Sediment entrainment in karst basins

Sediment entrainment in karst basins

Jordi Colomer*, John Alan Ross and Xavier Casamitjana

Environmental Physics, Department of Environmental Sciences, University of Girona, Spain

Key words: Sediment, lutocline, groundwater, jet, Lake Banyoles.

ABSTRACT

In this paper, the suspension of sediments induced by groundwater jets in two basins of a karst lake(basin I and II of lake Banyoles, Catalonia) is studied. Field experiments were carried out duringthe period 1989–1994 to investigate the sediment dynamics within the basins. During this period,the sediment in basin I (B1) was found to be permanently in suspension while the sediment inbasin II (B2) remained at the bottom of the basin, except on two occasions when the ground waterdischarge increased and caused resuspension. A two-dimensional k-e turbulence model was usedto simulate the suspension of the sediment and the formation of the lutocline (the interface of thesuspended sediment). The model predicts a reduction of the turbulent kinetic energy at the luto-cline due to the buoyancy flux. This is used to estimate the inflow into the basins and the maximumheight that the lutocline can rise, which is found to depend on the settling velocity, the mean inflowrate and the geometry of the basin. Also, the model is used to predict the water circulation belowthe sediment interface.

Introduction

The study of suspended sediment transport comprises both laboratory, experi-ments, and their application to the field. Studies have emphasized the description ofsediment transport when processes are governed by turbulence. It has been ofspecial interest to describe the processes that lead to the resuspension of sedimentand the interaction between sediment and turbulent flows.

From a physical point of view, sediment transport mechanisms include mainlychannel flow (DeVantier and Larock, 1987; Lyn et al., 1992) and turbidity currents(Noh and Fernando, 1991b, 1992; Bonnecaze et al., 1995; Huppert and Woods,1995; Lane-Serff et al., 1995). The mechanism of turbulence generation in the firstcase is the shear stress at the boundaries and, in the second, the shear acting ateither the bottom or the interface of the current. Examples of turbidity (density)

Aquat.sci.60 (1998) 338–3581015-1621/98/040338-21 $ 1.50+0.20/0© Birkhäuser Verlag, Basel, 1998 Aquatic Sciences

* Current address: Jordi Colomer, Departament de Ciències Ambientals, Universitat de Girona,Campus de Montilivi, 17071 Girona, Spain. (e-mail: [email protected])

currents include fine silt in rivers flowing into a reservoir, lake or sea, sand in bottomocean currents, ash in pyroclastic flows down the slopes of volcanoes, snow crystalsin avalanches and phenocrysts in convecting magmas, etc. (Huppert et al., 1995).However, only in estuaries and shallow lakes has a steady state sediment layer offinite height been found. For example, sediment resuspension in an estuary occursbecause of the turbulence generated by the bottom stress, which, in turn, may begenerated by tidal currents or by water surface wind stress (Wolanski et al., 1988).In shallow lakes, surface waves associated with episodic wind events have beenidentified to be the forcing cause responsible for eroding the bottom sediments(Luettich Jr. et al., 1990; Hawley and Lesht, 1992). In turbidity currents a steady state suspension layer has not been found because of unstable conditions, such aseither particle settling or ignition on the erodible beds (Huppert et al., 1995).

In the laboratory context, mechanisms of turbulence generation have beenreported from experiments where the turbulence is generated by a vertical oscillat-ing grid and hence exhibit no mean shear (E and Hopfinger, 1986; Wolanski et al.,1989; Huppert et al., 1995) and from those where the turbulence is generated byconvecting heating or cooling at a surface (Koyaguchi et al., 1990). Only in oscillat-ing grid box experiments has a two-layer or continuous stratification been found. A well-mixed turbulent layer forms, bounded by one or more density interfaces,and propagates away from the oscillating grid as fluid is entrained into the stirredlayer. The intensity of turbulence, which decays with distance from the grid, is re-sponsible for maintaining the sediment in suspension up to a steady height (E andHopfinger, 1986; Huppert et al., 1995).

In both field and laboratory examples, sediment resuspension may induce theformation of a sediment front propagating in the upward vertical direction. Such afront, called a lutocline, separates the clear fluid at the top from a dense layer at thebottom. In both cases, the degree of turbulence and characteristics of the sediment(mainly particle settling velocity and concentration of sediment) have been used topredict the maximum height the sediment front can rise to and the mixing processesacross it.

In the present paper, the results of field measurements and computing simula-tions are reported with the purpose of understanding the dynamics of the sedimentsuspensions found in the V-shape basins of Lake Banyoles due to the action ofgroundwater jets. Here the water basin column can be divided into two parts: afairly clear upper layer and a turbid bottom layer, separated by a lutocline. Thecommon set of questions posed for stirring-box experiments and resuspension ofsediment in estuaries, which may be considered the benchmark problems in whichsteady sediment stratificatioin has been found, are translated into a model forvertical jets discharging below a sediment layer: can the turbulent jets keep theparticles indefinitely in suspension, and under what conditions? What is the result-ing height of the suspension layer?

Lake Banyoles

Lake Banyoles is a small multibasin lake of mixed tectonic-karstic origin, composedof several basins (Fig. 1). It is located 30 km from the Mediterranean coast at

Sediment entrainment in karst basins 339

340 Colomer et al.

42°07¢N, 2°45¢E in the Catalan prePyrennes, at 175 m a.s. l. Entry of lake water islargely subterranean through the bottom of the different basins of the lake (Abellà,1980; Roget, 1987). An underlying fault (at the East of the lake), which acts as abarrier to ground water movement in a complex series of confined aquifers, inducesthe vertical discharge of the ground water flow into the bottom of the lake basins.The aquifers are supplied by the percolation of precipitation in two watershedslocated 20 km to the north-west (Julià, 1980; Sanz, 1981).

100 m

10

10

10

20

20

20

30

10

30 40

10

14

12 15

5

5

5 5

5

510

8

85

5

5

Figure 1. Bathymetric map of lake Banyoles according to Moreno-Amich and Garcia-Berthou(1989). Depth contours are in meters. The lake is composed of six basins. B2 occupies the centrallobe and B1 the southern one


The main basin of the lake (B1 and B2 in Fig. 1), have a maximum depth of~ 70/75 m and 75/80 m, respectively. They have a cone-like basement structure as aresult of cumulative episodes of land subsidence. Sediments in B1 are normallyfound in suspension, as plotted in Figure 1B. The half angle (basin wall slope) of B1is around 15° and that of B2 is around 20°. Sediments in B2 normally remain at thebottom of the basin forming a consolidated bed. The thickness of this consolidatedbed is ~ 20 m (Fig. 1A). However, an increase in precipitation in the recharge areacan eventually resuspend the sediments (Casamitjana and Roget, 1993). Recentinvestigations made by Roget et al. (1994) point out that water inflow in B1 repre-sents 85% of the global flow into the lake.

Field experiments

During the field experiments (1989 to 1994), the sediments in B1 were always foundin suspension and the depth of the lutocline was always found to be between 24 and26 m depth. The temperature of the suspension was nearly constant through theyear (around 19°C) and only small changes of temperature occurred according todepth (around 0.25°C). On the other hand, the sediments in B2 formed a con-solidated bed at the bottom of the basin in the same way as is shown in Figure 1 A,except in two occasions, when a groundwater intrusion was strong enough to causesediment mixing and resuspension. Sediments were found resuspended during twodifferent periods. The first one from December ’91 to March ’92, and the secondone from autumn ’92 (we can not specify the month) to August ’93.

The first fluidization of the sediment in B2 coincided with maximum values ofthe monthly rainfall (December ’91) both in the recharge area (266 mm) and in the

Figure 2. Monthly precipitation rates during 1991–1992–1993 in the recharge area (Meteoro-logical station of Sant Privat d’en Bas) and in the lacustrine area of Lake Banyoles (BanyolesCouncil Meteorological station)

1991 1992 1993

342 Colomer et al.

lacustrine area of the Lake (258 mm) (Fig. 2). By January ’93 the lutocline at B2 wasalready found at 24 m depth, indicating that a new resuspension took place. This resuspension probably started around September ’92, when the rainfall in therecharge area was quite large (247 mm) (Fig. 2). In addition, during the basin fluid-ization events, the temperature of the suspended sediments increased, due to a rein-forcement of the water circulation in the basin. During the first fluidization of thebasin the temperature of the suspended had sediment increased around 2°C by theend of the process (from 17.45 to 19.36°C).

The groundwater inflow into the lake was measured at different times during thefield campaign. This inflow follows from a surficial water balance: outflow fluxes(eastern rivers and evaporation) minus inflow fluxes (western springs) (see Fig. 1).From Table 1 it can be seen that the mean annual ground water inflow is around500 l/s and that the maximum ground water inflow took place the 21st of January’92, coinciding with the resuspension of S2.

Moreover, monthly samples of sediments were taken every 5 m below the luto-cline from December ’92 to July ‘93 in B1 and B2 with a limnological bottle Rutner.During this period the mean sediment concentration at B1 was nearly constant withvalues ranging from 100 to 130 g/l (Table 2). Meanwhile the concentration in B2measured from January ’93 to July ’93, was found to vary between 180 and 280 g/l(Table 3). Therefore the fluidization flow in B1 was nearly steady while in B2 it was

Table 1. Water balance of lake Banyoles

Surface Inflows Surface Outflows Subterranean inflows(l/s) (l/s) (l/s)

199007–12 49 564 51514–12 49 636 58730–12 42 564 522

199107–01 55 605 55019–01 62 883 82123–02 72 534 46202–03 208 870 66210–03 97 808 711 28–03 136 792 65806–04 91 525 44413–04 74 550 47621–06 66 538 47212–07 55 472 41723–09 63 346 31331–10 55 499 44423–11 58 490 432

199215–01 119 791 67221–01 117 1024 90714–03 112 768 656


Table 2. Characteristics of sediment, taken at 5 meters increments below the lutocline, at thecenter of B1 of lake Banyoles

Depth C Hindered Median % of clays % of silts(m) (gl–1) settling velocity diameter

(mm/min) (mm)

15-12-92-30 113 0.49 4.90 17.3 82.1-35 125 0.49 5.14 19.4 79.8-40 121 0.50 5.17 19.8 79.3-45 120 0.44 5.25 19.1 80.0-50 119 0.58 5.26 20.2 78.7-55 117 0.50 5.35 19.7 78.9-60 122 0.49 5.42 19.6 78.5

21-01-93-30 118 0.39 5.49 19.1 80.1-35 123 0.43 6.15 10.8 88.5-40 124 0.45 6.37 9.0 90.3-45 119 0.43 6.50 10.0 88.9-50 122 0.45 5.98 18.2 80.1-55 128 0.43 6.15 17.4 80.2-60 123 0.42 6.11 17.3 80.6

10-03-93-30 110 0.40 6.14 9.2 90.4-35 110 0.42 6.29 8.6 90.9-40 120 0.37 6.30 10.4 89.1-45 125 0.38 6.59 8.2 91.0-50 105 0.56 6.47 8.8 90.7-55 126 0.60 6.07 14.8 84.9

19-05-93-30 103 0.67 6.30 9.4 90.0-35 107 0.64 6.39 8.2 91.2-40 100 0.60 6.24 11.3 87.7-45 105 0.59 6.19 11.9 86.9-50 112 0.55 6.24 11.4 86.7-55 117 0.60 5.73 18.7 80.3-60 116 0.62 6.34 10.1 87.7

28-06-93-25 111 0.56-30 114 0.61-35 114 0.55-40 111 0.58 Not measured-45 116 0.63-50 118 0.58-55 130 0.59

16-07-93-30 104 0.40 Not measured-35 109 0.43-40 112 0.43-45 117 0.46 6.41 9.4 88.8-50 118 0.52 6.28 10.2 89.0-55 111 0.48 6.53 9.0 89.4-60 128 0.61 6.33 11.1 88.0

344 Colomer et al.

unsteady. Also, by the end of July ’93, the lutocline at B2 moved downward, and thefluidization stopped. This is also corroborated by the increase in the concentrationall through the depth found in July the 29th (Table 3).

In addition, the mean diameter sediment of each sample was measured using anHe-Ne laser analyzer (Malvern Matersizer) which works on a laser diffraction basis.Results presented in Tables 2 and 3 show diameter values smaller than 10 mm, indi-cating that the dispersed particles are in the silt-clay range. Also, the percentage ofclays (particle diameter < 2 mm) and silts (particle diameter between 2 mm and50 mm) is nearly constant in depth. In B1 the percentage of clays was found to vary from 8 to 20% and the percentage of silts to vary from 78 to 91%. In B2 thepercentage of clays was found to vary from 7 to 21% and the percentage of silts tovary from 78 to 91%. At both basins, a small percentage of sand (particle diameter

Table 3. Characteristics of sediment, taken at 5 meters increments below the lutocline, at thecenter of B2 of lake Banyoles


(mm/min) (mm)

26-01-93-25 188 0.41 5.88 10.8 88.8-30 189 0.40 5.99 10.5 87.9-35 185 0.65 6.31 8.8 90.2-40 188 0.58 5.86 15.1 84.5-45 180 0.56 6.38 10.9 88.5-50 186 0.54 6.15 11.3 87.8-55 189 0.59 6.05 11.8 87.6-60 192 0.52 6.01 10.5 88.6-65 187 0.56 6.32 12.0 87.6

19-02-93-25 194 0.50 5.82 10.3 88.8-30 199 0.56 5.91 10.6 87.9-35 189 0.67 5.71 9.5 90.0-40 185 0.64 5.75 12.1 84.9-45 188 0.62 6.12 10.8 88.1-50 186 0.58 6.05 11.3 87.5-55 193 0.69 6.00 11.0 86.4-60 191 0.62 6.07 10.0 88.5-65 190 0.59 6.22 11.6 88.1

17-05-93-25 197 0.40 5.88 10.9 88.9-30 200 0.36 5.99 10.6 88.9-35 185 0.75 6.31 7.4 91.3-40 188 0.56 5.86 15.2 84.6-45 178 0.52 6.38 10.8 88.5-50 187 0.53 6.15 12.4 87.5-55 190 0.59 6.05 11.7 87.9-60 196 0.52 6.01 10.6 88.5-65 177 0.49 6.32 12.1 87.4


>50 mm) was also detected. In Figure 3 the size distribution of sediment particles ofB1 at different depths and different dates is presented. As can be seen no significantdifferences between these distributions are observed.

It is well known that for concentrations higher than 10 gl–1, hindered settlingoccurs. Also, sediment with clay particles presents a flocculent network which sett-les extremely slowly in quiescent water in the form of a descending interface. As aconsequence, the settling velocity is dependent on the suspended sediment con-centration, decreasing with increasing concentration, as found in basins of LakeBanyoles. An example of this can be seen by comparing the values of the days 16-07-93 and 29-07-93 in Table 3. In the present paper, the empirical expression forthe relation between settling velocity and concentration, developed by Wolanski et al. (1989) will be used:

wS = a1 C/(C2 + a2)2 (1)

Here, wS is the settling velocity measured in ms–1 and C the sediment mass con-centration expressed in gl–1. The coefficient values a1 and a2 were obtained by

Table 3 (Fortsetzung)


(mm/min) (mm)

14-06-93-25 185 0.42-30 223 0.28-35 209 0.45-40 225 0.33-45 184 0.57 Not measured-50 245 0.35-55 236 0.34-60 222 0.37-65 215 0.36

16-07-93-30 193 0.29 6.04 12.5 86.9-35 207 0.30 5.89 12.7 86.6-40 192 0.33 5.66 20.5 77.8-45 226 0.30 6.14 12.6 86.3-50 229 0.34 6.24 10.4 88.7-55 232 0.27 6.23 11.3 87.9-60 204 0.26 6.21 11.4 87.4-65 232 0.24 5.64 19.5 79.9

29-07-93-35 267 0.24-40 271 0.20-45 268 0.18 Not measured-50 276 0.23-55 285 0.19-60 264 0.15

346 Colomer et al.

Figure 3. Particle-diameter distribution of dispersed sediment in basin I at different depths, takenduring Winter-Spring 93

means of the non-linear regression analysis of the measured variables wS and Cpresented in Tables 2 and 3. Values obtained are a1 = 89 mg3/sl3 and a2 = 915 g2/l2.Equation 1 predicts an increase of wS with C up to the value of C = 17.46 gl–1 obtai-ned when wS = 0.10 cms–1. For sediment concentration larger than 17.46 gl–1 wS

decreases with C.Casamitjana et al. (1996) suggested the presence of particle aggregates at the

deepest part of the basins, where they found higher rates of particle settling in spite


of the high sediment concentrations there. Settling velocity also depends on particlesize, thus, if the particle size is higher in the deepest part of the basin, then there the settling rate should increase in spite of the higher concentration. As is shown in Figure 3, the measured dispersed particles have the same size. Higher measured settling rates of sediment (Tables 2 and 3) imply that aggregates of particles arepresent near the bottom.

In our field experiments, this was found to occur in B1 three times (Table 2);during the rest of the days there was no significant sediment stratification at the verybottom of the basins. Also, in order to investigate the presence of aggregates in anyparticular basin of lake Banyoles, 20 samples of sediment were taken at B1 at 30 and60 meters depth during the last 3 days of the experiments. Sediment was removedfrom the basins and immediately frozen to avoid the formation of new aggregatesduring the sedimentation process. The sediment was frozen by introducing thesamples into liquid nitrogen containers. From the frozen sediment, one smallsample was taken and deposited on a nucleopore paper. This sample was thenanalyzed by a scanning electron microscope which provides surficial images of thesediment at different specific scales and zooms.

In Figure 4 three images of the sediment at different scales are presented. Sedi-ment in Figures 4A and 4B was obtained at 30 m depth and sediment in Figure 4Cat 60 m depth. It can be seen that the larger particles are located at 60 meters depth(Fig. 4C). In addition, particle aggregates can clearly be detected in all the samples,with characteristic diameters ranging between 10 and 100 mm. These measurementsindicate the presence of particle aggregates at any depth of the fluidized bed B1,

Figure 4 A–C. Scanning electron microscope photographs of suspended sediment of basin I at30 m depth: A and B and at 60 m depth: C

348 Colomer et al.

Figure 4B

Figure 4C

with slightly larger particle diameters nearer the bottom basin (60 m depth) thanthe lutocline (30 m depth). This explains the larger particle settling velocities at thebottom of the basin in spite of larger concentrations.

Mathematical model

Governing equations

A numerical model is applied in this section in order to assess the magnitude of theinflow into the basins and to describe the water circulation below the sedimentinterface. We will solve the problem of a slot jet with a certain amount of solids insuspension discharging into a uniform body of water with sloping boundaries. Inorder to do so we will use a 2-D model with the following equations:

∂u ∂v5 + 5 = 0 (2)∂x ∂y

∂u ∂(u2) ∂(uv) ∂p ∂ ∂u ∂ ∂u ∂v5 + 9 + 0 = – 5 + 2 4 1neff 412 + 41 3neff 141 + 4124 (3)∂t ∂x ∂y ∂x ∂x ∂x ∂y ∂y ∂x

∂v ∂(uv) ∂(v2) ∂p ∂ ∂v ∂ ∂u ∂v5 + 9 + 0 = – 5 + 2 4 1neff 412 + 41 3neff 141 + 4124 – hcg (4)∂t ∂x ∂y ∂y ∂y ∂y ∂x ∂y ∂x

∂k ∂(uk) ∂(vk) ∂ neff ∂k ∂ neff ∂k nt ∂c5 + 9 + 0 = 5 141412 + 41 141412 + G – e + hg 45 (5)∂t ∂x ∂y ∂x sk ∂x ∂y sk ∂y sc ∂y

∂e ∂(ue) ∂(ve) ∂ neff ∂e ∂ neff ∂e5 + 9 + 0 = 5 141412 + 41 141412∂t ∂x ∂y ∂x se ∂x ∂y se ∂y

e e 2 e nt ∂c+ C1 3 G – C2 3 + C1 3 (1 – C3)hg 45 (6)

k k k sc ∂y

∂c ∂(uc) ∂[(v – ws)c] ∂ neff ∂c ∂ neff ∂c 5 + 9 + 09 = 5 141412 + 41 141412 (7)∂t ∂x ∂y ∂x sc ∂x ∂y sc ∂y

where (2) is the continuity equation, (3) and (4) are the Navier-Stokes equations,(5) and (6) are the k-e equations for the turbulence and finally (7) is the sedimenttransport equation. The velocities u and v are the velocity components of the fluidin the Cartesian directions, x is horizontal and y vertically upward, g is the accele-ration due to gravity, h is (Çs–Ç)/Ç, Ç is the fluid density, Çs is the density of the sedi-ment particles, k is the turbulent kinetic energy, e is the rate of turbulent energydissipation, c is the volume concentration, and ws is the settling velocity of sediment.


350 Colomer et al.

The effective viscosity, neff = nt+n , is the sum of the turbulent (nt) and the molecular(n) component, the former being nt = Cmk2/e, where Cm = 0.09. p = P + 2k/3 is themodified pressure, where P is the mean flow pressure divided by the fluid density.In addition, G is the production of k due to mean velocity gradients

6 ∂Ui ∂Ui ∂u 2 ∂v 2 ∂u ∂v 2

G = – uiuj 7 = 2nt Di j 7 = nt 32 152 + 2 152 + 15 + 52 4 (8)∂xj ∂xj ∂x ∂y ∂x ∂y

Here, Dij is the mean rate of strain tensor. The values of the empirical constantswhich have been extensively examined for shear flows away from the walls are C1 = 1.44, C2 = 1.92, C3 = 0.8, sk = 1.00 and se = 1.30 (Lyn et al., 1992). For theturbulent Prandtl number, sc, we will use the value sc = 0.5. This value is adequatefor the vertical mixing in channels and pollutant-spreading calculations (Celik andRodi, 1988; van Rijn, 1984; Lyn et al., 1992). Due to the symmetry of the basins B1and B2 of Lake Banyoles (Fig. 1) and in order to save time calculations, the equa-tions (2)–(8) will be solved for the domain represented in Figure 5. This domainrepresents half of a V-shape basin and is characterized by the solid wall slope (tan a), i.e. the ratio between the basin height hB and the length L f – L0 (Fig. 5)which are the basin outlet and inlet lengths, respectively.

Figure 5. Coordinates and boundaries for computational domain


Boundary conditions and solution method

The boundaries where conditions have to be established can be seen in Figure 5 andare placed in the inflow (line AB in Fig. 5), the outflow (line CD in Fig. 5), the solidwall (line AC in Fig. 5) and the center line (line BD in Fig. 5).

In the sloping wall (AC) the normal velocity, the normal gradient of the tur-bulent kinetic energy and the sediment flux are taken equal to 0. Also, the energydissipation e in the wall is taken as:

(C m1/2 k) 3/2

e = 08 (9)kyn

where k = 0.40 ist the von Kármán constant and yn is the standoff distance from eachsolid wall to the edge of the computational mesh (Ross, 1993). In addition, thefriction wall velocity u* is

k Uwu* = 00081 (10)

(C m1/2 k)1/2

ln 3E yn 10824n

where Uw is the tangential velocity along the wall domain and E is a constant whichdepends on the wall smoothness. For the wall stress we used the expression:

tw = Ç [1 + (Çs /Ç – 1) c] (u*)2. (11)

In order to preserve the symmetry in the line BD at the center of the basin, the dif-ferent flux of momentum mass and energy are required to be zero.

In the inlet line AB, the horizontal velocity u is taken to be zero. The sedimentconcentration is set at the constant value c = c0. For the rest of the basin the initialconcentration was set to 0. V0 is the velocity at the center of the inlet (Fig. 5) and isdetermined from the expression V0 = Re (n/L0), where L0 is the length of the lineAB. The velocity profile in the inlet follows the logarithmic turbulent boundarylower law (Ross and Larock, 1995).

The initial values of the turbulence parameters k and e were determined fromthe expressions:

dUw2

k = C m– 1/2 3lm 84 (12)

dn

and

dUw–1

e = Cmk 2 3lm2 84 (13)

dn

352 Colomer et al.

where lm is the Prandtl mixing length and n is the direction normal to the wall. Inaddition we use the values of Ç = 1 gcm–3, ÇS = 2.4 gcm–3, n = 0.01 cm2/s and wS iscalculated from equation (1).

The equations governing the flow field [(2)–(7)] were solved according theBoussinesq approximation, therefore the difference in density between the sedi-ment and the water is included in the equations through the buoyancy term h (seeequation (4), (5) and (6)). The basic approach was a modified Galerkin finiteelement method. The galerkin method spatially discretizes the transient flow equa-tions into a system of ordinary differential equations, which are then integratedusing an explicit forward Euler techique (Ross and Larock, 1995). As is well known,this is a destabilizing method because of the negative diffusion created, especially inconvection-dominated flows. To counter this false numerical diffusion, a balancingtensor diffusivity scheme was used (Gresho et al., 1984). In this method, a term ofthe form UiUj∆t/2 should be added to the usual diffusive term. In addition the k-emodel time integration scheme was modified somewhat to make it actually semi-implicit (Ross, 1993; Ross and Larock, 1995). A nonuniform grid with 26 ¥ 101nodes was used with close nodes near the jet line and more spaced nodes far fromthe inlet. Finally, numerical experiments and sensitivity analysis were carried out toeliminate the effects of size of computational domain and number and distributionof grid points on model results.

Results and analysis

The major parameters characterizing the discharge are the jet nozzle Reynoldsnumber (Re), the sediment concentration at the bottom (c0) and the slope of thesolid wall (tan a). Different numerical simulations have been computed for Re =8,000 and Re = 32,000, tan a = 0.364 (a = 20°) and 0.839 (a = 40°), and c0 = 0.004.These values of the Reynolds number correspond to jet lake-basin discharges of 0.3 and 0.6 m3/s and L0 values of 10 and 20 m (Fig. 5). The equivalent mass concen-tration of suspended sediments used is then C0 = 10 gl–1. Although this value issmaller than the measured values in Lake Banyoles, the Boussinesq approximationstill applies to the liquid phase. Although a two-phase model would be more realisticto describe the dynamic of the sediment in the basins, we will see that the modelused will describe the main trends of the basin sediment dynamics in a suitable way.

In Figure 6, the steady state results of a simulation carried for Re = 8,000 and a = 20° is presented. Other simulations with different values of Re and a exhibit asimilar behaviour. A recirculating zone below the sediment interface can clearly beseen. The arrow in the figure indicates the height of the mixing zone. Below thisheight the concentration of sediments equals the concentration in the inlet. Also, atthe sediment interface the water circulation is damped, inhibiting mixing processesacross it.

A contour plot for the normalized sediment concentration, C/C0, is presented inFigure 7A. Here we can see a layer of constant sediment concentration at thebottom and a layer of clear water on top. The layers are separated by a lutocline.The height of the constant concentration layer is zi~ 7.4 L0. In Figure 7B the non-dimensional viscosity, neff/n, is presented for the same simulation. This value is


higher than 300, coinciding with the recirculation zone. Additional simulationscarried out without sediment (c0 = 0) and the same Re and a, presented results withthe same behaviour but here neff/n ≥ 800. The decrease of neff with the sediment con-centration is a known effect and is due to the killing of turbulence when negativebuoyant particles are present (Hetsroni, 1989; Colomer and Fernando, 1997).

Also, the concentration gradient at the lutocline (Fig. 7 A) is smooth and not assharp as lutoclines found in Lake Banyoles (Casamitjana and Roget, 1993). Thesharp interface in the field situation can be explained taking into account that if theconcentration is larger than 17.5 gl–1 the settling velouty decreases with the con-centration (as predicted by equation (1)). If a clump of sediment is entrained in theupper parts of the lutocline it will be diluted and its settling velocity will increase.Therefore a sharper front would be expected.

In Figure 8 the vertical profiles of c/c0 and k/V02 at the steady state along the

line BD (Fig. 5) are depicted. Figure 8A corresponds to Re = 8,000 and a = 40° andFigure 8 B to Re = 8,000 and a = 20°. In both simulations it was found that theturbulent kinetic energy, k, increases with height, reaching a maximum value justbelow the lutocline. At the bottom of the lutocline k is severely damped and goes to zero. Also, taking into account that neff ~ nt = Cmk2/e, the effective viscosity, neff ,will be also 0. Therefore the lutocline act as a barrier for the propagation of theturbulent kinetic energy. Simular results are found by Wolanski and Brush (1975)and Noh and Fernando (1991a). As pointed out by the latter authors, when a sedi-ment front is formed the turbulent kinetic energy decreases rapidly to a minimumat the elevation corresponding to the depth of the suspension layer. On the other

Figure 6. Computed flow field at the steady state at a Re = 8,000 and a basin slope of 0.364

↑ v/V0 = 1

↑

354 Colomer et al.

hand, Zhou and Ni (1995) found a relamination tendency of the mean velocityprofile, which, however, does not imply a reduction of turbulence. However, in theircase the concentration decreases very smoothly making it impossible for a front toform as in the present paper.

If equation (7) is applied at the lutocline height, zi , and at the steady state, thefollowing expression is obtained:

u ∂c/∂x + (v–wS) ∂c/∂y = 0. (14)

In addition, if ∂c/∂x = 0 (Fig. 7A), one obtains

(v–wS) ∂c/∂y = 0 (15)

which gives v = wS ant zi, because ∂C/∂y is non-zero (Fig. 8).

Figure 7. Computed contour plot of normalized sediment mass concentration, C/C0 (A) andcontour plot of effective viscosity, neff , normalized by n (B), at the steady state, for a Re = 8,000 andbasin slope of 0.364

C/C0 = 0.2

neff /n = 100

neff /n = 200

neff /n = 300

C/C0 = 0.6

C/C0 = 1

Outlet basin

Hei

ght (

21L

)

Half angle

Inlet basin (L)


In the idealized axisymmetric lake flow if we consider continuity

vbL02 = wSL2 (16)

where vb is the mean inflow velocity at the inlet and L is the width corresponding toa lutocline level (Fig. 5), and geometric considerations, we can finally write

9zi/hB = (L0/Lf – L0) (kvb/wS – 1). (17)

In Figure 9, equation (17) is plotted for different values of the ratio L0/Lf – L0 andvb/wS.

The minimum value of L0/Lf – L0, 10–2, corresponds to an outlet length almost100 times the inlet length, and the maximum value, 1, corresponds to an outletlength double the inlet length. This figure shows that zi/hB increases with vb/wS, andtherefore with Re. Also, the larger Lf – L0 is the less zi/hB is.

If we take into account that the lutocline in basin B1 is at zi/hB ≈ 0.81 (hB ≈ 70 m)and hB/Lf – L0 ≈ 0.364, a calculated water basin inflows of 0.5 m3 s–1 is obtained foran inlet radius of 15 m and a sediment concentration of 100–120 gl–1, which agreeswith the mean measured value in Lake Banyoles obtained during the field experi-ments. A better description of the basin dynamics could probably be obtained with

Figure 8. Jet centerline profiles of c/c0 (dashed line) and k/V02 (dotted line) simulated with the 2D

model: Re = 8,000 and basin slopes 0.839 (let) and 0.364 (right)

356 Colomer et al.

an axisymmetric model instead of a plane model. However, the main trends of thebasins are well described with the present approximation.

Conclusions

Resuspension of fine cohesive sediment occurs in the main basins of Lake Banyoles(B1 and B2) because of the intrusion of ground water at its bottom. As a conse-quence, the water column is stratified into a bottom turbid layer and a fairly clearupper layer with a lutocline in between.

In the basin B1 the depth of the lutocline changes very little through the year andthe suspension is nearly steady with a mean flow around 0.5 m3/s. In B2 differentepisodic inflows linked to an increase in the pressure of the aquifer that feed thelake result in the resuspension of sediment that otherwise remains consolidated atits bottom.

The formation of the lutocline has been predicted by a two-dimensional k-e tur-bulent. The model also predicts a recirculation zone below the lutocline and thesevere damping of the turbulent kinetic energy and effective viscosity at the bottomof the lutocline. Therefore the lutocline acts as a barrier for the propagation of theturbulent energy and as a consequence, at the lutocline level, the settling velocity isequal to the mean upward velocity of the water. This fact is used to estimate theinflow in the basins and the maximum height that the lutocline can rise to, which isfound to depend on the settling velocity, the mean inflow rate and the geometry ofthe basin.

Figure 9. Computed zi/hB versus the ratio L0/Lf – L0 for different values of vb/wS

ACKNOWLEDGEMENTS

Support for this project was provided by the DGYCIT (Dirección General de Investigación Cientí-fica y Tecnológica) of the Spanish Government; grant PB-93-0548, and by the “Fundació Catalanaper a la Recerca” who permitted us to use their CRAY YMP-232.

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Received 22 January 1997;revised manuscript accepted 5 November 1997.

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