa”, Constanta (Mateescu et al. 2012) for the
most relevant patterns considered.
From the analysis of the current and wave con-
ditions performed in Rusu (2010) the main current
and wave patterns were defined and considered in
the present study. Thus, according to most of the data sources, in this area, the currents induced in the sea by the river at the Sulina channel in nor –
mal to high flowing conditions usually varies from 1.2 m/s at the river mouths to 0.3 m/s at about seven
kilometers offshore. The most common wave pat-tern is from northeast, although waves from east
and southeast are also encountered. For this rea-
son the directional range considered in the model simulations is from 30ș to 150ș in nautical conven-tion. As regards the significant wave height (Hs)
the range considered was between 1 m and 5 m.
SW AN simulations were performed in the ranges
defined for Hs and the wave direction with a step
of 0.5 m for Hs and 10ș for the wave direction. In
this way, most of the possible situations that may
occur in the coastal environment considered are
covered. The effects of the currents on waves cor –
responding to high wave conditions are illustrated in Figure 6 while for average energetic conditions
in Figure 7. Moreover, the transformation of a
Figure 5. The bathymetric map of the high resolution
computational domain and the currents induced by the
Danube River outflow.

983Index (BFI) was also computed. BFI, or the
steepness-over-randomness ratio, has been intro-
duced formally by Jansen (2003) and is defined as:
BFIS tQp =⋅2π
(3)
where St represents the integral wave steepness and
is computed as the ration between the significant
wave height and the wave length and Qp repre-
sents the peakedness of the wave spectrum and it is defined as:
QEd d
Ed dp=()
()()∫∫
∫∫22
2σσθσθ
σσθσθ,
,
(4)
Hence BFI is a spectral shape parameter that can be
related to the kurtosis of the wave height distribu-
tion. In particular, for Gaussian-shaped spectra in the narrow band approximation Janssen (2003) showed that the kurtosis depends on the square of BFI. The
experimental results of Onorato et al. (2009) show
that for BFI = 0.2 the maximum wave heights are
Figure 6. Hs fields and wave vectors for high waves.
Initial boundary conditions Hs = 5 m, Tp = 8 s and Dir
(mean wave direction) 60ș, 90ș and 120ș, respectively. The
maximum Hs values are also indicated.
Figure 7. Hs fields and wave vectors for average incom-
ing waves. Initial boundary conditions Hs = 2 m, Tp = 5 s
and Dir (mean wave direction) 60ș, 90ș and 120ș, respec-
tively. The maximum Hs values are also indicated.
JONSW AP spectrum induced in the target area by
the currents and the bathymetric gradients is repre-sented in Figures 8 and 9, respectively for the wave
propagation normal to the shore.
Figures 6 and 7 show that the Danube river
outflow induces in the neighbouring coastal envi-ronment relevant enhancements of the significant wave heights. These Hs enhancements are higher
when the wave direction is from east-southeast. As Figures 8 and 9 also illustrate, the presence of the
currents modifies considerably the spectral shape especially by spreading the wave energy towards
the high frequency domain.
Abnormal, rogue or freak waves are transient
very high waves that can occur due to various
mechanisms (Kharif and Pelinovsky, 2003). In general they are identified when the abnormality index (Hmax/Hs) is larger than 2, which can be associated with other conditions as discussed for example in Guedes Soares et al. (2003).
In order to evaluate the risks related to the
occurrences of abnormal waves, the Benjamin-Feir
Figure 8. Transformation of the JONSW AP wave spec-
trum in terms of frequency and direction from offshore
to nearshore; Hs = 5 m, Tp = 8 s, Dir = 90ș.
Figure 9. Transformation of the JONSW AP wave spec-
trum in terms of frequency and direction from offshore
to nearshore; Hs = 2 m, Tp = 5 s, Dir = 90ș.

984very well described by the Rayleigh distribution while
for values of BFI of 0.9 and 1.2 the ratio Hmax/Hs
is substantially underestimated. Other results are reviewed in Guedes Soares et al. (2011).
Table 2 presents the maximum Hs values (Hs
max)
and the values of the BFI index (IBFI) for the most
relevant SW AN simulations performed in the Hs
and directional ranges considered. Greater values for the BFI index show that due to the currents the
waves are no longer Rayleigh distributed which
means that the ratio Hs
max/Hs, which in the case of
the Rayleigh distribution is 1.86, can be consider –
ably higher. This means also that the existence of
the currents does not enhance only the Hs param-
eter but abnormally higher waves can occur in this
area with much higher incidence. From the results
presented in Table 2 it can be noticed that the high-
est values of the BFI index occur in general when
the wave approach is normal to the shore (Dir =
90ș). As regards the relationship of the magnitude of this index with the Hs values, the results from
Table 2 show that the maximum BFI occurs for
about 3 m (I
BFI = 1.87).
4 A FIELD ExPERIMENT
The results of the high resolution model simula-tions presented in the previous section show that systematically the significant wave height has the highest value in about the same geographical loca-tion with its position just in front the Sulina chan-nel. In this respect, from Figures 6 and 7 resulted
that in 5 of the 6 cases presented, the maximum Hs
values occur in the same point located close to the isoline of 20 m, which is represented in Figure 5
and it was denoted as RP (reference point). More-
over, various other cases that were analysed (not illustrated in the present work) corresponding to all the situations presented in Table 2 show that in
about 80% of cases the maximum value of the sig-nificant wave height occur in the point denoted as RP, or very close to it.
In order to check if indeed exists in reality such
point with the same geographical location and proprieties, as those resulted from the modelling
process, a field experiment was performed in front
of Sulina channel in June 2012. In the first part of this experiment 5 buoys were deployed as illus-trated in Figure 10.
Thus, the buoy denoted as B3 was installed in
the Reference Point (RP), which is the point where the maximum Hs values resulted from the model
simulations, while the buoys denoted as B1 and B5 were installed close to the isoline of 17 m, and B2
and B4 close to the isoline of 18 m. The results
concerning the variation of the average Hs values
for the time interval 17–24 June 2012 are illustrated in Figure 11.
In processing the buoy data the methodology
developed by Makarynskyy et al. (2005) was used.
Since the results provided by the buoys B4 and B5 were very similar with those coming from B1 and B2, respectively only these last two buoys were con-
sidered in the comparison presented in Figure 11.
As the results presented in Figure 11 show, Hs
has systematically higher values in the reference
point where the buoy B3 operated.
At a further step, the experiment was repeated
for another eight-day period by keeping in its posi-tion the buoy B3 and moving the other four buoys in the offshore direction from B3. Thus B2 and B4 were deployed close to the isoline of 22 m while Table 2. Maximum Hs (Hsmax) and the values of the BFI index (IBFI).
Hs(m)/
Dir (°)1 2 3 4 5
Hsmax IBFI Hsmax IBFI Hsmax IBFI Hsmax IBFI Hsmax IBFI
30 1.23 0.73 2.35 1.25 3.33 1.22 4.33 1.14 5.3 0.91
60 1.30 0.78 2.50 1.47 3.56 1.6 4.60 1.50 5.64 1.40
90 1.38 0.87 2.73 1.75 4.01 1.87 5.20 1.83 6.17 1.67
120 1.42 0.94 2.77 1.40 4.06 1.71 5.27 1.67 6.21 1.52
150 1.38 0.85 2.55 1.27 3.62 1.38 4.71 1.38 5.68 1.29
Figure 10. Positions of the buoys deployed at the mouth
of the Sulina Channel.

985B1 and B5 close to the isoline of 24 m. The results
are similar with those presented in Figure 11 in the
sense that the maximum Hs values are still regis-
tered at B3.
It can be thus be concluded that the results of
the field experiment performed confirmed the
position and the propriety of the reference point identified in the modelling process. This point indi-cates a geographical location (close to the isoline of 20 meters) where, due to the interactions of the
incoming waves with the currents generated by the Danube River outflow combined with the bathy-metric particularities, systematically the significant wave height has higher value.
5 DISCUSSION
The results presented in the previous sections show
that the currents induced by the Danube River out-
flow generate at the mouth of the Sulina channel considerable wave enhancements both in terms of significant wave heights but also as regards the risk of occurrences of the extreme waves that can take even the form of the rogue waves. These are waves with the height greater than twice of the significant wave height and the probability of their occurrence is greater when the BFI indexed has higher values.
From this perspective, the results of the simulations
performed with the wave modelling system show
that the presence of the currents increases consid-erably the values of this spectral shape parameter at the mouth of the Sulina channel.
Obviously such conditions and effects affect
considerably the coastal navigation in the target area and, although in strong storm conditions the entrance in the Sulina channel is usually close, even moderate environmental conditions can generate accidents or incidents at the main entrance gate in the seventh Pan European transport corridor.The modelling process evidenced also a small
region (denoted in this work as a reference point) where, due to the wave-current interactions com-bined with the bathymetric particularities, system-atically the Hs values are greater in comparison with
the neighbouring conditions. The existence and the geographical position of this point were confirmed
in a field experiment that was recently performed.
Nevertheless, the discussion concerning the
navigation risks at the entrance of the Sulina
channel cannot be concluded without mentioning that in the Black Sea, near the Snakes’ Island, at about 45 kilometers north-west of Sulina, mag-netic faults periodically occur. Carefully studying this phenomenon the conclusions the researchers reached up to now are that it is a surface of about
8–10 kilometers—relatively triangular—in which
an unusual form of magnetism is manifested, very modified compared to the one detected as being ‘normal’ (see for example Letouzey et al., 1977,
Heirtzler et al., 1968).
Such anomaly was a source of accidents and
it can continue to be in the future. Nevertheless, mainly because of the fact that the area mentioned is little frequented and usually avoided, the fre-quency of the accidents induced by this phenom-enon was small in the last years. However, this magnetic anomaly slowly moves in the Black Sea’s area and currently the area moves towards the Romanian littoral, more precisely exactly towards Sulina where the navigation traffic is usually very
high (Ivan et al., 2012, Gasparotti & Rusu, 2012).
From this perspective, the navigation conditions
of the mouths of the Danube River will become an
issue that should be consciously and much more carefully studied in multidisciplinary approaches.
6 CONCLUSIONS
The area targeted in the present work is the coastal
sector in front of the Danube Delta and especially the entrance in the Sulina channel, which repre-sents the main gate for the seventh Pan European transportation corridor. For this reason, this area is subjected in general to high navigation traffic and especially in the winter time the environmen-tal conditions become often very dangerous for navigation, mainly due to the strong interactions between waves and currents.
Since a detailed knowledge of the environmental
conditions in this coastal sector represents an issue
of highest importance, a wave modelling system
was developed and focused with increasing resolu-tion on the target area.
The main objective of the present work was to
develop a high resolution computational framework connected to the wave prediction system that allows a
Figure 11. v ariations of the average Hs (cm) at the
buoys deployed at the mouths of the Sulina Channel.

986better assessment of the interactions between waves
and currents at the entrance of the Sulina channel. The results show that these interactions lead to con-siderably enhancements of the waves both in terms of significant and maximum wave heights. The out-
puts provided by this modelling system, related to
the position where usually the effect of the wave cur –
rent interaction has maximum effect, were validated also in a field experiment. Thus, the results provided by the wave modelling system implemented appear to be in general reliable.
Finally it has to be highlighted also that the
above developed computational framework based on numerical wave modelling techniques allows
both hindcast studies and operational forecast but
also the analysis of various possible scenarios that might be encountered in this very important area from the point of view of the coastal navigation.
ACKNOWLEDGEMENTS
This work has been financed by the Portuguese Foun-
dation for Science and Technology (FCT), through the Plurianual funding assigned to the Centre for Marine Technology and Engineering (CENTEC).
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