Desalination 309 (2013) 148–155

Contents lists available at SciVerse ScienceDirect

Desalination
journal homepage: www.elsevier.com/locate/desal

Predicting the near-field mixing of desalination discharges in a

stationary environment
C.J. Oliver, M.J. Davidson ⁎, R.I. Nokes
Department of Civil and Natural Resources Engineering, University of Canterbury, Private Bag 4800, Christchurch, New Zealand

H I G H L I G H T S

► Modified integral model predicts the near-field behaviour of desalination discharges.

► Modified model incorporates a reduced buoyancy flux (RDF) approach.
► RBF model predictions compared with laboratory data and existing integral models
► RBF model predicts effects of the additional mixing noted in previous studies.
► RBF model is superior to existing integral formulations in this respect.

a r t i c l e i n f o a b s t r a c t

Article history: A modified integral model is developed to predict the near-field behaviour of negatively buoyant discharges,
Received 8 June 2012 which are typical of those created when releasing brine from desalination plants into a marine environment
Received in revised form 25 September 2012 via a submerged outfall system. These predictions are compared with available laboratory data and the pre-
Accepted 28 September 2012
dictions from other integral formulations, both analytical and numerical. Based on these comparisons, it is ev-
Available online 31 October 2012
ident that the modified model is capable of predicting the effects of the additional mixing noted in previous
Keywords:
studies, for the range of initial conditions relevant to a submerged discharge from a desalination facility. The
Desalination modified model is therefore superior to existing numerical integral formulations in this respect and is reason-
Negatively buoyant ably consistent with the predictions from previously published analytical solutions. A critical feature of the
Numerical model modified integral model is the reduction in buoyancy flux of the main flow, which provides a mechanism
to account for the influences of additional mixing created by buoyancy induced instabilities on the inner
side of the flow.
© 2012 Elsevier B.V. All rights reserved.

1. Introduction buoyant (for example, the disposal of an unmixed waste stream from
a reverse osmosis plant) and thus the impact boundary is the seabed.
Predicting the behaviour of turbulent negatively buoyant discharges While relatively simple integral model formulations are available to
has become increasingly important in recent years, because of their ap- predict the near field behaviour of these discharges, it is evident that
plication to the disposal of brine discharges from desalination plants. these models have significant weaknesses. In particular they are unable
During this period there has been a rapid growth in the number and to accurately predict the dilution of the effluent at key locations such as
scale of these plants [11], which has highlighted concerns about their the centreline maximum height and the location where the flow returns
potential environmental impacts. Important impacts are associated to its source height (the return point). A recent study by [16] assessed
with the large volumes of concentrated brine that are released back the predictive capabilities of the VISJET, Cormix (CorJet) and Visual
into the environment, and in assessing these impacts it is necessary to Plumes models and in the more critical case of a stationary environ-
predict, with reasonable accuracy, the mixing of that effluent in the en- ment, they concluded with reference to their predictive capabilities in
vironment. A critical component of this mixing is that which takes place the near-field region:
in the near-field region, where rapid mixing reduces pollutant concen-
“Validation reveals that these models underestimate jet dimen-
trations as the wastewater flows from its point of release to the point
sions in all cases. Terminal rise height (Zt) deviations are between
where it impacts a boundary. The effluent is typically negatively
10% and 30% and increase with the initial discharge angle. CorJet
yields the best agreement, with deviations around 10%–17%. With
⁎ Corresponding author. respect to dilution at the impact point (Si), all models significantly
E-mail address: mark.davidson@canterbury.ac.nz (M.J. Davidson). underestimate the values, with deviations ranging between 50%

0011-9164/$ – see front matter © 2012 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.desal.2012.09.031
 C.J. Oliver et al. / Desalination 309 (2013) 148–155 149

and 65%. The commercial models are therefore very conservative goes some way to achieving this goal. Influences of the additional
when estimating dilution rates.” mixing associated with the buoyancy-induced instabilities are incor-
porated through a modified formulation of the integral relationships,
Thus it is evident that there is mixing taking place in addition to so that the buoyancy flux of the main flow is no longer conserved. The
that predicted by these models; suggesting that they are not captur- concept behind the modified model is similar to that published re-
ing at least one key physical process, which has a significant influence cently by [21], however, the present formulation retains the simplic-
on the dilution of the effluent. Past experimental studies have noted ity of existing integral model approaches and does not require the
the additional mixing associated with the presence of buoyancy in- adjustment of a coefficient to fit existing data.
duced instabilities ([7,10] and others) on the inner (lower) side of
the flow and the influences of this physical process are not captured
in the above integral formulations. This is not surprising given the 2. Modified integral formulation
limited information available with respect to these influences at the
time these models were developed. However, more recent experimen- A schematic diagram of the generic discharge configuration employed
tal studies have provided detailed centreline dilution data [9,14,18,20]. in the development of the integral relationships is shown in Fig. 1, where
It is evident from these and earlier studies that the above formulations a discharge of diameter d releases effluent at a source inclination of θ0. At
provide reasonable predictions of the geometric parameters for these this source location the density and velocity of the effluent are ρ0 and U0
flows, suggesting that influences of the additional mixing on the mo- respectively. At a specified location downstream the main flow has a ra-
mentum fluxes are relatively small. However, as noted above the dius bT, velocity uT and density ρT, where “top hat” or uniform profiles are
same is not true with respect to available dilution data where the effects assumed for simplicity. The ambient fluid is assumed to be stationary and
are more significant. to have a density of ρa. A Cartesian coordinate system is introduced with
One difficulty in assessing the accuracy of integral model predic- its origin at the source and important geometric parameters include the
tions is the variability in the recently obtained dilution data, particu- coordinates of the centreline maximum height (xm, zm), those of the re-
larly at or near the return point. The return point is defined as the turn point (xR, 0) and the maximum height achieved (zme). It is impor-
location where the flow returns to the source height and this can dif- tant to note that this schematic representation of the flow becomes
fer from the impact point which is defined as the location where the invalid as the source inclination approaches 70°, because the rising
flow impacts the seabed (lower boundary). The latter being problem- and falling regions of the flow begin to interact significantly through a
atic for comparative purposes, because the location of the impact re-entrainment process that is not modelled in the present formulation.
point is dependent on site specific conditions. The variability in As noted above, comparisons of model predictions with experimen-
recently obtained dilution data is discussed in some detail in [15], tal data to date suggest that existing integral models are able to predict
where it was noted that dilution coefficients vary by more than 50% geometric parameters with reasonable accuracy; therefore implying
for source inclinations of 30°, 45° and 60° respectively and that one that the additional induced mixing has little influence on the momen-
possible reason for this variability is differences in the bottom bound- tum fluxes of the main flow. However, the experimental data also
ary conditions. To help clarify this issue [15] conducted a detailed set shows that the additional mixing distorts the mean cross-sectional pro-
of Laser-induced Fluorescence (LIF) experiments, where the influ- files of concentration and velocity on the inner side of the flow, so that
ences of the bottom boundary at the return point were removed these profiles are no longer self-similar. Thus the application of an inte-
(the return and impact points were separated). This data set provides gral model to the whole flow is problematic, because the assumption of
a sound basis for assessing and developing integral models, which do self-similar mean profiles is critical in retaining the simplicity of these
not specifically model boundary influences and hence conditions at models, which is essential to their popularity in engineering design.
the impact point. Separate models of boundary interaction will then However, the experimental data also show that self-similarity of the
be required to provide a more accurate representation of the process- mean profiles is maintained on the outer side of the flow. Here we retain
es that take place as the effluent impacts on the seabed. However, be- the simplicity of existing integral formulations by defining the main
fore developing such models it is important that bulk parameters flow as a self-similar flow embedded within the flow as a whole,
prior to this impact are predicted with reasonable accuracy. Here where this self-similar form is defined by conditions on the outer-side
we present a modified formulation for the integral equations, which of the flow.

Fig. 1. Schematic diagram showing the idealized discharge configuration employed in developing the RBF integral model.
150 C.J. Oliver et al. / Desalination 309 (2013) 148–155

Although this definition of the main flow is somewhat artificial, it re- assumption rather than the spread assumption (Eq. (5)). Either as-
flects experimental observations where significant portions of the con- sumption could be employed here, but the spread assumption is pre-
taminated fluid do not follow the normal path of a buoyant jet, but ferred because of its simplicity and its consistency with the observed
instead descend along predominantly vertical paths due to their nega- behaviour, as noted above. Where the current system of equations
tive buoyancy. They therefore detach (or detrain) from the main flow differs from existing formulations is in the relationship that describes
and in doing so they induce additional mixing to that expected the evolution of the buoyancy flux. It is assumed that the standard ap-
(or currently modelled) for a buoyant jet. These detrainment and proach of conserving the buoyancy flux along the flow path is inappro-
mixing processes are expected to reduce the buoyancy flux of the priate for these flows because of the additional buoyancy-induced
main flow as contaminated (higher density) fluid is replaced with mixing. To provide a platform for incorporating the influence of this
less dense fluid from the ambient, but their negligible impact on additional mixing on the main flow the buoyancy flux relationship
'
the momentum fluxes suggests that the velocities associated with (B* = gT* Q*) is differentiated to give:
the fluid leaving the main flow are relatively small. On this basis
0
the horizontal momentum flux equation remains as: dB
0 dQ
dg

¼ gT
þ Q
T : ð8Þ
ds
ds
ds

dMx

¼ 0: ð1Þ
ds

To close the system of equations the gradient of the reduced gravity
must be defined. Guidance in this respect comes from the analytical so-
Note that the subscript “*” indicates a dimensionless parameter.
lutions developed by [7], where it is assumed that the flow behaves es-
The scales used to create non-dimensional length, momentum flux,
sentially as a jet as it rises to maximum height. With regard to dilution,
volumes flux and reduced gravity terms are respectively the source
this approach has been shown to provide superior predictions when
diameter (d), initial momentum flux (M0 = U02d 2π/4), initial volume
compared to those from standard integral models [15]. However, it is
flux (Q0 = U0d 2π/4) and initial reduced gravity (g0' = g(ρa − ρ0)/ρa).
worth noting that while Kikkert et al.'s approach provides a valuable
The variation in the vertical momentum flux (Mz*) can then be writ-
set of analytical relationships, this is achieved by overlaying jet and
ten in the following form:
plume solutions and thus the overall physics of the flow is not accurately
0
2 captured. For example, predictions at maximum height are based on a jet
dMz
4g T
bT

¼ ð2Þ solution that does not take account of the reduced vertical momentum
ds
F 20 flux at this location. Thus, while Kikkert et al.'s approach provides more
 qffiffiffiffiffiffiffiffi accurate dilution predictions, it lacks the sophistication of numerical in-
0
where F0 is the initial densimetric Froude number ¼ U 0 = g0 d . tegral models such as VISJET and CorJet that in contrast capture the ver-
tical momentum flux variations correctly, but their dilution predictions
With the momentum fluxes defined, the geometric relationships can are relatively poor. The present formulation addresses this inconsistency
be written as: by incorporating the behaviour evident in Kikkert et al.'s analytical
model into a numerical model that also correctly models the variation
dx
M x

¼ ð3Þ in vertical momentum flux. It therefore provides reasonably accurate
ds
M s

predictions of dilution and the inconsistency between the analytical
and numerical approaches is resolved through a reduction in the buoy-
and
ancy flux of the main flow, which is consistent with the detrainment
dz
M z
and additional mixing associated with the buoyancy induced instabil-
¼ ð4Þ ities. This reduction in the buoyancy flux from the main flow is therefore
ds
M s

defined so that the reduced gravity gradient initially mimics the tracer
where Ms* is the dimensionless form of the total momentum flux of gradient of a pure jet (following Kikkert et al.'s analytical solution).
the main flow. Briefly reviewing the pure jet solution for completeness, the initial
Experimental evidence (for example [9]) to date suggests that the momentum flux of a jet is conserved, so that M0 = πbT2UT2. In dimen-
spread of the outer edge of the flow can be adequately described by sionless form this becomes:
the spread assumption, so the scale of the main flow is defined by:
2 2
1 ¼ 4bT
U T
: ð9Þ
dbT

¼ kT ð5Þ
ds
If a conservative tracer is present in the jet its flux is also con-
served; i.e. C0Q0 = CT Q. In dimensionless form this becomes:
where kT is the “top hat” spread coefficient, which is assumed to have
a value of 0.15 ([4], for example) and this value does not change as 1 ¼ CT
Q
ð10Þ
the flow develops. The variation of the total momentum flux can be
written in terms of that of the vertical momentum flux, such that where C0 represents the initial tracer concentration and CT the local
we have: “top hat” concentration. Eq. (10) can be differentiated to give:

dMs
Mz
dMz
C T dQ

¼ : ð6Þ dC T

ds
Ms
ds
¼−
: ð11Þ
ds
Q
ds

Similarly the volume flux can be related to the total momentum

A relatively simple solution is obtained by invoking a virtual source
flux and flow spread through the following relationship:
assumption and combining the spread assumption (Eqs. (5) and (9)).
  This solution can be employed to show that the dimensionless volume
dQ
2 db
2 dM s

¼ 2M s
bT
T þ bT : ð7Þ flux gradient is 2kT, so that Eq. (11) becomes:
ds
Q
ds
ds

Eqs. (1) to (7) are typical of existing integral model formulations for dC T
C
2
¼ − T 2kT ¼ −C T
2kT : ð12Þ
this problem, although it is more common to employ the entrainment ds
Q

 C.J. Oliver et al. / Desalination 309 (2013) 148–155 151

Thus if the negatively buoyant jet solution is to initially mimic the In order to make direct comparisons between the predicted and
jet solution, the reduced gravity gradient is then defined as: measured values, it was necessary to map the predicted values, based
on the assumed top-hat profiles, with values extracted from the more
0  
dgT
dC T
0
2 complex measured profiles. Reasonable estimates of the coefficients
¼ ¼ −gT
2kT : ð13Þ
ds
ds
that map information between these profiles can normally be obtained
by matching the mass, momentum and tracer fluxes at a given
Substituting Eq. (13) into Eq. (8), then gives the rate of change of cross-section (for example, [4]). This process is simplified with the use
buoyancy flux in the jet region as: of the embedded model, because by definition the mean profiles are
Gaussian. Therefore standard mapping coefficients can be employed so
 
dB
0 dQ
0
2 B dQ
that the measured mass, momentum and tracer fluxes are maintained
¼ gT
−2kT gT
Q
¼
−2kT B
: ð14Þ
ds
ds
Q
ds
between the top hat model and Gaussian profiles of the embedded
model. These Gaussian profiles are defined by the self-similar profiles
Eq. (14) is unique to this Reduced Buoyancy Flux (RBF) model and measured on the outer side of the flow (above the flow centreline).
represents the incorporation of a component of Kikkert's successful With regard to dilution this process yields a standard mapping coeffi-
analytical solution into a more standard numerical integral model cient of 1.61; that is, the top-hat dilutions were divided by 1.61 to obtain
framework (consistent with those of VISJET and Corjet). Eqs. (1) to the equivalent minimum dilution, so that the measured and embedded
(7), along with Eq. (14) provide a system of ordinary-differential model fluxes remain the same.
equations that can be solved numerically in MatLab with a standard Predictions from the CorJet model [6], VISJET Model [8] and the
Runge–Kutta routine (ODE45) to provide predictions of negatively modified analytical solutions [15] are also presented in Figs. 2 and 3.
buoyant jet behaviour. Eq. (14) is employed initially until the buoyan- Predictions from the analytical solutions are similar to those from
cy flux gradient reaches 0, thus providing the initial reduction in the reduced buoyancy flux (RBF) model, which is expected at maxi-
buoyancy flux necessary to mimic the jet solution. Beyond this the mum height (Fig. 2), because the RBF model is designed to mimic
buoyancy flux is assumed to be constant as the flow evolves. The ini- the analytical solution at this location. However the fact that the
tial conditions for this RBF model are defined such that initially Ms* = numerical RBF model is able to capture the overall physics of the
Q* = 1 and hence bT* = 0.5 and s* = bT*/kT. Geometric considerations problem more accurately is reflected in its ability to also provide
then define initial values for x*, z*, Mh* and Mv*. reasonable dilution predictions at the return point (Fig. 3). In contrast
the analytical solutions have to be modified through an empirical co-
3. Model predictions efficient to provide similar agreement with measured coefficients
[15]. Predictions from the CorJet and VISJET models are clearly con-
Comparisons of predicted and measured dilution coefficients at servative, by approximately 50% at the return point for a source incli-
the centreline maximum height and the return point are shown in nation of 60°, which is consistent with the observations made by [16].
Figs. 2 and 3, where it is evident that the RBF model predicts these di- Predictions from [21] have a tendency to overestimate the dilution
lutions reasonably accurately for the range of source inclinations that coefficients, being almost 50% above the measured values at the re-
would be considered for a submerged discharge from a desalination turn point for the same source inclination. In contrast predictions
plant (30° to 60°). The quality of the predictions deteriorates as the from the RBF model are clearly consistent with the measured data
source inclination approaches 70° and the re-entrainment process be- at this source inclination. Indeed for the range of source inclinations
comes increasingly important. It is important to note that when relevant to desalination discharges (30° to 60°), the RBF model
assessing model performance at the return point a greater emphasis predictions are consistent with measured values, particularly those
has been placed on the data from [15], because in this study bottom where influences of the bottom boundary have been removed. Impor-
boundary influences on return point results have been clearly removed. tantly, this model incorporates the effects of an additional physical
As noted above this is consistent with the model formulations. process and from it estimates of the extent of reductions in the

Fig. 2. Predicted and measured dimensionless centreline dilution coefficients as a function of initial discharge angle at maximum height.
152 C.J. Oliver et al. / Desalination 309 (2013) 148–155

Fig. 3. Predicted and measured dimensionless centreline dilution coefficients as a function of initial discharge angle at the return point.

buoyancy flux necessary to achieve dilutions comparable to the mea- Fig. 4 it is evident that these bulk effects are significant and that the re-
sured values can be obtained. Computed magnitudes of the reduced ductions in buoyancy flux increase with discharge angle. For source in-
buoyancy flux with dimensional vertical height, for source inclina- clinations of 15° and 60°, buoyancy flux reductions are 2% and 29%
tions ranging from 15° to 60°, are shown in Fig. 4. Reductions in buoy- respectively, providing dilution coefficient predictions that compare
ancy flux occur on the rising side of the flow where the jet solution is well with measured values at the maximum height and return points
dominant, which reflects the model formulation but not necessarily (Figs. 2 and 3). The reductions of 7% and 16% for source inclinations of
the details of the detrainment and mixing processes associated with 30° and 45° respectively result in predicted dilution coefficients that
the buoyancy-induced stabilities. The effect of the buoyancy induced are more conservative at the return point, but these are within 10% of
instabilities is likely to be greater on the rising flow, because the the measured values. The reduction in buoyancy flux is overestimated
detrained fluid is moving in the opposite direction to the main flow as the source inclination approaches 70° and interaction between the
and is therefore less likely to be re-entrained into the main flow. In rising and falling limbs of the main flow becomes significant, hence
contrast detrained fluid is falling with the main flow beyond maximum the predictions of bulk parameters and experimental data diverge at
height and thus re-entrainment becomes more probable, particularly as these higher angles (evident in Figs. 2 and 3). While the estimates of
the detrained fluid retains some horizontal momentum flux. It is per- the reduced buoyancy fluxes are undoubtedly affected by the underly-
haps reasonable to argue that the effect of the buoyancy-induced insta- ing assumptions built into the model, they provide a plausible mecha-
bilities is less significant beyond maximum height, but difficult to argue nism that accounts for discrepancies between the predictions from
that they do not exist. The fact that the buoyancy reduction in the RBF existing integral models and the measure data.
model ceases beyond maximum height is a reflection that it does not di- The formulation of the RBF model assumed that the influence of
rectly model the detrainment and additional mixing associated with the the additional mixing on the momentum fluxes was small and the va-
buoyancy instabilities, but rather the bulk effect on the main flow. In lidity of this assumption can be explored through comparisons with

Fig. 4. Variations in buoyancy flux predicted by the RBF model for initial discharge angles ranging from 15° to 60°.
 C.J. Oliver et al. / Desalination 309 (2013) 148–155 153

Fig. 5. Predicted and measured dimensionless coefficients for the vertical coordinate of the maximum centreline height as a function of initial discharge angle.

trajectory data. Evidence of the quality of the RBF trajectory predictions is mapped from its associated top hat value (bT) through multiplication
is shown in Figs. 5, 6, 7 and 8, where model outputs are compared with of the conversion coefficient (0.74) and the ratio of the tracer to velocity
available experimental coefficients along with predictions from the ana- spread (λ=1.1). The consistency of the data and model predictions for
lytical solutions of [7] and the CorJet model. In Figs. 5 and 6, variations of the maximum centreline (Fig. 5) and maximum edge height (Fig. 7) in-
coefficients for the location of the centreline maximum height with dicates that predictions of the flow spread are also reasonable. Note
source inclination are presented. Variations of similar coefficients for data sources for the above comparisons that have not been specifically
the maximum edge height and the location of return with source inclina- mentioned in the text include [1,2,3,5,12,13,17,19,22].
tion are shown in Figs. 7 and 8. The RBF model predicts these important In addition to providing reasonable predictions at the key geometric
geometric parameters with reasonable accuracy and these predictions locations, the RBF model also provides reasonable descriptions of the
are consistent with those of the analytical solutions and less conservative evolution of the bulk parameters with distance from the source. This
than those from the CorJet model. It is worth noting that the increased is clearly evident in Figs. 9 and 10, where the evolution of centreline di-
path lengths of the RBF model also improve its dilution predictions, but lution as a function of vertical height is shown in Fig. 9 and the variation
the effect is less significant than the reduced buoyancy fluxes. The defini- of the centreline and edge trajectories is presented in Fig. 10. The com-
tion adopted when determining the maximum height from the RBF parisons of centreline and edge trajectories indicate how effectively the
model in Fig. 7 was the same as that adopted by [7], that is, it is assumed model predicts the outer spread of these flows. Model predictions are
the flow edge occurs at distance 2bc above the flow centreline, where bc compared with data for a source inclination of 45°, where the initial

Fig. 6. Predicted and measured dimensionless coefficients for the horizontal coordinate of the maximum centreline height as a function of initial discharge angle.
154 C.J. Oliver et al. / Desalination 309 (2013) 148–155

Fig. 7. Predicted and measured dimensionless coefficients for the maximum edge height as a function of initial discharge angle.

Froude numbers ranged from 14.9 to 106.4 for the trajectory data and unmixed wastewater from a large-scale reverse osmosis desalination
21.0 to 106.4 for the dilution data. The predicted behaviour remains facility is released via a submerged outfall system into the ocean. The
consistent with the collapsed data throughout the flow's evolution, in- new model is developed for the critical case where there is no motion
dicating that the reduction in the buoyancy flux as the flow rises to in the surrounding ambient fluid. This model defines a self-similar
maximum height, along with the assumed constant spreading rate for main flow, based on the measured Gaussian and self-similar profiles
the outer flow, provides a reasonable basis for capturing the bulk effects on the outer side of these flows, and thereby retains the simplicity
of the buoyancy induced instabilities on the main flow. Thus the RBF of existing integral models. The influence of the buoyancy-induced
model can be employed with some confidence to predict bulk parame- instabilities on the inner side of the flow is incorporated through a re-
ters at locations other than the two described above and this includes duction in the buoyancy flux of the main flow. The reduction in buoy-
the region beyond the return point, where predictions may be required ancy flux is designed so that the dilution of the discharge mimics a jet
for discharges on a sloping seabed. initially, which is consistent with previously developed analytical so-
lutions. The new model predicts dilutions and geometric parameters
4. Conclusions to higher degree of consistency than previously developed models.
There are no additional coefficients introduced to the model, so it is
A modified integral formulation has been presented in the context not tuned to match the available data. Estimates of the extent of
of negatively buoyant discharges, typical of those created when buoyancy flux reduction in the main flow can also be obtained from

Fig. 8. Predicted and measured dimensionless coefficients for the horizontal coordinate of the return point as a function of initial discharge angle.
 C.J. Oliver et al. / Desalination 309 (2013) 148–155 155

Fig. 9. Predicted and measured centreline dilutions as a function of vertical height for an initial discharge angle of 45°.

Fig. 10. Predicted and measured centreline and edge trajectories for an initial discharge angle of 45°.

the model; while the accuracy of these estimates is not clear, the [10] G.F. Lane-Serff, P.F. Linden, M. Hillel, Forced, angled plumes, J. Hazard. Mater. 33
modified integral formulation demonstrates a plausible mechanism (1993) 75–99.
[11] S. Lattemann, M.D. Kennedy, J.C. Schippers, G. Amy, Global desalination situation, Sus-
to explain discrepancies between previously developed predictive tainability Sci. Eng. 2 (2010), http://dx.doi.org/10.1016/S1871-2711(0900202-5).
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Kluwer Academic Publishers, 1994, pp. 131–145.
[13] C.L. Marti, J.P. Antenucci, D. Luketina, P. Okely, J. Imberger, Near field dilution
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