Hydrology of Natural and Manmade Lakes (Proceedings of the Vienna Symposium,
199 IAHS
" "Publ.
" no. 206,1991.
August Ï991).
Measuring and modelling wind induced flow in shallow lakes
J. SARKKULA
Water and Environment Research Institute,
National Board of Waters and the Environment,
PB 250, SF-00101 Helsinki, Finland
J. JOZSA & P.BAKONYI
VTTUKI, Water Resources Research Centre,
H-1453 Budapest, Pf. 27, Hungary
ABSTRACT As a continuation and improvement of the
past measuring and modelling activity, extended
current measurements and joint numerical modelling
were carried out in three shallow lakes in Hungary
and in Finland, focusing at the near shore flow
phenomena. The main goals of the investigations
were to explore wind induced flow characteristics
and the demands on wind input data for correct
flow and related transport modelling. The systematic behaviour of the lake currents in different
wind conditions at the lakes was observed with
recording current meters. Comparison between the
modelled and measured flow clearly showed that a
spatially uniform wind stress field over the modelled lake area results in non-realistic model
output. The use of corrected wind stress values,
related to wind speed and surface roughness estimates, gave an improved agreement between modelled
and measured currents. The realistic flow simulation is then of great importance for better estimation of water exchange and pollutant trasport.
INTRODUCTION
The computation of wind induced flow fields is an essential
part of transport and water quality modelling in lakes and
coastal waters. The models are a tool e.g. for planning
water pollution control measures and combating accidental
oil and chemical releases.
This paper deals with a Finnish-Hungarian research project where one of the main goals has been to improve the
reliability of the computed flow fields on the basis of a
series of field measurements.
The results from Lake Balaton (Hungary) indicated that
one of the most important points in shallow lake modelling
is the generation of a realistic wind stress field as input
data, in order to produce a correct model flow pattern
(Jôzsa et al., 1990). In the present paper an analysis of
the results from two other shallow lakes, Lake Pyhajarvi in
219
/. Sarkkula et al.
220
Finland and Lake Fertô-Neusiedlersee at the Austro-Hungarian
boarder are given. The applied current measurement technique
is also described.
INTERACTION BETWEEN MEASUREMENTS AND MODELLING
The work has proceeded in an interactive way between model
computation and verification of the results in the field.
Two series of current measurements were carried out in
Lake Pyhajârvi, the first one in autumn 1986 and the second
one in autumn 1987. In the measurements Anderaa recording
current meters RCM4S and RCM7 were used. Figure 1 shows the
set up of the current measurement points for a six week
period in 1986. The observations aimed at detecting the
large scale eddies induced by prevailing wind events. In
autumn 1987 the measurements concentrated between point 3
and the shore line in order to verify the near shore model
flow. The average depth of the lake is 5.4 metres. The
bottom is flat, except a narrow deep area at the western
shore. One current meter was deployed at each point at the
depth of 2 metres except points 2 and 3 where the vertical
structure of the flow profile was checked with an additional
current meter in a deeper layer.
FIG. 1 Bathymetry of Lake Pyhajârvi and measurement points
in autumn 1986.
The results clearly showed that one can make reliable
conclusions about the properties of the wind induced flow
pattern. Fig. 2 shows the time series of the flow component
along the sho're at point 3 (2 m depth) compared with the
corresponding regression values calculated on the basis of
221
Measuring and modelling wind induced flow
correlation analysis between wind and flow components. In
this case 87% of the variation of the flow component was
explained by the south-north wind component only. The
analysis was made with daily mean values and it also showed
that the flow .at point 3 was always directed against the
south-north wind component, thus compensating the windward
water transport in shallower areas.
Positive flow direction in Fig.2 is to the north-northwest (330°) and the regression flow values (m s"1) are based
on the regression equation v=-0,027+0,042WN, where WN is the
wind component (m s"1) from the north. Time lag between wind
and flow is 6 hours which gave the optimum value 0.87 of the
correlation coefficient squared.
The dependence between wind and flow was high at all
measurement locations. The explenation degree of the main
flow component varied between 46 and 92%, 72% beeing the
average.
15
25
SEPTEMBER
5
15
OCTOBER
FIG. 2 Variation of daily mean values of the flow component
to north-northwest (thick line) and corresponding regression
values based on analyzed wind and flow dependence (thin
line) in Lake Pyhâjârvi 12 September - 22 October 1986,
point 3, 2 m depth. Time lag between wind and flow is 6
hours.
No significant differences compared to the surface layer
could be detected in flow behaviour at the deeper measurements, 4.4 m at point 2 and 7.7 m at point 3. The difference
in flow direction was predominantly less than 20° and flow
velocity 20-30 % smaller in deeper layer. The uniformity of
J. Sarkkula et al.
222
the flow profile justifies well the use of a 2-dimensional
model described briefly below.
Wind induced currents were calculated in this work by
a 2-dimensional depth-integrated flow model (Bakonyi &
Jôzsa, 1988), based on the complete shallow water equations.
The solution is achieved with an ADI finite difference
method on orthogonal staggered grid. In areas of special
interest locally refined grid can be applied to obtain finer
scale resolution. For Lake Pyhâjârvi a grid with 500 square
cell size was used.
Discrepancies between measured and modelled flow fields
appeared first of all in the vicinity of the southwestern
shore and in the simulation of the high velocities measured
at point 3. The calculation with spatially uniform wind
stress over the lake gave much too slow current velocities
at point 3, furthermore, a windward model flow in the
gridpoints closest to the southwestern shore. According to
the measurements this is not the case during southern winds.
The computed steady-state flow field is shown in Fig .3.
An improved fitting between modelled and measured flow
was achieved when a fetch dependent wind stress field over
the lake was introduced. The increasing stress is supposed
to be related with higher wind velocities and bigger waves
on the downwind side of the lake. Fig. 4 shows the computed
flow field induced by a southern wind event, corresponding
to the measurements on 19-20 October 1986, shown in Fig. 3.
During that period the wind was blowing constantly from the
south at a speed of 3-8 m s"1 (average 4.7 m s"1). At point
3 currents to the south at an average speed of 28 cm s"1 (2
m depth) and 19 cm s"1 (7.7 m depth) were observed. The
modelled current velocity in the vicinity of point 3 rose
from 6 to 12 cm s"1 when the wind stress values starting from
zero at the sheltered southwest shore increased linearly to
the full constant value over a 2 km fetch. The new current
velocity values were in much better agreement with the
observations, taken into account the vertically and
horizontally averaged character of the model results.
Wind stress modification also affected the near shore
currents producing an unidirectional flow zone at the
western shore, proved by the measurements.
Furthermore, the measurements showed that the anticlockwise circulation induced by southern wind reaches point
1 at the northern end of the lake, correctly described in
Fig. 4.
CURRENT MEASUREMENT TECHNIQUE IN SHALLOW WATERS
Current measurements in shallow lakes cause special problems
for instrument deployment technique.
In this work currents were measured with Aaderaa RCM4S
and RCM7 recording meters, equipped with rotors designed for
measurements in the wave zone. The rotor itself has been
found to have low susceptibility to overread velocity values
in the presence of waves (Hammond et al., 1986).
223
Measuring and modelling wind induced flow
2-D DEPTH-INTEGRARED FLOW MODELLING OF LAKE PYHAJARVI
WIND-INDUCED STEADY-STATE DEPTH-AVERAGED VELOCITY FIELD
SPATIALLY CONSTANT WIND STRESS FIELD
WIND SPEED : 5 m/s
—> 10 cm/s
1 km
FIG. 3.
2-D DEPTH-INTEGRARED FLOW MODELLING OF LAKE PYHAJARVI
WIND-INDUCED STEADY-STATE DEPTH-AVERAGED VELOCITY FIELD
SHELTERING IN WIND STRESS FIELD ALONG THE S-W SHORE
WIND SPEED : 5 m/s
^ 1 0 cm/s
1 km
FIG. 4.
J, Sarkkula et al.
224
The instruments are normally moored with the help of an
anchor and subsurface floats. It means, however, that the
currents in the surface layer down till 1.5 metres can not
be measured. It is because the direct wave action on the
floats may cause errors in velocity and direction readings.
This indicates that in very shallow water, say less than 3
metres, this kind of deployment can not be used. Two of the
study lakes, Lake Balaton (Hungary) and Lake Fertô
(Neusiedlersee) at the Austro-Hungarian boarder belong to
this class. Typical depth in Lake Balaton is 2-3 m and in
Lake Fertô 1.2-1.5 m. In these cases wooden piers hammered
in the lake bottom were used. The instruments were hanged
from a console fixed in the piers. The structure was
balanced by a weight underneath the instrument, penetrating
tightly in the soft sediments.
The deployment method proved to be proper for very
shallow waters. An example from Lake Fertô in spring 1990
is given in the following. Results are shown from a point
sited at the western shore of the main basin of the lake,
indicated as No. 4 in Fig. 5. The depth at this point was
1.4 m and the measuring depth 0.7 m. The measurements were
made RCM7 meter using 10 min sampling interval.
FIG. 5 Measurement points in Lake Fertô in spring 1990.
Fig. 6 shows the half an hour averaged wind and flow
vector time series at points 2 and 4, respectively. Fig. 7
presents the behaviour of the flow component along the shore
line computed as vector average over 10 minutes and one
hour. The flow variation dominated by wind forcing was
225
Measuring and modelling wind induced flow
successfully measured. The wind speed measured over the lake
surface varied between 2 and 10 m s"1 and direction between
north and west. The instrument behaved in a very stable way
and did not show any sudden changes either in speed or in
direction. This implies that the flow direction is
vertically uniform in very shallow waters during moderate
or high wind speed, observed also in Lake Balaton (Jôzsa et
al., 1990). No signs of wave induced overestimation of the
flow velocity are included in the time series, even in the
presence of strong winds and related waves, since the
highest measured flow velocity was not more than 15 cm s"1,
related to 10 m s"1 wind speed.
Fig. 6 shows that near the reed shore the developed
currents are directed upwind whenever the shore area is in
wind shelter.
4*
Aw..,./
4.
IP
N
|\\,„ ,.Uu.,SCALE
On/s
WATER 1
crc/s
FIG. 6 Half an hour averaged vector time series, point 2
wind, point 4 flow. 28 April - 1 May 1990.
FIG. 7 Flow component to north-northwest in point 4 in Lake
Fertô. 28 April - 1 May 1990. 10 min averages (thin line)
and 1 hour averages (thick line).
/. Sarkkula et al.
226
It should be also pointed out that only very limited algae
growth appeared on the instrument surface, expected due to
the high nutrient concentrations prevailing in the lake.
CONCLUSIONS
The influence of wind stress field as input data in modelled
shallow lake circulation was investigated. The results were
compared with recorded flow data. It was concluded that a
realistic, spatially non-uniform wind stress field over the
modelled lake area has to be generated to obtain quantitatively and even qualitatively correct results. The qualitative errors mainly appear in the near shore areas. The
measurements carried out in the three study lakes focused
on the near shore phenomena and showed clearly that an
upwind water transport is regularly developed very close to
the wind sheltered lake shore. The tendency in numerical
models is to produce a downwind flow in the shallowest
areas, provided a spatially uniform wind stress field is
applied.
REFERENCES
Bakonyi, P. & Jôzsa, J. (1988) A coupled finite difference fluid element tracking method for modelling horizontal
mass transport in shallow lakes. In: Modelling Surface
and Subsurface Flows (Proc. VII. Int. Conf. Comp. Meth.
Water Res., Cambridge, USA, 1988), vol. 1, 289-294.
Elsevier, Amsterdam / CMP, Southampton.
Hammond, T.M., Pattiaratchi, C.B., Osborne, M.J. & Collins,
M. (1986) Field and flume comparisons of the modified
and standard (Savonius-rotor) Aanderaa self-recording
current meters. Dt.hydrogr.Z. 39, 41-63.
Jôzsa, J., Sarkkula, J. & Tamsalu, R. (1990) Calibration of
modelled shallow lake flow using wind field modification. In: Computational Methods in Surface Hydrology
(Proc. VIII. Int. Conf. Comp. Meth. Water Res., Venice,
Italy, 1990), 165-170. CMP, Southampton / SpringerVerlag, Berlin Heidelberg.