Hydrological Sciences - Journal - des Sciences Hydrologiques, 36,1,2V1991
Rhythmic karst springs
OGNJEN BONACCI & DAVOR BOJANIC
Civil Engineering Institute, Faculty of Civil Engineering Sciences,
58000 Split, V. Maslese bb, Yugoslavia
Abstract Rhythmic springs (ebb and flow springs, intermittent
springs, potajnice) belong to the group of springs which appear
exclusively in karstified terrains. The paper describes various types
of rhythmic springs and gives their classification. It also develops a
mathematical model for the functioning of this type of springs
based on the principle of recharge and emptying of the underground reservoir through siphon action. Applying this model,
according to the observed hydrographs of some rythmic springs
in Yugoslavia, the paper explains in detail the structure of the
underground reservoir located in the karst.
Sources intermittentes karstiques
Resume Les sources intermittentes appartiennent au groupe des
sources apparaissant exclusivement dans des terrains karstiques.
Dans ce travail nous avons décrit les différents types de ces
sources en présentant leur classification. Nous avons mis au point
un modèle mathématique de fonctionnement de ce type de source
établi sur des principes de remplissage et de vidange du réservoir
souterrain au moyen de siphon. D'après ce modèle nous avons
expliqué en détail la structure du réservoir souterrain pour
quelques sources intermittentes en Yougoslavie, pour lesquelles on
disposait des hydrogrammes enregistrés.
INTRODUCTION
Rhythmic springs are named in the literature in different ways, such as: ebb
and flow springs, intermittent springs, potajnice etc.. According to current
knowledge, they appear exclusively in areas consisting of soluble rocks.
According to Atkinson (1986), soluble rocks are those which dissolve in
water, leaving almost no residue. In such rocks weathering tends to widen
fractures without simultaneously blocking them, allowing water to penetrate
and to widen them further.
The characteristics of soluble rocks given in Atkinson's definition (1986),
as well as the presence of fissures and conduits, lead to conditions necessary
for the formation of rhythmic springs exclusively in karst terrains.
Undoubtedly, such springs represent an interesting karst phenomenon which
occurs relatively seldom and they do not play an important role either from
the hydrological or economic standpoint. Bôgli (1980) refers to the presence
of such springs in the USA (about ten) and in France (six springs). Gavrilovic
Open for discussion until 1 August 1991
35
Ognjen Bonacci & Davor Bojanic
36
& GavriloviC (1985) refer to the presence of about twenty rhythmic karst
springs in the karst terrains of Yugoslavia. Those authors state that it is
impossible to establish in some of those springs whether their outflows are
really rhythmic. The same authors state that there are about thirty rhythmic
karst springs in the world, i.e. in Bulgaria (two), Romania (two), Hungary
(three), France (seven), Belgium (two), Germany (one), Switzerland (two),
England (two), Czechoslovakia (one), USA (one), the Soviet Union (one)
and Israel (one). Although data on rhythmic springs in China are not
available there certainly must be some there as well.
It is impossible to expect that any survey paper will include all the
existing rhythmic karst springs in the world, but it is evident they are quite
rare, only about one hundred. Since the water demand in the world is
increasing, interest in the study of the functioning of these springs has
become greater. Consequently, the objective of this paper is primarily to
explain the hydraulic and morphological aspects of the functioning of rhythmic
springs according to the hydrological characteristics of their outflow
hydrographs.
HYDROLOGICAL CHARACTERISTICS
Katzer (1909) was the first to explain the phenomenon of rhythmic springs
(RS) functioning by a siphon system. The scheme of the functioning is
presented in Fig. 1(a) (Bonacci, 1987). When the water level in the cave rises
Fig. 1 Schemes of rhythmic karst springs functioning.
to H2, all the water in the cave from H2 to H3 suddenly outflows. This
emptying is effected according to the siphon principle. When the water level
is about Hx, and when the inflows through the underground channel and the
cracks in the karst mass are greater than the maximum capacity of the siphon,
then the spring does not operate rhythmically, but functions as any other
karst overflow spring.
37
Rhythmic karst springs
Bôgli (1980) explains the possibility of the RS functioning in the
following four situations:
(a) the intermittent action continues the whole time but the length of the
period changes with the water supply, since this determines the duration
until the basin is full;
(b) at high water level the siphon becomes flooded and does not function
because of the lack of air but it becomes intermittent at low and mean
water levels;
(c) the basin is not watertight. When the inflow of water is small the
siphon cannot be filled over the level H2 (Fig. 1) but with an increasing
supply of water, siphon action sets in and is intermittent at mean and
high water levels; and
(d) a combination of (a) and (b) results in an intermittent spring only at
mean water level.
The authors prefer the term rhythmic springs to the term intermittent
springs. The reason is to stress the presence of the siphon effect which
influences the formation of rhythmic effects in the outflow hydrographs of
such springs. The basic meaning of the term intermittent springs can be
related to the notion of the springs functioning with interruptions, or even
can be connected with the term temporary springs which are quite common in
the karst and are caused by entirely different hydrological and morphological
reasons. GavriloviC (1967) gives the following classification of rhythmic
springs:
(a) permanent rhythmic springs;
(b) seasonal rhythmic springs;
(c) (i) occurring during the rainy season;
(ii) occurring during the dry season; and
(d) sudden rhythmic springs.
Permanent rhythmic springs are emptied during the whole year by siphon
action. Only in special situations, lasting for a short time, do the hydrographs
of these springs not display rhythmic oscillations of the outflow discharge.
Seasonal rhythmic springs are the most common type. When the underground
reservoir through which the emptying by siphon action takes place has small
capacity, then rhythmic springs function only during the dry period, when the
groundwater levels are low and their inflows small. When the capacity of the
groundwater reservoir is large, i.e. its recharge requires large quantities of
water, the spring functions as a rhythmic spring only seasonally, i.e. in the
rainy period when there are sufficient water inflows to recharge the
groundwater reservoir. Such springs should not dry up during the dry period
if the inflow reaches the spring opening by other routes and not by the
siphon or groundwater reservoir. Sudden rhythmic springs appear exclusively
after heavy precipitation and are located in areas of vertical circulation of
groundwater in the karst, i.e. in the areas were only temporary karst springs
occur. Such springs are emptied only once or several times during rainfall.
Subsequently, they stop functioning. This type of spring could be classified as
seasonal rhythmic spring functioning during rainy periods ((c)(i)); however, it
is mentioned separately to stress the fact that these are exclusively temporary
karst springs whose catchment is located in the vadose area of the karst mass
38
Ognjen Bonacci & Davor Bojanic'
and only in rare situations recharged by groundwater. Pseudorhythmic springs
do not actually belong to the rhythmic karst springs mentioned. Their
rhythmic form of outflow hydrograph is caused by other reasons and not by
the emptying of the groundwater reservoir by siphon action. One of the best
known springs of this type is the Stockende Quelle in Switzerland. During the
summer the outflow hydrograph of this spring starts increasing daily and
reaches its maximum at midnight, after which it starts to decrease. The
rhythmic form of its hydrograph can be explained by the fact that the spring
is charged by the water thawed from snow and ice from the poljes located at
higher horizons. The snow and ice thaw during the day and their water leaks
to the spring. The thawing stops during the night. It should be noted that
these springs also appear exclusively in karst regions.
Figure 1 presents the principle of rhythmic karst spring functioning. The
scheme plotted in Fig. 1(a) has already been explained, whereas the scheme in
Fig. 1(b) is used to show that a large karst conduit can have the same
function as a groundwater reservoir, and that the spring functioning as a
rhythmic spring depends upon the relationship between the piezometric level
Ht and the siphon level H2Figure 2 presents four types of hydrograph appearing in rhythmic karst
springs. In the case presented in Fig. 2(a) there exists a continuous basic
flow, Qv When the siphon is emptied the discharge increases to a maximum,
Qj + Q2- In the case presented in Fig. 2(b) the basic flow is equal to zero.
Fig. 2(c) presents the hydrograph of a spring whose reservoirs are not
uniformly formed. This will be discussed in detail in the next section.
Figure 2(d) presents the shape of the Kojin Spring hydrograph (Yugoslavia),
(GavriloviC, 1967). This spring probably has a great number of groundwater
reservoirs either connected in series or in parallel. Finally it should be noted
that rhythmic karst springs often appear in the vicinity of a permanent karst
spring.
£
Q
[m3/s]or [t / s ]
Fig. 2
(a)
£ Q
Types of hydrograph for rhythmic karst springs.
Rhythmic karst springs
39
MODELLING OF RHYTHMIC SPRINGS FUNCTIONING
Figure 3(a) presents a general schematic model of a longitudinal cross section
of the underground karst part of a rhythmic spring. It was used to simulate,
according to hydraulic principles, the functioning of three rhythmic karst
springs in Yugoslavia whose hydrographs, obtained by measurements, were
used to verify the model. The underground karst reservoir is charged by a
continuous inflow quantity, QQ, which directly depends upon the general
groundwater level. The reservoir, Rv followed by a siphon, copes with the
recharge and emptying phases. This reservoir is continuously filled due to a
continuous inflow QQ, and its water level Hv is thus increased. When it
reaches the water level, H^, then the overflow through the bottom of the
siphon pipe starts. With further recharge, great water quantities overflow with
a gradual air entrainment. The problem of air entrainment in siphons has
been analysed by Casteleyn et al. (1977). Figure 3(b) presents one phase of
the water flow through the siphon immediately before the beginning of the
siphon outflow action. The simulation performed in this paper used the
experience and the mathematical formulations of Casteleyn et al. (1977).
When the whole of the air is entrained from the siphon pipe, the flow
becomes a siphon outflow with the gross decrease H1 - H^. In this phase,
the outflow quantity, Q , is relatively high, and the reservoir is rapidly
emptied; thus the water level is decreased. When the level in the reservoir
decreases below the level Hy which is the level of the inflow siphon pipe, air
enters into this pipe, and the flow through the siphon is interrupted. This
sequence is repeated. It should be stressed that the value of the water inflow
into the reservoir, Qn, is not a constant value but changes with time, which
QSIPHON -
Qs
(a)
Fig. 3 (a) Schematic longitudinal cross section through the karst
underground part of rhythmic spring, (b) flow through siphon
(according to Casteleyn et al. (1977)).
Ognjen Bonacci & Davor Bojanic'
40
can cause significant problems. Since the process is fast and non-stationary,
the simulation should be performed with short time intervals, which for the
computations performed in this paper were At = 1-20 s. The continuity
equation for the reservoir presented in Fig. 3 is expressed by:
—
A1 = QQ-QS
(1)
Equation (1) can be approximately integrated into:
QQ - Qp)
HJt + At) = HJt) +
1
*
Q0 - Qp * At)
(1 - 9) At +
AJHJt))
9 • At
AjHJt + U)]
(2)
where:
HJt)
= water level in reservoir 1 at time instant /;
HJt + At)
= water level in reservoir 1 at time instant (t + At);
At
= time interval of the integration;
Q0
= constant inflow into reservoir 1;
Qs(t)
= outflow from reservoir 1 at time instant /;
Qft + At)
= outflow from reservoir 1 at time instant (t + At);
8
= integration factor;
Afttift))
= reservoir 1 area at time instant t; and
AftHftt + At)) = reservoir 1 area at time instant (t + At).
The outflow from reservoir 1 at time t is expressed by:
d\n
Qs(t) = -
{2g {Hx{t) - H^)]*
(3)
4
[ i + cK + x 1 (0/ 1 /rf 1 f J
where:
dx
/j
H^
\u
= siphon pipe diameter;
= siphon pipe length;
= level of the siphon pipe exit;
= coefficient of the energy loss at the siphon pipe
entrance (= 0.5);
Xj(/)
= friction coefficient in the siphon pipe at time instant t;
and
\1(t + At) = friction coefficient in the siphon pipe at time instant
(t + At) (the friction coefficient is computed using the
Colebrook-White equation).
When the water spills from reservoir 1, the discharge is computed
according to equation (4) for the time instant, t:
«2/0 = 0.42 • B • {2g)y> (HJt) - W% ) 1 S
where:
0.42 = overflow discharge coefficient; and
(4)
Rhythmic karst springs
41
B = overflow discharge width s d.
During water overflow (Fig. 3(b)) the air is entrained from the overflow
pipe. The quantity of the entrained air, DVZ, has been estimated according to:
DVZ = 0.5 [Q/0
+
Q£ + A0]<2ZL UIQ*
'S*ax
(5)
where:
Dl^Z = volume of entrained air during time At;
Q^i = estimated average air entrainment in a time unit; and
Q
= overflow discharge for H. = H2.
In equation (2) the water level Ht(t + ht) is not known, and it is
determined by applying Newton's method. Q^ can be determined from the
air volume VZ in the part of the siphon pipe from the overflow to the pipe
end and the estimated overflow time, ATP, according to the expression:
Q2X = VZI ATP
(6)
The computation for reservoir 2 is similar to that for reservoir 1, with the
continuity equation
oW4
At
A2 = QS+Qt-Q
(7)
where:
=
#4(0
water level in reservoir 2 at time instant t;
Qt
= additional inflow or outflow into/from reservoir 2;
Q(t)
= spring discharge at time instant f; and
A2(H^(t)) = reservoir 2 area for the water level H^t).
In further modelling it was supposed that the water from the siphon
pipe enters reservoir i?2> which in this case does not function as a reservoir,
since its dimensions are small, but it maintains the water level, H4, which
dictates Q , the discharge quantity from the siphon. This reservoir can be
recharged by the basic water quantity, Qv from the other part of the
catchment. It can be supposed theoretically that one part of the water from
reservoir R2 is lost, which is expressed by -Qt in Fig. 3, and that this part
does not flow to the analysed spring outlet. This assumption seems to be
almost theoretically possible, but is rare in practice. The general groundwater
level in the karst mass around reservoir i? 2 will be decisive in determining
whether it is an inflow +Q1 or a loss -Qv If the groundwater levels are
higher than H^, a positive inflow +Q1 should be expected, whereas in the
opposite case, when Qx < 0 there are losses. Consequently, the level H4 in
reservoir R2 directly influences the capacity of the spring in two ways:
(a) dictating the discharge Qs according to the gross decrease Hl - H^, and
(b) by the inflow or outflow of water from the reservoir.
From the reservoir to the rhythmic spring outlet there are one or more
karst conduits, whose diameter d2 and length l2 also dictate the form of the
outflow hydrograph.
42
Ognjen Bonacci & Davor Bojanicf
roENTTFICATlON OF PARAMETERS
The model described was used for the identification of parameters of the
following rhythmic karst springs in Yugoslavia: (a) Presihajoci Studenec (Fig.
4), (Gavrilovié, 1967); (b) Zaslapnica (Figs 5 and 6), (Gavrilovié & Gavrilovié,
1985); (c) Promuklica (Figs 7, 8 and 9), (Gavrilovié, 1967; Petrovic, 1981).
Q [ 1/s J
5.0 i
RESERVOIR
2
0B5ERVED 12 JUNE 1986
SIMULATED
4.5
4.i
J1JH5* V15m
3.5
3.02.5
2.0
1.51.
0
750.0
1500
2250
t
[ s j
RESERVOIR 1
, A , -- 0.9 m 2 ; l,= 5 m ; «1,-0.1 m ; Q 0 -- OAT Us
H2 - H
3
- 0.5m ; H2 - H 3 : 1 . 0 m
Fig. 4 Simulated and observed hydrographs of Presihajoci Studenec
spring.
Figure 4 gives the hydrograph of the rhythmic karst spring at Presihajoci
Studenec. This hydrograph was presented in Fig. 2 as case (b) without the
basic discharge, Qv which is zero. It is a typical example of a rhythmic karst
spring, which at the time of measurement had a continuous discharge, QQ, of
0.47 1 s"1, and a rhythmic period of 840 s. A continuous inflow into the
reservoir, Rv results in continual rhythmic recharge fillings of the reservoir
and emptyings through the siphon. The volume of the reservoir and the pipe
dimensions are given in Fig. 4. When the inflow, QQ, increases, the time
interval between the two emptyings is decreased. Presihajoci Studenec
operates as a seasonal rhythmic spring only during the dry season.
Figure 5 presents the hydrograph of the rhythmic karst spring at
Zaslapnica. This hydrograph has been presented in Fig. 2 as typical for case
(c). The basic discharge in the measurement period was 0.0140 m3 s"1. The
Zaslapnica spring belongs to the group of seasonal rhythmic springs in the
dry period (GavriloviC & Gavrilovié, 1985). During the rainy period (winter
and spring) Zaslapnica represents an intensive karst spring without significant
oscillations in its discharge. During the driest period of the year, Zaslapnica
becomes a typical rhythmic spring with rare and quite long water eruptions.
In the measurement period the eruption lasted about 6 h (the period of
hydrograph concentration and retardation) and the new eruption started 6 h
after the end of the preceding one). Accordingly, the time which passed
Rhythmic karst springs
43
LEGENDA:
[ l/s ]
180-
OBSERVED 8 August 1985
SIMULATED
165
150135
120
105
90
7560
45
30
15
^ A ^ 1000 m 2
600!
12000
18000
24000
30000
360E0
t
42000
I s ]
Fig. 5 Simulated and observed hydrographs of Zaslapnica rhythmic
spring.
36000
42000
Fig. 6 Simulated hydrographs for Zaslapnica karst rhythmic spring
as a function of different inflow discharges Q0 in reservoir Rff
between the centre of mass of two subsequent hydrographs was about 12 h.
Figure 5 shows the dimensions of the groundwater reservoirs and karst
conduits which were used to adapt the simulated hydrograph to the measured
hydrograph using model simulation. Figure 6 defines, by simulation, five
44
Ognjen Bonacci & Davor Bojanicf
Fig. 7 The Promuklica M and Z springs (12 July 1965) (taken by
D. Gavrilovié).
LEGEND :
OBSERVED ( M SPRING ) fiugust 1960
OBSERVED ( Z SPRING ) Rugust 1960
Q [ 1/s ]
0
1800
3600
5400
7200
9000
10800
+ [ s ]
Fig. 8 Simulated and observed hydrographs of Promuklica M and
Z springs.
different hydrographs of the Zaslapnica spring depending upon five different
discharges, QQ, into the reservoir, Ry It can be noted that by increasing the
inflow discharge, the time when single rhythmic hydrographs appear is
decreased, the emptying by siphon action becomes more frequent and the
hydrographs have a greater volume. When the discharge, QQ, exceeds the
value of 0.150 m3 s"1, the functioning of the Zaslapnica rhythmic karst spring
practically stops.
The rhythmic karst spring Promuklica (Fig. 7) is a special rhythmic
spring which consists of two openings defined as M and Z. Spring M has a
greater capacity and is located 200 mm above spring Z. The springs are 2 m
apart. It should be noted that 4 m below these two rhythmic springs there is
a permanent spring. According to PetroviC (1981), during high groundwater
levels, spring Z functions continually as a rhythmic spring but with changeable
outflow discharge. At the same time spring M functions as a rhythmic spring
with regular intervals. During the dry periods, when the groundwater levels
Rhythmic karst springs
45
15
14
OBSERVED ( M SPRING ) November I960
OBSERVED ( Z SPRING ) November I960
SIMULATED l M SPRING 1
SIMULATED ( Z SPRING Î
RESERVOIR
2
13
A? = 3 mz
12
H
A , = 6.5 m 2
IB
H5*i-2
98-
tQ,
76
-> , A - = 5 m '
.TIT H5 + 0.4n
543-
RESERVOIR 1
O.0-1Q51 /s , , A , i 12.5m2 ; I, - 10 m ; d, - 0.095 m
H2 - H 3 -- 1.0m ; H 2 " H3 - 3.0 m
L.L
T4zH 5 *Q2m^ H
015m
„
Md 2
= 0.10m
f
^4—J-j
M,
^H5+0.1m)^^;:H5-0.2n
2-
zd 2
=0.036 m
- 1 2 = 60 m
360B
720B
•t
Fig. 9
Z
>••-
90KZ
s s :
Simulated and observed hydrographs of Promuklica M and
Z springs.
are low, spring Z operates rhythmically, whereas spring M dries up for several
days, even for a whole month, and then has the characteristics of a periodic
spring.
The simulation used the data measured by VujisiC in 1960 on two
occasions, cited in papers by PetroviC (1981) and Gavrilovié (1967). It should
be noted that the measurement accuracy was not high; however, the simulation was attempted using the model presented in Fig. 3. The simulation was
performed for the two stages of water level, and the results are presented in
Figs 8 and 9. It was concluded that a pipe leaving reservoir R2 branches into
two pipes near the springs: one of them leads to the exit of the M spring,
and the other to the exit of the Z spring. The dimension of reservoir R2,
which is changeable in height, and the dimensions of these pipes, are plotted
in Fig. 9. The comparison of the measured and simulated discharges given in
Fig. 9 shows that the periodic functioning of the hydrograph is permanent,
but the maximum discharges change in time. This can be explained by the
changeable discharge QQ. The form of the reservoir and the characteristics of
the karst conduits given in Fig. 9 were used to simulate the hydrographs in
Fig. 8, with Q0 = 6.7 1 s"1; it was also established that there are losses from
the siphon pipe Q1 amounting to 55% of the overflow quantity emptied by
the siphon.
Regarding the functioning of the rhythmic spring based on the model
presented and sensitivity analysis, the following should be stated. The underground inflow, Q0, determines the frequency of the hydrograph appearance at
Ognjen Bonacci & Davor Bojanic'
46
the spring. The volume of the spring hydrograph depends upon the volume
of the reservoir, Rv The characteristics of the siphon pipe, while it is
functioning as a spillway, form the beginning of the rising part of the
hydrograph. A sudden rise of the hydrograph occurs at the moment when
the air is emptied out of the siphon pipe, i.e. when it starts functioning as a
siphon. The hydrograph shape, during the concentration period, depends
mainly upon the diameter, d, and upon the height difference, H^ - H^. The
shape of the hydrograph peak is a function of the discharge through the
siphon towards the end of the reservoir R^ emptying, and it also depends
upon the reservoir R2 surface at that moment. The recession part of the
hydrograph depends upon the reservoir R2 surface. The time of the
integration interval, At, does not significantly influence the shape of the
hydrograph until it is a maximum of 20 times shorter than the wave duration.
The contribution of the other parameters in the formation of the hydrograph
shape is of the order of magnitude of 5%.
CONCLUSION AND DIRECTIONS FOR FURTHER WORK
The paper suggests a model of the functioning of rhythmic karst springs. This
model was used to perform the simulation of the functioning of three
different types of such springs whose hydrographs were defined by measurement. The model presented showed that it can be widely applied: thus it can
be concluded with high reliability that the model displays the general characteristics of a real system. In addition to the satisfactory results achieved so
far, it is still an open question whether the model presented can duplicate the
flow in other situations. It is believed that the model is suitable in situations
when turbulent conduit flow is dominant and when the function of the
siphon is of primary importance for the transportation of water from reservoir
1 towards the outflow opening of the spring. Since such a hydrological and
hydrogeological state does not exist permanently, it is evident that, in other
situations, which primarily depend upon the groundwater levels in the spring
hinterland, the model presented cannot be used to achieve satisfactory
results.
An interesting question is the uniqueness of the parameters. They are,
in a certain sense, "provoked" by the scheme of the position of the reservoir
and the siphon, as given in Fig. 3, and by the numerical requirements for an
agreement between the observed and simulated hydrographs. It is necessary
to stress the influence of the measurement accuracy of the discharge from the
spring (which in such situations is not high) on the accuracy of parameter
definition. The results presented have shown that this is the correct approach
in solving the complex problems of the functioning of rhythmic karst springs.
The main value of this model is that it makes it possible to define the
dimensions of the reservoir, the connecting pipes and the siphon.
This is the first time a spring hydrograph has been duplicated by a
model of this type (according to the authors' knowledge).
Further work on improvement to the model should include the groundwater levels as boundary conditions. It was not possible to do so in this case
47
Rhythmic karst springs
since the necessary measurement data were not available. Evidently, a more
complex model will require a greater number of measurement data, so that it
cannot be verified only according to the measurements of the outflow
hydrograph of the spring. It should be noted that rhythmic springs appear
exclusively in karst terrains, and that further analyses should treat separately
the diffuse type flow and the conduit type flow. The model presented in this
paper used only the principles related to the conduit type flow, and the
diffuse type flow was assumed by the inflow, Q0, into reservoir Rt or by
inflows and outflows, ±QV into/from reservoir R2. In the following phase it
will be necessary to develop the modelling of the flow process with the
presence of a great number of reservoirs and siphons connected in parallel
and/or in series.
REFERENCES
Atkinson, T. C. (1986) Soluble rock terrains. In: A Handbook of Engineering Geomorphology, (ed.
P. G. Fookes & P. R. Vaughyn), Survey University Press, 241-257.
Bôgli, A. (1980) Karst Hydrology and Physical Speleology. Springer Verlag, Berlin.
Bonacci, O. (1987) Karst Hydrology. Springer Verlag, Berlin.
Casteleyn, J. A., Van Groen, P. & Kolkrnan, P. A. (1977) Air entrainment in siphons: Results of
tests in two scale models and an attempt at extrapolation. Delft Hydraulics Laboratory
Publ. no. 187.
Gavrilovid, D. (1967) Intermitentni izvori u Jugoslaviji (Intermittent springs in Yugoslavia).
Glasnik Srpskog Geografskog Drustva XLVII (1), 13-36.
Gavrilovid, D. & Gavrilovid, L. J. (1985) Intermitentni izvor Zaslapnica (Intermittent spring
Zaslapnica). Glasnik Srpskog Geografskog Drustva LXV (2), 35-41.
Katzer, F. (1909) Karst und Karsthydrographie. Zur Kde, Balkanhaldbinsel 8, Sarajevo.
Petrovid, J. (1981) Udvojena potajnica Promuklica (Double karst intermittent spring
Promuklica). Glasnik Srpskog Geografskog DruStva LXI (1), 333-43.
Received 26 March 1990; accepted 30 M y 1990