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FIELD STUDY AND SUPPORTING ANALYSIS OF AIR CURTAINS AND OTHER
MEASURES TO REDUCE SALINITY TRANSPORT THROUGH SHIPPING LOCKS
†
GEERT KEETELS
1
*, ROB UITTENBOGAARD
1
, JOHN CORNELISSE
1
, NICKI VILLARS
1
and HANS VAN PAGEE
2
1
Deltares, Delft, The Netherlands
2
Rijkswaterstaat, Centre for Water Management, Lelystad, the Netherlands
ABSTRACT
This paper presents an overview of a study on salinity intrusion through shiplocks that are located at a saltwater and freshwater
interface, and the possible measures that can be taken to reduce this salinity transport. The main focus of the study was to test the
effectiveness of several measures against salt intrusion through a shiplock. For this reason a series of field experiments was
conducted in the Stevin shiplock in the Afsluitdijk, near Den Oever, the Netherlands, in between the Wadden Sea and the IJsselmeer.
The measures tested include an air curtain at both ends of the shiplocks, alone and in combination with a water jet, as well as a rigged
sill to reduce the effective depth, and flushing of the lock with fresh water. A new type of air curtain with air injectors was designed
and built for this study. Prior to the field experiments, a series of laboratory scale experiments and computer simulations of lock-
exchange flow were conducted to gain insight into the salinity transport process and to support the design of the field study.
The study has shown that a significant reduction of salinity intrusion can be attained by using a combination of measures.
These findings are relevant for shiplocks located in a saline–freshwater transition zone for which salinity intrusion should
be reduced as much as possible. Copyright © 2011 John Wiley & Sons, Ltd.
key words: salt intrusion; air curtain; lock exchange; gravity current; shiplock
Received 11 October 2011; Accepted 11 October 2011
RÉSUMÉ
Ce document présente un aperçu d’une étude sur l’intrusion de la salinité à travers les écluses maritimes qui sont situées à l’
interface eau salée/eau douce, et les mesures possibles susceptibles d’être prises pour réduire ce type de transport de la salinité.
L’objectif principal de l’étude était de tester l’efficacité de plusieurs mesures contre l’intrusion du sel par une écluse maritime. Pour
cette raison, une série d’expériences a été menée dans l’écluse maritime Stevin dans l’Afsluitdijk, près de Den Oever, Pays-Bas,
entre la mer des Wadden et l’IJsselmeer. Les mesures testées comprennent un rideau d’air, seul et en combinaison avec un jet d’eau,
ainsi qu’un seuil pour réduire la profondeur efficiente, et le rinçage de l’écluse avec de l’eau fraîche. Un nouveau type de rideau
d’air avec des injecteurs d’air a été conçu et construit pour cette étude.Un rideau d’air a été installé aux deux extrémités de l’écluse
maritime, avec un système d’injection d’eaudouce (à côté de la mer des Wadden) et un seuil (sur le côté IJsselmeer). Dans une série
d’expériences il y avait aussi un flux constant d’eau douce à travers l’écluse. Les mesures sur le terrain ont été menées dans la
période avril-mai 2010. Avant les expériences de terrain, une série d’expériences en laboratoire et des simulations par ordinateur
des flux d’échange des éclusées, avec et sans mesures de réduction de l’intrusion de la salinité, ont été menées pour mieux
comprendre les processus de transport de la salinité et de soutenir la conception de l’étude sur le terrain.
L’étude a montré qu’une réduction significative de l’intrusion saline peut être obtenue en utilisant une combinaison de
mesures. Ces résultats sont pertinents pour des écluses situées dans une zone de transition saline-eau douce, pour laquelle l
’intrusion saline devrait être réduite autant que possible
mots clés: intrusion saline; rideau d’air, échanges dans les écluses; courant gravitaire; écluse maritime
INTRODUCTION
Salt intrusion from coastal waters can be a serious threat to
drinking water, industrial process water and agricultural
* Correspondence to: Mr Geert Keetels, Deltares, Delft, the Netherlands.
E-mail: geert.keetels@deltares.nl
†
Étude sur le terrain et analyse de soutien de rideaux d'air et autres mesures
visant à réduire les transports de salinité par écluse.
IRRIGATION AND DRAINAGE
Irrig. and Drain. 60 (Suppl. 1): 42–50 (2011)
Published online in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/ird.679
Copyright © 2011 John Wiley & Sons, Ltd.
water supply, in particular in tidal river systems with mildly
sloping beds.
To reduce salt intrusion (chloride concentration) it was
proposed around 1960 to apply air curtains in open channels
and at the entrance of shiplocks. A set of experiments by van
der Burgh (1962) in the Kornwerderzand shiplocks at the
Afsluitdijk in the Netherlands demonstrated that it was
indeed possible to reduce salt intrusion significantly.
A recent issue in the Netherlands as been the proposal to
reconnect the fresh water Volkerak-Zoommeer with the
North Sea. This would result in an unacceptable amount of
salinity transport through the Volkerak shiplocks towards
the Hollandsch Diep and yield too high values of chloride
concentration at the water intake locations for drinking,
agriculture and industrial water supply. Motivated by this
recent problem, the concept of salinity reduction by air cur-
tains was revised in this study by testing several combina-
tions of an air curtain and a (plane) freshwater jet, a sill
and flushing the sluices with fresh water during ebb tide.
Figure 1 gives an illustration of these methods that could
be applied in a shiplock. In addition, an innovative design
of air injectors was tested that yields a closely packed air
curtain and a more evenly distributed air flux over the width
of the lock entrance when compared with the traditional
design of air injector (Figure 2).
DESIGN STRATEGY
The objective is to reduce salt transport through shiplocks to
an acceptable level with a minimum usage of fresh water.
Moreover, salt reduction measures should not cause pro-
blems for the manoeuvring of ships towards and inside the
lock and thus delay the lock cycle. Figure 3 gives an over-
view of the design strategy followed in this study. Starting
points are the ship traffic requirements and the acceptable
chloride concentrations at the water intake points of the
freshwater system. A large-scale model assesses the maxi-
mum acceptable salt flux through the shiplock. By using a
conceptual model for salt transport through a shiplock, we
can compute salinity transport through the shiplock if a reli-
able estimate for the effectiveness of the different measures
(indicated as the salt transmission factor) is available. The
description and validation of this model will be published
elsewhere. The scope of this paper is marked by the dashed
box in Figure 3. The focus is to assess the value and robust-
ness of the salt transmission factor as a function of air and
Figure 1. Illustration of the considered measures to reduce salt intrusion in a shiplock at a freshwater and saltwater interface
Figure 2. New design of air injector for a closely packed air curtain with
evenly distributed air flux over the width of the lock entrance
43AIR CURTAINS AND OTHER MEASURES TO REDUCE SALINITY INTRUSION
Copyright © 2011 John Wiley & Sons, Ltd. Irrig. and Drain. 60 (Suppl. 1): 42–50 (2011)
water flux. This parameter describes the effectiveness of a
measure against salt intrusion. It is the ratio between salt
mass intrusion when a measure is present and salt mass intru-
sion in the absence of any salt reduction measure, i.e. lock-
exchange flow. As a reference time window, we consider
one internal period of an undisturbed lock-exchange flow,
i.e. the time that is required for a gravity current to traverse
the length of the lock twice. This factor is the most critical
and uncertain parameter in the design process. The essential
physical processes of salt intrusion through an air curtain are
not well understood despite the theoretical study of Abraham
et al. (1973). For this reason, it was necessary to conduct a
large number of detailed numerical simulations in combina-
tion with laboratory experiments in a flume tank in advance
of the field experiments at the Stevin shiplock at Den Oever,
the Netherlands.
SET-UP OF THE LABORATORY EXPERIMENTS
Figure 4 gives an overview of the experimental set-up in the
laboratory. For each experiment in the laboratory flume tank
a large reservoir was filled with salt water and a smaller reser-
voir with fresh water. The water depth was approximately 30
cm in both reservoirs. A gate in the flume separated the two
reservoirs. The air injector and freshwater injector were situ-
ated inside the saltwater reservoir near the gate. The air injec-
tor consisted of a perforated tube with a diameter of about 1
cm. This yields a closely packed air curtain with bubble sizes
ranging from 3 to 5 mm (Figure 5). Fresh water was injected
through an opening of 3 mm over the width of the flume.
The air curtain and freshwater jet were started before the
opening of the gate. Water could leave the flume at the
end of the saltwater compartment in order to prevent an
Figure 3. Overview of the different parts of the overall study. The dashed box indicates the scope of the present paper
Figure 4. Experimental set-up and dimensions
44 G. KEETELS ET AL.
Copyright © 2011 John Wiley & Sons, Ltd. Irrig. and Drain. 60 (Suppl. 1): 42–50 (2011)
increase in the water level by the injected fresh water during
the experiment. Within a few seconds the gate was opened
and the salt water of the gravity current started to enter the
freshwater compartment while fresh water moved towards
the saltwater compartment. Salinity was measured at 2
locations at 12 positions distributed over the vertical
direction (Vezo). The position of the measurement section
varied per experiment. In some experiments additional
salinity measurements were performed to verify if the total
salt mass computed by averaging over 2 12 vertical
measurement sections is sufficiently accurate. About 30
combinations of air and water flux were tested. As a reference
case, a lock-exchange experiment without any measures
against salt intrusion was conducted. Figure 6 demonstrates
the progressing interface between salt and fresh water of a
gravity current that develops in the lock-exchange experiment.
SET-UP OF THE NUMERICAL MODEL
A detailed numerical model of lock-exchange flow was devel-
oped using the computer code Ansys-CFX that covers the entire
experimental set-up of Figure 4. Bubbles are not resolved
individually but the air is considered as a dispersed fluid phase
inside a continuous water phase. The air can leave the domain
at the surface by means of a degassing boundary condition. For
each fluid phase, a separate set of equations for momentum,
mass and energy is resolved. Empirical relations give the inter-
face forces between the bubbles and the water phase. The most
important interface force for this problem is the drag force. The
bubble radius changes as a function of water depth. Complex
bubble behaviour such as coalescence and break-up was
neglected. These processes can be important at the field scale
but are not of significant importance for the present laboratory
experiments. Turbulence inside the continuous phase (water) is
modelled by equations for turbulent kinetic energy and
turbulent energy dissipation. Salinity is considered as an active
scalar transport quantity. An equation of state is used to relate
the salinity with the density of the continuous phase. The
model was validated against velocity measurements and
salinity measurements obtained from several laboratory
experiments and the theoretical formulation for gravity
currents derived by Shin et al. (2004). After the validation of
the model against laboratory experiments, the same model
was applied to simulate salinity intrusion in the Stevin
shiplock. The computed velocities in this model are consistent
with the velocity measurements around air curtains in deep
water by Bulson (1961). The main purpose of the simulation
was to support the design of the field experiments.
RESULTS OF LABORATORY EXPERIMENTS
AND SUPPORTING SIMULATIONS
Figure 7 shows a computed gravity current in a classic lock
exchange without measures against salt intrusion. The reser-
voir on the right-hand side of the gate contains fresh water
and the reservoir on the left-hand side (partially shown) is
filled with salt water. After the removal of the gate salt water
moves into the reservoir while fresh water flows out. The
propagation speed of the gravity current and layer thickness
are consistent with the theory of Shin et al. (2004). Salt water
does not replace all the fresh water. About 80% of the fresh
water will be replaced by intruding salt water. This well-known
phenomenon can be related to energy dissipation in the
propagating salt wedge, i.e. a part of the potential energy
released in the saltwater compartment is not restored in the
freshwater compartment. Salinity measurements in the
laboratory experiments also reveal this behaviour (not shown).
Figure 8 shows the typical flow pattern and salt intrusion
path observed in the laboratory experiments. At relatively
high air fluxes two circulation cells emerge around the air
curtain. Salt water transfers towards the surface layer and
mixes with fresh water. As a result a weak density current
develops at a distance from the air curtain equal to
Figure 5. Closely packed air curtain in the laboratory
Figure 6. Gravity current of an undisturbed lock-exchange experiment in a flume
tank without measures against salt intrusion. The arrow below indicates the
displacement of salt water and the arrow above the displacement of fresh water
45AIR CURTAINS AND OTHER MEASURES TO REDUCE SALINITY INTRUSION
Copyright © 2011 John Wiley & Sons, Ltd. Irrig. and Drain. 60 (Suppl. 1): 42–50 (2011)
approximately twice the water depth. The corresponding nu-
merical simulation is shown in Figure 9.
Figure 10 shows the effect of different combinations of air
flux and water flux on the total salt intrusion. The salt ex-
change is normalized with the total amount of salt contained
by a reservoir that is completely filled with salt water. When
there is no air or water flux (i.e. classic lock exchange) the
air flux parameter is zero and the salt exchange is about
80%, as illustrated in Figure 7. The first series of experiments
was focused on a high flux of air and the second series of
experiments was conducted to find an optimal combination
of air flux and water flux. The numerical simulations were
performed in advance of the second series of experiments in
order to provide some guidance for the set-up of these experi-
ments. In both the numerical simulations and experiments, a
route towards optimal salt reductions was found by making
small steps in the air flux and water flux.
SET-UP OF THE FIELD EXPERIMENT AT DEN
OEVER
Figure 11 gives an overview of the set-up of the field exper-
iment at the Stevin shiplock at Den Oever. An air curtain
was installed at both entrances of the lock. On the Wadden
Sea side there was a plane freshwater jet installed. In a
few experiments a sill was added next to the air curtain on
the IJsselmeer side.
Conductivity meters for measuring salinity were positioned
at five locations on one side of the lock. At each location there
were five measurement points in depth. The difference in
water level between the Wadden Sea and IJsselmeer varies
with the tide. Therefore, it was necessary to adjust the vertical
position of the salinity measurements with the tide. Additional
salinity measurements were taken inside the harbours at each
end of the shiplock. An extensive data management system
was developed in order to record all the essential parameters
such as the water levels, valve positions, opening and closure
times of the doors, air flux, water flux, salinities and type and
load of the passing ships.
RESULTS OF THE FIELD EXPERIMENTS AND
SUPPORTING SIMULATIONS
Figure 12 shows the salt transmission factor versus the recip-
rocal of non-dimensional circulation (definition given in the
Appendix) for the experiments at the Stevin sluices and other
field experiments and laboratory studies. It can be deduced
that if the non-dimensional circulation is larger than approxi-
mately 4 (1/C<4) the salt transmission factor strongly
depends on the reciprocal of non-dimensional circulation
and thus the air and water fluxes. This can also be observed
in the data obtained from the air curtain experiments by van
der Burgh (1962) in the Kornwerderzand shiplocks. Our
experiments in the Stevin shiplock with only a plane freshwa-
ter jet can also be found in the unsaturated regime with non-
dimensional circulation larger than 4.
The value of the reciprocal of non-dimensional circulation in
the fieldexperimentsattheStevinlockwithanaircurtainand
freshwater jet is between 0.25 and 0.4. The salt transmission
factor is 0.25 0.05 if only an air curtain is applied and 0.15
0.05 if both an air curtain and a freshwater jet are applied.
The results of the field experiments at the Kornwerderzand
and Stevin locks can be compared with the present laboratory
results and the laboratory experiments on salt intrusion
reduction by saltwater jets performed by Bruyn (1963).
In some experiments in the Stevin shiplock with a small air
flux and relatively large water flux smaller values for the salt
Figure 7. Computed lock-exchange flow with the numerical model. Salinity
distribution at different times 20, 35, 60 and 90 s after the release of the
gate. Black lines indicate the minimal and maximal thickness of the salt
wedge according to the theory of Shin et al. (2004). The contours range
from 0 to 35 ppt. The yellow line marks the original position of the gate
(removed instantaneously)
Air curtain
Figure 8. Typical flow pattern around an air curtain at a salt- and freshwater
transition in the laboratory flume experiment. The circulation cell on the fresh-
water side is shown. Air flux is 92 Nl s
1
at atmospheric pressure, the salinity
difference is 35 ppt, Vezo1 is the first salinity measurement location
46 G. KEETELS ET AL.
Copyright © 2011 John Wiley & Sons, Ltd. Irrig. and Drain. 60 (Suppl. 1): 42–50 (2011)
transmission factor were found. Note that the fresh water has
multiple effects, i.e. buoyancy, replacement of salty lock water.
Moreover, the application of a freshwater jet during many se-
quential levelling cycles will reduce the salinity in the harbour
at the salt end of the shiplock. In the laboratory experiments
and supporting numerical simulations the transmission factor
was not smaller than 0.1. Further analysis is necessary to
explain the results of these experiments in the Stevin lock.
Figure 13 shows the typical flow patterns that can occur
around an air curtain on a transition between salt and fresh
water for different values of the non-dimensional circulation
(air flux). At low air fluxes a single circulation zone develops
Figure 9. Numerical simulation that corresponds with the laboratory experiment shown in Figure 8. The arrow marks the position of air injector. Salt water is
situated on the left-hand side and fresh water on the right-hand side. Contours range from 0 to 35 ppt.
Figure 10. Relative salt exchange versus the air flux parameter (see Appendix). Experiments at high values of the air flux parameter, numerical simulations and
experiments with modest values for the air flux parameter. GC: gravity current, A: air and W: fresh water. Dashed arrow indicates an increase of air flux and
solid arrow a change in water flux
air curtain and plane fresh
water jet
Wadden Sea
IJssel lake
air curtain and sill
salinity
measurements
air curtain and plane fresh
water jet
Wadden Sea
IJssel lake
air curtain and sill
salinity
measurements
Figure 11. Experimental set-up at the Stevin shiplock, Den Oever, the Netherlands. The shiplock has a length of 150 m, the width is 14 m and the depth varies
by the tide (5 m on average)
47AIR CURTAINS AND OTHER MEASURES TO REDUCE SALINITY INTRUSION
Copyright © 2011 John Wiley & Sons, Ltd. Irrig. and Drain. 60 (Suppl. 1): 42–50 (2011)
around the air curtain at the salt side. Salt water penetrates
through the air curtain at a certain level. At higher values of
the air flux a second circulation zone develops (reduces the
non-dimensional circulation) around the air curtain. Salt water
is transferred to the surface layer and mixes with the fresh
water, which yields a weak density current. Increasing the
air flux further increases a larger circulation zone, but does
not result in a reduction of the salinity intrusion.
Table I summarizes the obtained salt transmission factors
found in the Stevin lock experiments. Note that the obtained
results depend on the particular limitations such as the
maximal amount of fresh water that can be used for flushing
the lock chamber or for the water jet or the allowed sill
height in this study.
CONCLUSION AND DISCUSSION
In this paper, we focus on salt intrusion during the time win-
dow the doors are open on one side of the lock. This is only
a part of the total lock cycle. Using the robust estimates for
the salt transmission factors obtained in this study it is now
possible to estimate the total salt transport per lock cycle as a
function of lock design parameters by a conceptual exchange
Figure 12. Salt transmission factor (n= 1 lock exchange, n= 0 no salt transmission) versus the reciprocal of non-dimensional circulation (C)defined in the
Appendix, for several field and laboratory experiments. Air flux is defined at atmospheric pressure (Nl s
1
)
1/C=0.19, n=0.3
1/C=0.26, n=0.14
1/C=0.37, n=0.15
Figure 13. Typical flow pattern transitions in the numerical simulation. Contours range from 0 to 35 ppt. The arrows indicate the position of the air injector. Cis
the non-dimensional circulation and nthe salt transmission factor
48 G. KEETELS ET AL.
Copyright © 2011 John Wiley & Sons, Ltd. Irrig. and Drain. 60 (Suppl. 1): 42–50 (2011)
model. The amount of reduction that can be achieved for the
total lock cycle strongly depends on these parameters.
This study demonstrates that with a closely packed air
curtain in combination with a freshwater jet it is possible to
obtain a salt transmission factor (on one side of the lock) of
0.15. This implies a possible reduction of 85% of the salt mass
transport during the time window the doors are open on one
side of the lock. As a refrerence time window the internal period
of a gravity current that develops in the absence of measures
against salt intrusion has been considered.
If a salt transmission factor (on one side of the lock) of
0.15 is not sufficient to reduce the total salt mass transport
per lock cycle to the desired level, additional measures
against salt intrusion can be considered. For example,
flushing the lock chamber with fresh water or pumping
intruding water back to the harbour on the saltwater side.
Note that these additional measures might yield extra
demands in the amount of fresh water or energy supply.
ACKNOWLEDGEMENTS
WewishtothankDickMastbergenforperformingthelaboratory
experiments and Arno Nolte for helpful comments on this paper.
The study was funded by and carried out with cooperation of
the Dutch Ministry of Infrastructure and the Environment.
CONFLICTS OF INTEREST
None of the authors have any conflicts of interest to declare.
REFERENCES
Abraham G, van der Burgh P, de Vos P. 1973. Pneumatic Barriers to Reduce
Salt Intrusion through Locks. Rijkswaterstaat communications No. 17.
Government Publishing Office: the Hague, the Netherlands.
Bruyn J. 1963. Waterschermen ter bestrijding van zoutbezwaar van
schutsluizen aan zee. Waterloopkundig Laboratorium. M799: Delft, the
Netherlands (in Dutch).
Bulson PS. 1961. Currents produced by an air curtain in deep water. Dock
and Harbour Authority 42(487): 15–20.
Shin JO, Dalziel SB, Linden PF. 2004. Gravity currents produced by lock
exchange. J. Fluid Mech 521:1–34.
Van der Burgh P. 1962. Proeven met luchtschermen. Rijkswaterstaat Dienst
voor de Waterhuidshouding: the Hague, the Netherlands (in Dutch).
APPENDIX A: DEFINITION OF THE
NON-DIMENSIONAL CIRCULATION
Energy transfer rates
Bulson (1961) derived an expression for the power deliv-
ered by the air curtain to the water. If one assumes that the
air is injected at a pressure that is just sufficient to overcome
the hydrostatic head and that the temperature of a rising air
bubble is constant, the energy transfer from the bubble to
the water is
Pair ¼QSPSln 1 þrgH
PS
in ½W
where ris the density of the water (kg m
3
), gis the grav-
itational acceleration (m s
2
) and Hthe water depth (m) and
Q
S
represents the volume flux (m
3
s
1
) of air at atmospheric
pressure P
S
. For a buoyant jet the power that is given to the
rising water reads:
Pbuoy ¼gH rjet
r
Qjet in ½W
where Q
jet
is the volume flux of jet water m(
3
s‾¹) and
ris
the density of the ambient water.
Pjet ¼1
2rjetU2
jetQjet in ½W
where U
jet
is the inlet velocity of the water jet. The energy
that is transferred to the water results in both turbulent and
mean flow motion. According to Bulson (1961), the power that
is given to the mean flowcanbecomputedbyconsideringthe
current in the surface layer on one side of the air curtain. The
total power that is given to the current in the surface layer is
Pc¼1=2rB
Z
T
0
v3dtin ½W
where Bis the width of the lock and Trepresents the thickness
of the surface layer. In the experiments of Bulson (1961) it is
found that the horizontal velocity at a water depth distance from
the air curtains is almost linear with depth and the thickness of
the layer is approximately H/4. The maximum and average hor-
izontal velocity in the surface layer can than be estimated as
Table I. Summary of the obtained salt transmission factors in the
Stevin lock experiments
Method against
salt intrusion
Salt transmission
factor N
Blockage/
efficiency 1N
None (classical
lock-exchange flow)
1.00 0.00
Traditional design of
air injector
0.40 0.60
New air injector 0.25 0.75
Freshwater jet 0.40 0.60
New air injector
+ freshwater jet
0.15 0.85
New air injector + sill 0.20 0.80
New air injector + flushing during
ebb
0.20 0.80
49AIR CURTAINS AND OTHER MEASURES TO REDUCE SALINITY INTRUSION
Copyright © 2011 John Wiley & Sons, Ltd. Irrig. and Drain. 60 (Suppl. 1): 42–50 (2011)
Vmax ¼2
V¼16Pair
rBH
13
=
where the energy transfer ratio is definedby2P
c
=P
air
.Note
that there are two surface currents towards both sides of the air
curtain. Bulson (1961) conducted several experiments with air
cuntains in a dry dock. Based on these data he found the follow-
ing expression for the energy transfer ratio:
¼0:125 1 þH
Hatm
1
:
Non-dimensional circulation
An important non-dimensional circulation for steady (quasi)
two-dimensional vortices is the non-dimensional circulation
C¼Γ
ffiffiffiffiffiffi
2E
p
where Γis the total circulation around a given curve around
the vortices and Eis the total kinetic energy per unit density.
The circulation cells around an air curtain or water jet are
confined in a rectangular box with aspect ratio 4. Therefore,
the circulation and total kinetic energy can be estimated as
~
Γ¼8HUgrav
~
E¼2
V2H2
where the volume average velocity over the circulation cells
is computed by
V¼1
2
16Ptot
rBH
13
=
where P
tot
=P
air
+P
jet
+P
buoy
is the total power that is given
to the water and
Ugrav ¼1
2ffiffiffiffiffiffiffiffiffiffiffiffiffi
gΔrH
rs
s
represents the propagation speed of a gravity current in the
absence of dissipation (Shin et al., 2004). The non-dimensional
circulation can be related tot the air flux parameter in the case
where P
tot
=P
air
, which yields
1
C¼
4
13FL
=
where the air flux parameter is defined as
FL¼Qsg
B
1=3
Δr=rgHðÞ
1=2
GEERT KEETELS
Deltares, Delft, The Netherlands
ROB UITTENBOGAARD
Deltares, Delft, The Netherlands
JOHN CORNELISSE
Deltares, Delft, The Netherlands
NICKI VILLARS
Deltares, Delft, The Netherlands
HANS VAN PAGEE
Rijkswaterstaat, Centre for Water Management, Lelystad,
the Netherlands
50 G. KEETELS ET AL.
Copyright © 2011 John Wiley & Sons, Ltd. Irrig. and Drain. 60 (Suppl. 1): 42–50 (2011)