On the Distribution of Blue-Green Algae in Lakes: Wind-Tunnel Tank Experiments

On the Distribution of Blue-Green Algae in Lakes: Wind-Tunnel Tank ExperimentsAuthor(s): Paul A. Hutchinson and Ian T. WebsterSource: Limnology and Oceanography, Vol. 39, No. 2 (Mar., 1994), pp. 374-382Published by: American Society of Limnology and OceanographyStable URL: http://www.jstor.org/stable/2838337 .

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Limnol. Oceanogr., 39(2), 1994, 374-382 ? 1994, by the American Society of Limnology and Oceanography, Inc.

On the distnbution of blue-green algae in lakes: Wind-tunnel tank experiments

Paul A. Hutchinson Research School of Earth Sciences, Australian National University, GPO Box 4, Canberra ACT 2601

Ian T. Webster CSIRO Centre for Environmental Mechanics, GPO Box 821, Canberra

Abstract

In this study, we demonstrate in the laboratory that the distribution of weakly floating algae in wind- driven, steady state, two-dimensional flow in a water body is in accord with theoretical predictions. We confirm the theoretical results that the concentrations of algal colonies of uniform flotation speed should increase exponentially in the downwind direction and that the length scale of this concentration variation should be inversely proportional to the colony flotation speed. We observed accumulation of a surface film at the downwind shore of our tank. This film dampens surface waves, inhibits surface mixing, modifies the nearshore water circulation, traps the algae, and allows the algae to accumulate into mats.

In a recent paper, Webster (1990) presented a theory to explain how wind-induced flows and turbulence combine to determine the horizontal and vertical distributions of a weakly floating (or weakly sinking) phytoplankton population in a lake. He assumed that the distribution of phytoplankton under steady state conditions in a lake was determined by a com- bination of vertical mixing, horizontal transport by the mean wind-driven circulation, and the flotation tendency of the individual colonies or cells. A broadly similar problem con- cerned with distributions of weakly buoyant particles near a coast has been considered theoretically by Smith (1991). Webster (1990) predicted that the concentration of a phytoplankton population having a uniform, posi- tive flotation velocity would exponentially increase toward the downwind end of a flat- bottomed lake. Further, his theory asserted that the length scale of concentration variation (his parameter D) is directly proportional to windspeed and water depth and inversely proportional to flotation velocity.

The measurements of the distribution of chlorophyll a in a small Welsh lake by George and Edwards (1976) supported the model predictions that the degree of phytoplankton aggregation toward the downwind end of a lake decreases with increasing windspeed. Unfor- tunately, George and Edwards did not measure plankton flotation rates, so it was not possible to test the quantitative validity of the theoretical expression for the length scale for phytoplankton variation. However, Webster

(1990) showed that the observed length scales implied flotation velocities considered reason- able for the phytoplankton species that were present.

In February 1992 a bloom of Microcystis aeruginosa in Lake Burley Griffin, Australian Capital Territory, provided us with an oppor- tunity to test features of Webster's (1990) model in our laboratory. Samples of the M. aeruginosa bloom were collected and placed in a water-filled tank in the floor of a wind tunnel. We were able to measure the concentrations of algal colonies along the length of this "lake" as "wind" blew across its surface and so test the dependence of concentrations on downwind position and on the flotation rate of the algae. During the course of these experiments, it became apparent that the accrual of a film on the water surface altered water circulation and caused the algae to accumulate into scums. These surface films could very well play a sig- nificant role in algal distribution dynamics in larger lakes as well.

Experimental equipment The experimental facility consisted of a wa-

ter-filled, glass-walled tank (5.5 m long, 1.0 m wide, 0.15 m deep) installed on the centerline of a 16-m-long wind tunnel (Fig. 1). The tank base rested on the tunnel floor and the airflow was raised to the height of the tank by a gravel- covered false floor. Hot-wire anemometry has shown that a constant stress boundary layer 10 cm thick developed before the airflow reached the water surface. The wind tunnel,

374



Laboratory algal distributions 375

h ?Wind

fn 15.5 m Water-filled k-5-

tank Side

15cm

ti [ - - -. Wcamera

End Light box

Fig. 1. Schematic diagram of the water tank installed in the wind tunnel. The light box and camera were used to measure the distribution of the algae.

designed for atmospheric boundary-layer studies, is of the open-return blower type and has a working cross-section 1.8 m wide by 0.75 m high. Tunnel details are given by Mulhearn et al. (1976), except that the working section length has been extended to 16 m.

The horizontal distribution of the algal colonies was measured with an optical technique. Twin 1,500-W linear halogen lamps, mounted end to end in a metal cabinet and placed beneath a slotted aperture, produced a bright sheet of light. The cabinet was placed below and on the centerline of the tank. The light projected upward and illuminated algae within a region 1 cm wide and 60 cm long (Fig. 1). Photo- graphs of the algae were taken normal to the light sheet with a 35-mm SLR camera placed at the tank sidewall. The camera was equipped with a 50-mm fl.4 lens and high-speed Kodak TMAX 3200 ASA film. The light source and camera were shifted to obtain photographs at

different positions in the tank. Photographic negatives were digitized with a film scanner to a spatial resolution of 1 5 ,um per pixel, pro- ducing a half-tone (gray) image. We counted and sized the colonies by converting the half- tone images into line (black and white) images by applying a threshold light level. This level was chosen because it was high enough so that the colonies could clearly be distinguished from noise in the line image, but not so high that a colony's image was greatly reduced in area. The total range of colony sizes was divided into a number of smaller subranges, and the number of colonies in each subrange was counted for each image. Counting was performed by computer analysis.

Experimental procedure During the experiment, the free-stream

windspeed in the wind tunnel was set to 5.3 m s-1. The height of the tunnel roof was ad-



376 Hutchinson and Webster

justed so that this windspeed was constant over the full length of the tank. DISA (type 55P61 X-array) hot wires were used to measure the stress exerted by the wind on the water surface (by the eddy-correlation method) 5 mm above it (Tseng et al. 1992). The value of stress changed as the airflow adjusted to the new surface conditions, increasing from 29 mPa at 0.5 m downstream from the transition between the gravel-covered surface and the water to 37 mPa at 5 m downstream. The average value of the stress was 33 mPa.

Before the experiments, quantities of Mi- crocystis were collected from the nearshore regions of Lake Burley Griffin and stored in lake water in a darkened cool-room for 1 d. Thirty minutes after starting the wind, 800 ml of loosely packed algae with a small amount (-500 ml) of lake water were released at the upwind end of the tank. Photographic images for algal concentration determinations were obtained at fourteen positions along the length of the tank at hourly intervals over 7 h. A photographic pass along the tank took 20 min.

Observations Features of the circulation and turbulence

in the tank were ascertained from movements of the algal colonies in this experiment and from the movements of small particles of var- ious types in other experiments at similar windspeeds. The surface flow in the tank consisted of a thin (1-3 mm) laminar shear-layer at the upwind edge of the tank that gradually thickened downwind. At 0.6 m from the upwind edge of the tank, the shear layer became unstable and turbulent and suddenly thickened (1-3 cm). Farther downwind, the surface flow was turbulent and about a third to a half the depth of the tank in thickness; beneath the surface flow, a less turbulent return flow was evident. Every 3-6 s, parcels of fluid appeared to be ejected from near the surface downward into the interior of the flow.

The wind produced steep, short gravity waves at all locations downwind of the upwind edge of the tank, except in the first meter where only small capillary waves were evident. As the waves propagated downwind, they grew in amplitude and wavelength, acquiring signifi- cant cross-wind structure halfway along the tank and attaining maximum wavelength (5- 7 cm) and height (3-4 mm) at the downwind

end. The mean wave period at the downwind end was 0.2 s. The gravity waves developed finer scale (parasitic) capillary waves downwind from their crests (Fig. 2).

From the flotation measurements, all the algal colonies were determined to be positively buoyant. In the wind-tunnel experiment, the algae were actively mixed through most of the tank by turbulent water motions. Colonies that reached the water surface were transported rapidly downwind for 3-6 s before they were removed from the surface by turbulent ejections. Twenty minutes after release, the algae had dispersed throughout the tank and were more concentrated at the downwind end; the large colonies, 2-3 mm in diameter, showed strong downwind accumulations. Algal colonies of smaller size showed a more even distribution along the tank.

Soon after the algae were released into the tank, a surface film began to collect adjacent to the downwind beach (see discussion). The length of the film changed, extending 50 cm away from the shore 5 min after the experiment began to 100 cm after 2 h. Sharply crested surface waves, propagating down through most of the length of the tank, became smooth crested upon entering the film. Para- sitic capillary waves, evident on the downwind side of sharply crested waves, disappeared in the zone covered by the surface film. Before the film appeared, the downwind mean circulation reversed close to the end wall, and strong turbulence was created at the surface near the end wall. However, the film modified the horizontal downwind mean circulation, re- versing it near the edge of the film. There was no sign of active generation of turbulence beneath the film.

Turbulent eddies beneath the film appeared to have diffused from upwind of the film edge. Algae, transported beneath the film by the turbulent eddies, gradually floated toward the film and became trapped there. Ejections of parcels of near-surface fluid from beneath the film were not apparent. Colonies trapped in the film gradually moved through the film to accumulate in a dense mat adjacent to the beach (Fig. 2). The size of the mat increased with time. After 40 min, the mat extended 1 cm away from the shore (measured at the center of the tank); 80 min later it had increased to 6 cm.




beach turbulence wind circulation

15cm Q ,rj<3) (9 Q C (I3 ELEV.

.;ZS;, ; ; 1 . . . . ...-.-..

(V ~~~~~PLAN s.urae fi.. l Fig2 levtin.nd,la.vew-f,hefeaurs'bseve,a,th,dwninden'o-th-tnk ,,,, ..,-, W ............. J -

,,..,.,,,,,,,,,.,,,,..,,D ,,.,,,............. ........... F

g , , |

~~~~~~~~~~~~~~~~~~~.... . . . . . ...

X.{ .; . -., -. -,, - - -

\.. . . . . . . . . . . . . . . . . . . .

\algal mat Y ~~~~steep, short gravity waves surface film

Fig. 2. Elevation and plan view of the features observed at the downwind end of the tank.

Algalflotation rates We used a novel technique, developed from

the work of Martin and Nokes ( 1988), to measure the flotation velocity of the algae. Martin and Nokes reported on a theoretical model for the settling of crystals in subterranean magma chambers and verified their theory by observ- ing the settling of spherical beads in turbulent thermal convection.

Our technique uses the turbulent mixing generated by a horizontal grid that oscillates vertically to maintain a uniform distribution of floating colonies in a water-filled tank (Fig. 3). The tank was made of clear Plexiglas (60 cm high, 25-cm square); the grid was made from 1-cm-square Plexiglas bars spaced 5 cm apart. During operation of the grid tank, the colonies floated up through the turbulence and settled onto the water surface. The mean height of the grid, oscillation frequency, and stroke were adjusted so that colonies reaching the water surface could not be dislodged and mixed back into the water. Colonies were trapped at the surface, and the number of colonies in the water column decreased with time.

The theoretical equation describing the change in the concentration of algal colonies,

c, of a particular flotation velocity, F, is given by

c(t) = Coexp ( FI) (1)

C0 is the number of colonies in the interior at time t = 0, and H is the depth of the tank (Martin and Nokes 1988).

To verify this technique, we filled the tank to a depth of 32 cm with filtered city water and increased the water density to 1,045.16 kg m-3 by adding NaCl. Unexpanded spherical polystyrene particles were added to the water. The particles were 0.42-0.50 mm in diameter and had a density of 1,040.9 kg m-3. The grid was set to oscillate at 4 Hz at a mean height of 4 cm above the tank bottom and with a vertical stroke length of 4 cm. This choice of grid parameters produced a uniform distribution of beads throughout the tank, but the turbulence was not vigorous enough to dis- lodge beads from the water surface once they had collected there.

A similar optical technique to the one used to measure the distribution of the algae in the wind-tunnel tank was used to measure the




Water-filled

AI, tank

60cm

Light box

J Oscillating ELEV grid

25cm

25cm =O

PLAN

Camera

Fig. 3. Schematic diagram showing plan and side views of the grid tank.

change with time in the concentration of beads in the grid tank. The light cabinet projected a sheet of light through the side of the grid tank and photographs were taken at 1-min intervals. Photographs were then digitized and the beads counted by computer analysis. Figure 4 shows that bead concentration was reduced exponentially with time. With Eq. 1, the fitted line yields a flotation velocity estimate of 0.395 mm s-1. We calculated the flotation velocity for the mean diameter of 0.46 mm with the empirical equation of Morsi and Alexander (1972) and obtained a value of 0.386 mm s- 1. This empirical value is within 3% of the experimental value, an error similar to that obtained experimentally by Martin and Nokes (1988).

1.0

X

0.5

0.1~~~~~

0*1 0 t | l l ,Sl

0 200 400 600 800 1000 1200 1400 1600 1800

Time (s)

Fig. 4. Decay in bead concentration with time. Fitted line yields a flotation velocity estimate of 0.395 mm s- a 3% difference from the empirically determined value.

A quantity of algae (50 ml, densely packed) drawn from the same batch used in the wind- tunnel experiment was used to determine the flotation rates of the algal colonies. The flotation measurements were contemporaneous with the wind-tunnel experiments. The grid frequency was set to 1 Hz; the grid stroke and mean grid height remained at 4 cm. A series of photographs was taken over a period of 4 h and later digitized to a spatial resolution of 134 4Am pixel-1. The photographs showed a range of colony areas. Because we expected the colony flotation rate to depend on colony size, the flotation rate analysis was performed separately on each of seven subranges of colony area. For each photograph, the number of colonies in each subrange was counted. Figure 5 shows an example of the decay in colony concentration.

The flotation velocity for the complete range of imaged colony sizes plotted vs. the mean of each subrange image area is shown in Fig. 6. The flotation rate increases approximately lin- early with imaged area, but the relationship is not directly proportional. The flotation velocity and size of the algal colonies were suffi- ciently small so that their velocity could be described by Stokes' law; i.e. the flotation velocity is proportional to the square of the colony diameter (or circular colony area, A) and proportional to the difference between the density of the colony, p, and the water density, p' given by




1.0 00

0

0

0.5

0~~~~~~~~~~~ 0 0~ ~ ~~~~~

0.1 Z | } | i | | 0 2000 4000 6000 8000 100Q0 12000 14000 16000D

'rime (s)

Fig. 5. Decay in colony concentration for colonies having an image area of 0.30 MM2 (17 pixels). Fitted line yields a flotation velocity of 0.053 mm s-1.

2= gA(p'-p),- . (2) 9-r

Here, ,u is the water viscosity and g the accel- eration due to gravity. Equation 2 shows that the graph of flotation velocity vs. colony area should go through zero. We obtain Stokes' law if we assume that the physical colony area is equal to 0.225 MM2 added to the imaged colony area. Applying Eq. 2 to these modified flotation results gives an estimate of the reduced density (p'-p) = 0.145 kg m-3.

The reason for the difference between the physical colony and imaged colony area is unknown, but we hypothesize that it is due to one or more of the following imaging limita- tions: grain size of the photographic emulsion, spatial digitization resolution, diffraction effects, photographic depth of field, and contrast reduction due to backscatter from the very small colonies.

Algal distributions The following analysis of cgal distributions

was carried out on data collected 30 min after the beginning of the experiment. By that time, transients in concentrations associated with the beginning of the experiment were deemed to have disappeared.

The theory of Webster (1990) predicts that the depth-averaged concentration variation, c, for algal colonies of a particular flotation ve-

0.10

008

__006

E E

LL 004

002

0.00 00 0.2 0.4 0 6 0 8 1.0

Physical colony area (mm2)

-0.225 0.000 0 225 0 450 0.675

Imaged colony area (mm2)

Fig. 6. Measured flotation velocities of the algal colonies used in the experiment.

locity along a lake or our tank should be given by

c = Coexp(-x/D). (3)

CO is the concentration at the downwind end (x = 0), x is the distance from the downwind end, and D the length scale of concentration variation. D is calculated from flotation velocity F, windspeed at 10-m height Ua, and water depth H as

D 9.0 x 10-4UaH/F. (4)

We applied Eq. 4 separately to subranges of colony area (13 in this case), as we did with the measurements of flotation velocities. The experimentally determined length scale and flotation velocity for the ith subrange are de- noted by D, and Fi. For each subrange, the measured distributions of algal colonies along the tank could be represented by an exponen- tial function as in Eq. 3. Figure 7 shows an example of the measured concentrations vs. downwind distance for the fifth (i = 5) smallest imaged subrange. Also shown is the line given by Eq. 3.

Figure 8 shows the inverse length scales, Dj1, plotted against the mean imaged colony area of each subrange. The plotted data suggest a relationship between these two parameters which is linear but, like the flotation measure-




1.0 S

S

0.5

S

0.3 l l 0 1 2 3 4 5

x (m)

Fig. 7. An example of the horizontal, variation in the number of measured colonies having an image area in the range (D,) 0.70-0.77 mm2 (53-58 pixels). Fitted straight line yields an experimental length scale of 0.256 m-1.

ments, not directly proportional. We expect that a colony of zero area would have a zero flotation rate and would therefore necessarily be evenly distributed throughout the tank. D for zero colony area should be infinite. The measured relationship between D and colony area intersects at the origin if we assume that

040

030

E 0 20

0 10

000 I I 000 025 0.50 075 100 1 25

Physical colony area (mm2)

-0125 0125 0375 0625 0875 1 125

Image colony area (mm2)

Fig. 8. Inverse of the experimental length scale of concentration variation for each of the measured colony areas. Physical colony area explained in text.

0.60

020 .5

040 - 0

E 030~~~~~ S

S

0 20

0 10-

000 000 0.05 0 10 0 15 0.20 0.25

F (mms-1)

Fig. 9. Observed and theoretical relationships between the horizontal length scale of the algae and their corre- sponding fotation velocity. Dashed line is the theoretical relationship given by D = au*H/F, where a = 0.75. Solid line is a line of best-fit to the observations, modeled by this same relationship, but with a = 0.49.

the physical colony area is larger by 0.125 mm2 than the imaged colony area. Note that the difference between our estimated physical colony area and the imaged colony area varies between the flotation and algal distribution measurements. The variation is caused by the different light levels and distances of camera to photographic target used in the two cases.

We can use the transformations between imaged area and true colony area just outlined to combine the flotation data and the algal distribution data and obtain a plot of inverse length scale vs. flotation rate (Fig. 9). We see that D, and F, are inversely proportional to one another as predicted by Eq. 4. This equation assumes a relationship between the surface friction velocity [u* = (r/p)0-5] and Ua, given by Webster (1990) as

u* = 1.2 x 103Ua. (5)

Here, r is the applied stress on the surface due to the wind and p the density of the water. For comparison with the observations presented here, we eliminate Ua from Eq. 4 and use Eq. 5 to give the theoretical expression

D = au*H/F (6)

where a is 0.75.




We substitute our estimate of u* = 5.7 mm s-i, obtained from our measured r = 33 mPa, and our tank depth H = 0.15 m into Eq. 6 and get the theoretical relationship illustrated in Fig. 9. The best fit to the experimental data is modeled by Eq. 6 with the coefficient a = 0.49. The theory of Webster (1990) overestimates a by a factor of 0.5.

Discussion We believe that the results plotted in Fig. 9

give strong support to the principles underly- ing the theory of Webster (1990), although there is a 50% difference between theoretically and experimentally determined coefficients relat- ing D-1 and F. We suspect that most of the difference in the value of coefficient a is due to oversimplification of the parameters of turbulent mixing of plankton and momentum in Webster's theory. In particular, he assumed that the coefficient of turbulent diffusivity, K, is constant throughout the water column, yet it is well known that K is usually a function of distance away from a flat solid boundary (such as the bottom). Likewise, because of the influence of waves, Kis likely to depend on distance from the water surface in the upper part of the water column. Cheung and Street (1988) have shown that momentum transfer and current profiles in the near-surface zone are modified in the presence of waves. Webster and Hutch- inson (1994) present an analysis for algal distributions that accounts for depth variations in K; values of a (obtained from this new analysis) for the wave conditions and the length scales appropriate to our experimental ar- rangement are in accord with our measured value.

Our observations show that algae were con- tinuously removed from the body of our water tank into a mat adjacent to the beach; this makes us question whether we can apply a conservative steady state model to the distribution measurements. This question is ad- dressed by comparing the time rate of change of the concentration term (ac/lt) in the ad- vection-diffusion equation for plankton concentration,

ac+ ua- + F-c = azLOzJ (7) at ax+ dz azaz 7 with one of the other terms in the concentra-

tion balance, such as the advective term, uac/ Ax. Comparison of the volume-integrated concentrations between the first and second tran- sects of the tank allows us to estimate ac/lt for each colony area subrange. Likewise, ac/lx can be estimated from the colony distributions. From these estimates and after assuming a value for the horizontal velocity scale u = 0.02 m s-', we find that

Oc/Ot <0.1,

implying that the algal distributions were in quasi-steady state, and our theoretical as- sumption was justified.

The gradual accumulation of algae into a surface film at the downwind end of the tank was an unexpected feature of the experiments. Surface accumulations of algae extending from the leeward shore of Lake Burley Griffin were also observed around the time of our experiments. Because of the lack of capillary waves throughout the region of accumulation (which extended 10 or more meters from the shore of the lake), we assume that a surface film existed there too. In our experiments, the wind was quite incapable of mixing algae downward from the film, even though vertical mixing was vigorous upwind. We suggest that in lakes such films may represent an efficient mechanism for trapping algae along the windward shore.

The origin and chemical nature of the surface film is unknown. We know that it was not a contaminant contained in the city water, as no film was observed in the tank without the algae. It is certain that the film material was either released by the algae or introduced with the lake water. The turbulence and flow un- derneath the film were what they would be if the film acted as a thin and rigid lid. Never- theless, we believe that there was a slow horizontal motion within the film. Algal colonies were observed to circulate slowly in two sym- metric gyres moving generally downwind in the middle of the tank and flowing upwind along its sides. The algal colonies must have been moving relative to the film, though, because over time these colonies gradually ac- cumulated in a mat along the beach. We suggest that management strategies for dealing with problem blue-greens in natural or man-made water bodies might be based on manipulation




of surface films. Studies of film formation, film composition, and the effects of these films on algal aggregation are areas open to research.

References CHEUNG, T. K., AND R. L. STREET. 1988. The turbulent

layer in the water at an air-water interface. J. Fluid Mech. 194: 133-151.

GEORGE, D. G., AND R. W. EDWARDS. 1976. The effect of wind on the distribution of chlorophyll a and crus- tacean plankton in a shallow eutrophic reservoir. J. Appl. Ecol. 13: 667-690.

MARTIN, D., AND R. NoKEs. 1988. Crystal settling in a vigorously convecting magma chamber. Nature 332: 534-536.

MORSI, S. A., AND A. J. ALEXANDER. 1972. An investi- gation of particle trajectories in two-phase flow sys- tems. J. Fluid Mech. 55: 193-208.

MULHEARN, P. J., H. J: BANKS, J. J. FiNNIGAN, AND P. C.

ANNIs. 1976. Wind forces and their influence on gas loss from grain storage structures. J. Stored Prod. Res. 12: 129-142.

SMITH, R. 1991. Wind-augmented transport and dilution in shallow-water flows. J. Fluid Mech. 228: 549-560.

TSENG, R. S., Y. H. L. Hsu, AND J. Wu. 1992. Methods of measuring wind stress over a water surface-discussion of displacement height and von Karman constant. Boundary Layer Meteorol. 58: 51-68.

WEBSTER, I. T. 1990. Effect of wind on the distribution of phytoplankton cells in lakes. Limnol. Oceanogr. 35: 989-1001.

, AND P. A. HUTCHINSON. 1994. Effect of wind on the distribution of phytoplankton cells in lakes rev- isted. Limnol. Oceanogr. 39: 365-373.

Submitted: 11 December 1992 Accepted: 16 June 1993 Amended: 14 July 1993



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On the Distribution of Blue-Green Algae in Lakes: Wind-Tunnel Tank Experiments