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Influence of the interactions between waves
and currents on the navigation at the entrance
of the Danube Delta
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JOURNAL OF ENVIRONMENTAL PROTECTION AND ECOLOGY
· JANUARY 2012
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Angela Stela Ivan
Universitatea Dunarea de Jos Galati
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Universitatea Dunarea de Jos Galati
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INFLUENCE OF THE INTERACTIONS BETWEEN WAVES AND
CURRENTS ON THE NAVIGATION AT THE ENTRANCE OF THE
DANUBE DELTA

A. IVAN *, C. GASPAROTTI, E. RUSU
‘Dunarea de Jos’ University, Galati, Romania
E-mail : [anonimizat]

Abstract . The Danube delta is a complex system that was sub jected in the last decades to significant
transformations. This is mainly due to the strong d ynamics of the environmental matrix and it is corre lated with
the global changes of the climate that are inducing relevant evolutions in the coastal environment. On the other
hand, the target area is very important from econom ical point of view since the Sulina channel represe nts the
main entrance in the seventh pan-European transport ation corridor defined by the system Rhine–Main–Dan ube,
which is the most important inland water-way in Eur ope that links the Black Sea with the North Sea. Th e wave
conditions are usually significant and strong curre nts induced there by the Danube river outflow lead to
interactions between waves and currents. This proce ss modifies both waves magnitude and direction affe cting
also the navigation. The objective of the present w ork is to develop a system with the capability to a ssess the
wave propagation and the wave-current interactions, in the Black Sea at the entrance of the Danube del ta. The
SWAN model was principally considered to perform nu merical simulations.

Keywords : the Black Sea, the Danube delta, wave-current int eractions, numerical modelling, SWAN.

AIMS AND BACKGROUND
The objective of the present work is to evaluate th e interactions between waves and currents
at the mouth of the Danube. This represents an impo rtant gate in the seventh pan European
transportation corridor and the above phenomenon af fects considerably the navigation. This
objective will be accomplished in principal by perf orming simulations with a wave prediction
system, SWAN based. The main local effect that will be taken into account is related with the
interactions between waves and currents at the Danu be mouths.
The magnitude of changes in the wave field due to currents is a problem of crucial
importance in many engineering applications 1, especially as regards the effort of decreasing
the navigational hazard. Moreover, wave-current int eraction has been also proposed as a
possible mechanism for the formation of giant waves known to occur often in the presence of
strong coastal currents 2,3 .
When waves propagate on a variable current several mutual interactions occur.
Physically, wave-current interaction is a problem o f wave propagation in an inhomogeneous,
dispersive, dissipative and moving medium, which al so interacts with the wave. Longuet-
Higgins and Stewart 4,5 were the first to describe the interaction between waves and currents.
They presented the correct energy equation introduc ing the concept of radiation stress and
proved the existence of the energy transfer between waves and currents.
The Danube is the second longest river in Europe, a fter Volga, and also the longest river
in the European Union. Originating in Germany, the river flows eastwards for a distance of
almost 3000 km (2850 km), before emptying into the Black Sea via the Danube delta.
The so-called maritime Danube extends up to Braila in Romania and in this sector most
ocean ships can navigate. By river ships, the river is navigable to Kelheim, Bavaria but
smaller craft can navigate further upstream to Ulm. In 1992 the Danube become part of the
canal Danube-Rhine-Main and in this way a direct in land waterway link was accomplished
between the North Sea and the Black Sea. From this reason, in 1994 the Danube becomes the
seventh pan-European transportation corridor. At th e level of the Danube delta the river is

* For correspondence.

divided into three branches Chilia, Sulina, and Sfâ ntu Gheorghe (Saint George). Sulina is the
central arm, and being also the shortest, represent actually the main entrance gate from the sea
for the inland navigation in the canal system Danub e-Rhine-Main. The alluvium process is
very dynamic at the Danube mouths and that is why S ulina channel is systematically dragged
in order to facilitate navigation. A channel that e nters gradually into the sea, called Sulina bar,
is maintained (at this moment this bar is about 10 km long).
Nevertheless, Sulina still represents an extremely sensitive point for navigation and this is
mainly due to the strong interactions between waves and currents that may occur especially in
the case when sever environmental conditions occur. Hence during the past 2 decades many
accidents and incidents happened in the Sulina chan nel and in the neighbouring coastal
environment.
Taking into account that the dominant wind in the r egion is blowing from east to west
and that its intensity is often very high, the west ern part of the Black Sea basin is usually
more energetic than the rest. Strong currents induc ed at the mouth of the Danube river lead to
significant interactions between waves and currents , affecting both wave magnitude and
direction and implicitly the coastal navigation. Th e study was focused mainly on the sector in
the proximity of the Sulina channel, which is subje cted to high navigation traffic.

INFLUENCE OF THE CURRENTS ON THE SIGNIFICANT WAVE H EIGHTS AND
WAVE DIRECTIONS
Ivan and Rusu 6 and Rusu 7-9 performed some previous analyses concerning the wa y in which
the currents generated by the outflow of the Danube river influence the wave conditions at the
entrance of the Danube delta. These analyses referr ed especially at the modification of the
parameters that describe the short term wave statis tics (significant wave height, mean period
and mean wave direction).
A SWAN-based wave prediction system was implemente d and validations have been
performed both using in situ measurements and remot ely sensed data.
In Ref. 9 three case studies, which correspond to real situations and cover the most
relevant environmental patterns, were considered. T hese case studies are: CS I (weak wind
conditions) corresponding to the time frame 2002/04 /16/h22, CS II (characterised by average
to high wave conditions and strong wind coming from north east) that corresponds to the time
frame 2002/02/04/h09 and CS III (average wave condi tions and wind blowing from west) that
corresponds to the time frame 2002/04/18/h15.
The field distribution of the significant wave hei ght and the variations of the main wave
parameters due to the influence of the current fiel ds were assessed and analysed. Moreover, 2
reference points were identified. These points corr espond to the location where the
interactions between waves and currents induce the maximum variations in terms of
significant wave height. Reference point 1 (denoted as RP 1) is located in front of Saint
George arm and reference point 2 (denoted as RP 2) is located in front of the Sulina channel.
As a continuation of this previous work an additio nal discussion will be employed at this
point concerning the results of the model system si mulations. Thus, Fig. 1 presents for the
three case studies mentioned above a quantitative a nalysis of the influence of the currents
over the waves in the two reference points. The par ameters assessed are significant wave
height, mean wave direction and water depth and the y were compared with the maximum
values in the computational domain of the same para meters. The 3 main environmental
vectors: wave, wind and current are also represente d.

Fig. 1 . Analysis of the main wave parameters for the thre e case studies considered (I- CS I – 2002/04/16/h22 ; II-
CS II – 2002/02/04/h09; III-CS III – 2002/04/18/h15 ). Comparisons, main parameters in the point select ed
versus the maximum value in the computational domai n. RP 1 ( a), Hs (b), TM01 ( c), water depth ( d);
Representation of the local directions of the 3 vec tors (current, wind and wave): RP 2 ( e) Hs (f), TM01 ( g),
water depth ( h). Representation of the local directions of the th ree vectors (current, wind and wave)

Fig. 2 . 2D spectral analysis at the RP 1: CS I – withou t currents ( a), CS I – with currents ( b); CS II – without
currents ( c); CS II – with currents ( d); CS III – without currents ( e); CS III – with currents ( f)

The transformation of the 2D wave spectrum due to the action of currents for the 3 case
studies considered is illustrated in Fig. 2. for RP 1.
Since the objective of the present work is to focu s on the extreme wave conditions, another
case study will be illustrated bellow in addition t o the above case studies. This will be denoted
as CS IV and corresponds to the real conditions fro m the time frame 2007/03/24/h03. The
situation is illustrated in Fig. 3 and reflects hig h-wave conditions when, however, the
navigation is still allowed. It has to be mentioned that the situation illustrated does not
represent a peak of storm, and actually such situat ions are not relevant for the present work
because in these extreme circumstances the navigati on at the Sulina bar is usually closed.

Fig. 3. CS IV corresponding to the time frame 2007/03/24/h0 3: a – in foreground the current field is represented
while in background the bathymetric map is illustra ted, the mean wind direction and intensity is also represented;
b – in foreground the wave vectors are represented w hile in background the significant wave height scal ar field is
illustrated. Two reference lines at the entrances o f Saint George arm (line 1) and the Sulina channel (line 2) are
represented and also the positions of the two refer ence points are also illustrated

Figure 3 clearly illustrates the enhancement of the significant wave height field at the
entrance of the Danube arms.

OCCURRENCE OF ABNORMAL WAVES DUE TO THE PRESENCE OF CURRENTS
For narrow-banded spectra the wave heights are cons idered to be Rayleigh distributed 10 while
the distribution of the free surface is in general Gaussian. Theoretical relationships derived
from the Rayleigh distribution generally agree well with the values determined directly from
the records. Very often the Rayleigh distribution f its this data well, even though the frequency
spectra of sea waves may not always be narrow-bande d as assumed in the Rayleigh
distribution. Nevertheless, field measurements some times deviate from the Rayleigh
distribution, and the deviation appears to increase with increasing wave heights, and decrease
as the wave spectrum becomes sharply peaked.

According to the Rayleigh distribution the signifi cant wave height and maximum wave
height can be expressed as a function of rms H as follows :
rms s H HH 416 . 13 1== (9)
rms sH H H 634 . 2 86 . 1max = = (10)
with root mean square wave height rms Hdefined as:
∑
==N
jj rms HNH
121 (11)
The value of Hmax can be projected to a longer period of time by adj usting the value of N
based on the mean zero-upcrossing period 10 .
A method to evaluate the deviation from the Rayleig h distribution for the wave height is
to analyse the Benjamin-Feir index (BFI). This is a spectral shape parameter that is related
with the kurtosis of the wave height distribution. Janssen 11 showed that in the case of the
narrow banded Gaussian-shaped spectra the kurtosis depends on the square of BFI. Onorato et
al.11 made some experiments which showed that for BFI=0. 2 the maximum wave heights are
well described by the Rayleigh distribution while f or values of BFI of 0.9 and 1.2 the ratio
Hmax /Hs is substantially underestimated.
The expression of BFI was introduced in Ref. 11 and is defined as follows :

pQSt 2BFI ⋅ =π (12)

with St the integral wave steepness that is computed as the ratio between the significant wave
height and the wave length and Qp – is a quantity related with the elevation of the spe ctral
peak 11:
()
( )( )22
,,2
∫∫∫∫=
θσθσσθσθσσ
ddEddEQp (13)

Figure 4 presents the BFI variations corres ponding to the SWAN model simulations
performed with and without including the effect of the currents. The time period considered is
2007/01/01 – 2007/03/31 and the points where this i ndex was evaluated are the point that
corresponds to the location of the altimeter node (30șE, 45șN) which is in intermediate water
depth (about 40 m) and the two reference points loc ated in front of Saint George arm and the
Sulina channel, respectively. By analysing Fig. 4 s ome comments can be made. First would
be that the currents produce in general an enhancem ent of BFI and this is fully illustrated in
Fig. 4a when even a relatively weak current may induce som etime strong peaks of this
parameter. For RP2, although the average current ve locity is relatively high (0.68 m/s), Fig.
4c illustrates smaller enhancements for BFI and relat ively smooth variations. The sector in
front of Saint George arm is subjected to a very hi gh risk of strong waves occurrences not
only from the point of view of the significant wave height but also with maximum heights
much greater than those resulting from the standard Rayleigh distribution. These conclusions
are supported by the results illustrated in Fig. 4 b.

Fig. 4. Variation of the Benjamin-Feir index (time interv al 2007/01/01 – 2007/03/31): a – offshore point
corresponding to the altimeter node (30șE, 45șN); b – RP 1, in front of Saint George arm; c – RP 2, in front of the
Sulina channel

DISCUSSION
In the costal sector at the Danube mouth, a current system is induced by the Danube river outflow.
These currents produce significant changes in the w ave heights and direction and affect strongly the
coastal navigation. On the other hand, this current system drives a very dynamic alluvium process.
In this context the present work is focused on the evaluation of the extreme waves at the
entrance of the Danube delta highlighting also the main physical process that affects the wave
conditions in that area. This is the interaction be tween the incoming sea waves and the
currents generated by the outflow of the Danube riv er.
Since the Sulina channel represents the main gate for the seventh pan-European transportation
corridor, the entrance in the Sulina channel is usu ally subjected to high navigation traffic and hence
represents a very critical point for coastal naviga tion 12-15 .
The present work is a continuation of previo us studies 16-19 that use wave modelling system in
the coastal environment and has the particularity t hat is focused especially on the most severe
navigation conditions.
The target area is usually characterised through e levated wave and wind conditions and the
currents induce relevant enhancement of the waves. As the present work fully illustrated, these
enhancements are reflected in the increase of the s ignificant wave heights but also by the occurrence
of maximum wave heights much greater than those res ulting from the standard Rayleigh
distribution. Such abnormal waves are very dangerou s for coastal navigation and are usually called
rogue waves or freak waves.

CONCLUSIONS
The economical developments taking place in the Bla ck Sea basin in the last decades increased also
the importance of studying the main characteristics of the environmental matrix from this region.
Among the most relevant recent studies related with the climate and the characteristics of the Black
Sea are those presented in Refs 20-25.

The present work is focused on the entrance in the Danube Delta which is a very hot coastal
sector in the Black Sea due to the enhanced navigat ion traffic but also due to the fact that the
currents induced by the Danube River outflow intera ct with the waves producing relevant increase
of the wave heights, both in terms of average and m aximum wave heights.
The results obtained up to now give a first overvi ew on this important process and of its effects.
The work is still ongoing and, in the near future i n order to assess better the interactions between
wave and currents, simulations with the SWAN model will be performed considering a higher
resolution computational domain. Some field experim ents in order to validate the model results will
be carried out and will complete the present work.
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Received 19 March 2012
Revised 18 May 2012