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Y.R. Rao and C.R. Murthy National Water Research InstituteBurlington, Ontario, Canada
paper discusses several physical processes that are relevant to water quality
and sustainable management of small and large lakes. Knowledge of water
movements is important because circulation influences the distribution of
dissolved substances, nutrients, microorganisms and plankton. Although there is
a tremendous amount of variability in the origins of a lake (natural) and a
reservoir or impoundment (artificial), they share several common physical,
chemical and biological characteristics . In particular, reservoirs have
controlled outflow, whereas the lakes are uncontrolled. In addition to these
aspects, the physical limnology of these water bodies are governed by the shape
and size of the basin. Two aspects of size that have a strong bearing on water
quality are residence time and depth. Shallow lakes (<10 m) are generally
well-mixed, and deeper lakes (>10 m) are often subject to thermal
stratification during certain times of the year. Therefore, the water balance of
a lake or reservoir
generally depends on the inflow, outflow, groundwater flow,
precipitation, evaporation over the water shed region of the lake. Discussion of
large scale water motions includes water levels, seiches, currents, waves and
turbulence. Wind, solar radiation, stratification, earth’s rotation are
important forces causing water movements of lakes.
of water bodies may occur due to several reasons. Natural lake systems were
generally formed during the ice ages because of tectonic or volcanic activities.
In contrast man induced developmental activities are responsible for
ever-increasing number of reservoirs and artificial impoundments. In these cases
we have taken advantage of natural topographic characteristics which with minor
modifications like construction of dams or embankments lend themselves to large
storage facilities of freshwater. Drainage basins of reservoirs are much larger
in relation to the lake surface areas. Because reservoirs are formed almost
always in river valleys and at the base of the drainage basins, the morphometry
of reservoir basins is usually narrow and elongated. Whether artificially or
naturally created, all lakes share several common physical, chemical and
2. Characteristics of Lakes
2.1 Lake Basin characteristics
analysis of a lake often requires a detailed knowledge of morphometry,
particularly the volume characteristics of the water body. Depth analyses,
including areas of sediments and of water strata at various depths, volumes of
strata, shoreline characteristics are critical to detailed analysis of physical,
biological and chemical analysis. In order to characterize the physical
limnology of a lake, a distinction has to be made between a large lake and a
small lake. Generally large lakes tend to be deeper than small lakes. Moreover,
the ratio of the volume of the water body to its surface area is considerably
greater than in small lakes. Table 1 gives morphometric and hydrological
differences between Large and small lakes (Imboden,1990).
area per boundary
lake is divided physically into several zones. The ecological description
involves dividing the lake into a littoral, limnetic and profundal zones. The
littoral zone is the shallow part of the lake where the light reaches the
bottom. The limnetic zone is the offshore part of the lake down to the depth of
light penetration. This depth is referred to as the compensation level and
describes the point at which photosynthesis and respiration are equally
balanced. The term euphotic zone is used to refer to the total of littoral and
limnetic zones. The profundal zone includes all the bottom waters below the
compensation level. In very shallow lakes and ponds generally the profundal zone
are also physically divided by their thermal characteristics. Although this
discussion is mainly suitable for temperate lakes, warmer or cooler climates
also exhibit thermal characteristics which are basically a subset of these.
Since fresh water is most dense at 4oC, a temperature slightly above
the freezing point the lake freezes at the surface in the winter. Except for
very shallow lakes, the complete freezing rarely occurs and dense waters remain
at the bottom. With the onset of spring the ice melts and surface water begins
to warm. During this period, when the vertical temperature gradient is weak wind
mixing induces the spring overturn. Continued warming during the summer results
warming of surface layers, and wind induced mixing remains in the surface
layers, forming typically a three layer structure. The top well-mixed warm layer
called epilimnion will be separated with cold bottom hypolimnion waters by a
metalimnion or thermocline (Fig. 1). Cooler air temperatures in the fall and
winter will lower the epilimnion water temperatures resulting the elimination of
thermocline. Mixing of upper and lower layers is then enhanced, resulting in
fall overturn. In the tropical belt, although seasonal variations of water
temperature are minimum, deeper lakes exhibit partial to strong stratification
in the major part of the year. However, hypolimnion rarely forms in the shallow
One of the most important characteristics of the lake is its thermal structure. The heat content of a water body is of vital importance in the studies of water quality in the lakes. The metabolism, and behavior of aquatic organisms are directly related to the temperature of the water body. Because of high specific heat of water, large volumes of water change temperature slowly. Therefore, large lakes tend to moderate local climates, provide longer growing seasons for aquatic life, and serve an integrated recorders of recent climatic phenomena. Temperature is related to heat content of the water body but does not measure it. The general equation which applies to the heat balance of a water body in a given time interval is
where qR = net radiation, qE =latent heat exchange, qL = sensible heat exchange, qV = net advective exchange, qS = change in heat storage and qB = conductive heat exchange
net radiation can be measured directly by a net radiometer positioned over the
surface of the lake. Alternatively, net radiation may be estimated from the
difference between total incoming short-wave radiation, albedo and net long-wave
radiation. Latent heat exchange transfer refers to the conduction and convection
of heat from the surface of the lake to the air, or vice-versa. Bottom
conduction through the sediments is often neglected in the heat balance of small
and medium sized lakes. Energy added is considered positive, while energy lost
is negative. Over the course of an annual cycle, assuming no climate change, the
heat gain is generally equal to heat lost.
A water balance for a well-mixed lake can be written as
= dV/dt = Qin-Qout +G +PAs-EAs
many instances lakes and impoundments (especially large ones) do not experience
drastic volume changes for the time periods addressed by water quality models.
For such cases water balance equation takes steady state form. Precipitation is
measured as the vertical depth in millimeters or inches to which water would
accumulate on a level surface in no portion of it is evaporated or runs off, and
if frozen precipitation is melted. Evaporation from the water surface is
obtained by a simple formula as
es is the saturation vapor pressure at the water surface, ea
is saturation vapor pressure of air above the water, u is the wind velocity, and
a & b are empirical climatic constants of the lake. Also for small lakes it
is easier to measure inflow and outflow, other quantities are generally
neglected. Although this simplification is often invoked for expediency, it
should be checked for validity.
important concept useful for water quality studies in the lakes is ‘Residence
time’ of water in the lake. If we assume that the precipitation is equal to
evaporation in a lake, the sink of water from a lake is measured by the
magnitude of the outflow. Then the water residence time is given Tw=
V/Qout, physically speaking this is the time that would be required
for the outflow to replace the quantity of water in the lake. Thus it is a
measure of lake’s flushing rate. As shown in Table 1, for large lakes since
the volume is large compared to outflows, their residence times are high, i.e.
they are slow flushers.
hydrodynamics of water movements is an integral component of a functional lake
system. Physical limnology deals with methods similar to oceanography except
that it largely concentrates on the responses of closed basins to applied forces
and exchanges of heat. The overall circulation of large lakes is characterized
by complicated variations in space and time. With the exception of the
circulation induced by hydraulic component of flow in shallow basins wind is the
principal source of mechanical energy for water movements in lakes. Except for
very large lakes the wind stress is uniform over the lakes. Wind exerts a mean
= Cd ra
U2) or drag on the surface, parallel to the wind direction, and
proportional to square of the wind speed (U). The coefficient of proportionality
(Cd), known as drag coefficient, varies with several environmental
factors. The best known of all water movements influenced by wind are surface
waves, however, it is of subordinate interest to most of the water quality
considerations because their effect is limited to uppermost strata and therefore
they will not take part in the displacement of large water masses. However, in
the littoral zone of lakes wave action becomes important because of its role in
sedimentation. When the horizontal dimensions of the lakes are sufficiently
large, the apparent force due to the rotation of the earth (Coriolis force) has
an important effect on the structure of currents and long period waves. The
force is proportional to the velocity of the fluid particle and acts at right
angles to the velocity.
3.1 Homogeneous Lakes
Seiches: Standing waves cause much greater water
displacements than surface waves and are therefore much more important in
physical limnology. Standing waves are a phenomenon occurring in all lakes, but
only in large basins we observe periodic rise and fall of the water surface.
They are generally known as ‘seiches’.
The seiches are free surface waves, governed by similar dynamics as
short, wind generated waves. The principal ingredients in the wave dynamics are
acceleration of the water particles and pressure gradients generated by
displacement of the free surface and the force of gravity. The speed of these
waves is C=ÖgH,
where H is local water depth and g is the acceleration due to gravity. In large
lakes the earth’s rotation is often important and may influence the motion in
the lake. When the natural period of the oscillation is comparable to or greater
than inertial period
the motions are affected by the earth’s rotation. The inertial period is
dependent on the latitude (j)
of the lake.
Storm surges: A sudden wind will produce not only
oscillating seiches, but also cause the water surface to set up or tilt, more or
less in opposition to the wind stress, and for the duration of the wind. These
changes in water level observed in response to extremely vigorous wind forcing
are known as storm surges. The largest change in water level is produced by the
sum of storm surge and seiche. Storm surges are largest at the ends of an
elongated basin, particularly when the long axis of the basin is aligned with
the wind. In low-lying shores such events may cause flooding and increased
erosion, with property damages and risk to human lives.
Topographic gyres: The wind drag is transferred from the
surface downward by turbulent friction. Because of the closed basins, the
transport of water through any cross-section averaged over the period of
fundamental seiche is zero. Surface wind-driven flow must be balanced by a
subsurface flow that is driven by pressure gradients. Close to the shore, wind
drag is experienced all the way to the bottom, and this water is accelerated in
the direction of the alongshore component of the wind. The balancing return
transport occurs in the middle of the basin. Thus the forced, vertically
averaged circulation takes the form of double gyre. The complicated vertical
shear maintained during the active wind-forcing soon dies out, leaving this
two-gyre motion behind. Within such cross-shore flows, the earth’s rotational
force and pressure gradients do not balance and a wave like motion sets up. The
two-gyre motion rotates counter-clockwise around the basin in the Northern
Hemisphere. These motions are called topographic or vorticity waves. Unlike the
influence of topography, the curl of the wind stress generates a single
basin-wide gyre that can rotate around the basin, depending on the wind stress.
the lake is stratified, the possibility of vertical displacements of the
thermocline as well as those of free surface, introduces more complexity in both
wave-like motions and whole-basin circulation.
Coastal Jet: During strongly stratified regions the force of gravity suppresses
turbulence. The vertical transfer of wind-imparted momentum is thus inhibited so
much so that the shear stress in the horizontal planes within the thermocline is
usually small. This is not true all of the time or everywhere, however, it has
been observed in large lakes at least at some distances from shore the momentum
of the wind induced coastal current is concentrated in the top, warm portion of
the water column above the thermocline. This concentration of momentum in
relatively shallow layer results in increased velocities, compared to their
depth-averaged values. The region where such concentration was pronounced
occupies a band of 5-km width. Their high velocity, shallow depth, and narrow
width make it appear to describe the flow structure as ‘coastal jets’ (Csanady,
Upwelling and downwelling: When wind blows over the stratified lake, the initial transport is confined to the upper layer, which slides over the unperturbed lower layer. At the shores of the lake, accumulations of warm water force the thermocline down (downwelling), and where the warm water moved offshore, the thermocline must rise (upwelling). Figure 2 shows upwelling along the north shore and downwelling along the south shore of Lake Ontario forced by westerly winds.
enough time, a steady wind would create a steady setup of the thermocline that
would in effect mirror the setup of free surface in such a way that below the
thermocline the pressure gradients set up by the slope of the free
surface were exactly cancelled by those created in the lower layer by the tilt of the
thermocline. The strong tendency for the Coriolis force to steer flows in such a
way that the pressure gradients are balanced by the Coriolis force limits the
upwelling and downwelling zones to a narrow band along the shore line typically
within the Rossby radius of deformation. The Rossby radius of deformation
can be defined as the ratio between the typical velocity scale of surface
or internal waves, and theCoriolis frequency.
When the wind stops, the initial unbalanced state described above relaxes
through the mechanism of internal Kelvin waves. Kelvin waves propagate
alongshore in a counter-clockwise direction in the Northern Hemisphere. Internal
Kelvin waves are confined to a few kilometers from the shore, and with no motion
in the perpendicular direction to the coast. The near surface currents that
moved in the downwind direction during the active wind phase now reverses during
the propagation of these waves.
motions: During the
stratified season in the offshore areas of the lake, currents exhibit clockwise
rotary motions close to the inertial period (Fig. 3). Similar motions occur in
the oceans, anywhere the water can move horizontally without the hindrance from
the shore. The main features may be explained in terms of balance between the
Coriolis force and the centrifugal force. A sudden wind impulse lasting less
than half the inertial period is favourable to the creation of inertial motions.
Observations also showed that similar motions in the deeper layers where the
direction is generally opposite to that of surface oscillations. These motions
are called Poincare waves, which are similar to internal seiches in small lakes.
The currents are accompanied by vertical oscillations of thermocline at the wave
period. These waves are hybrid between pure inertial motion described above and
gravity waves; the current vector rotates in clockwise direction at a frequency
close to but usually larger than local inertial frequency.
and Outflow currents:
Currents brought about by inflow and outflow of water is of special importance
in lakes on larger rivers. Hypolimnetic water is usually replenished by a cold
water inflow. To illustrate these consider the mixing of a large river plume.
The receiving water circulation, strength of the river plume, wind direction,
the formation of the basin and the effect of the earth’s rotation, fixes the
path this inflowing current takes in the lake. The outflow normally draws off
water from the surface and the strata immediately below it, and thus brings
about a considerable loss of heat in small and medium lakes. This withdrawl of
heat, and thus also the surface temperature of the lake, is influenced by the
form and profile of the outlet. It the outlet is wide and shallow the loss is
greater than when it is narrow and deep. For small outflows and/or strong
stratification the water is removed by a thin layer adjacent to the level of
outflow which is called as selective withdrawal.
Vertical convection currents: Apart
from wind or river induced circulation, currents can also be generated
internally due to stratification effects. As we have seen earlier in spring and
fall overturns, these currents draw their energy from changes in density due to
surface cooling and heating. Differential cooling and heating is also very
important in shallow lakes and may be responsible for flushing of littoral
Mixing processes in lakes cover a wide spectrum of different time and length scales. At the small end of these scales, mixing processes are similar in oceans and lakes. With increasing size and duration of the mixing structure the different dimensions of the water bodies become more apparent. Typically horizontal exchange of heat, energy and momentum occur at scales generally much larger than vertical exchanges, given the large horizontal lengths of lakes compared to their depths. This has prompted many researchers to de-couple horizontal transports from the vertical ones, even though horizontal and vertical processes interact. Spectral analysis is the method commonly used to isolate the various phenomena. For instance, time series of currents or temperature measured at a fixed station in lakes can be decomposed by Fourier transformation into modes of different frequencies (Fig. 4 ).
In the inertial sub-range the similarity theory predicts that the turbulent kinetic-energy spectrum E(k) is given by the familiar - 5/3 power law , where c is a universal dimensionless constant; c is the rate of dissipation of turbulent kinetic energy and k is the wave number. We assume that turbulent eddies larger than the size of the diffusing cloud does not contribute much to the diffusion process. Furthermore, if we designate a length scale i = k-1 to the eddies responsible for the diffusion of the cloud, then for a point source initially released into a turbulent medium consisting of a spectrum of eddies of several sizes, the turbulent kinetic energy available for diffusion of the cloud
would be . Combining the above two equations the turbulent velocity
with length scale, l, is given by:
an example typical sizes characterized by energy and momentum fluxes in large
lakes are given in Table 2.
eddy diffusity (Kz)
scales of mixing
of energy dissipation
mixing processes in lakes are of singular nature, this means that they are
triggered by some external or internal force and then evolve along a
characteristic pathway determined by the hydrodynamic laws. For example the
phenomena that was described earlier about storms producing upwelling and
downwelling at opposite shores, produces mixing through the subsequent
relaxation through the generation of internal waves and smaller scale processes.
Boundary mixing is very important mechanism for mixing in small lakes. An
effective vertical transport is realized by vigorous mixing at the boundary
fluid intruding gravitationally into the hypolimnion. Turbulence is also
generated by a variety of internal wave instability and interactions (Fisher et
al.,1979). Since internal waves are generated at the underside of the
thermocline and at lake boundaries, energy may be transferred from wind through
the thermocline to the internal waves which then interact with each other in a
variety of possible instability mechanisms to produce local mixing event.
exists a variety of other less spectacular events. Many of them are connected to
density induced mixing. For example river-induced currents may be significant in
some lakes for the exchange of water from below the thermocline. The river plume
often enlarged in volume by water entrained from the lake surface, push
hyplomnic water upwards, thus adding to vertical mixing. The daily interaction
between meteorological forcing and mixing at the lake surface also belongs to
the category of events. The diurnal cycles of heating and cooling cause a
complicated temporal and spatial variation of temperature distribution in the
mixed layer. Langmuir circulation cells are often referred as one important
mechanism for mixing in the upper mixed layer.
Csanady, G.T. (1982) Circulation in the coastal ocean, D. Reidal Publishing company, Boston, pp. 279.
D.M. (1990) Mixing and transport in Lakes: Mechanisms and ecological relevance,
Large Lakes: Ecological structure and Function (Eds: M.M. Tilzer and C. Serruya).
Fisher, H.B. et al. (1979) Mixing in inland and coastal waters, Academic Press, New York,150-222.
Fig. 1: Vertical thermal structure in a large temperate lake.
Fig. 2: Satellite picture showing upwelling along the north shore and downwelling along the south shore of Lake Ontario during a westerly wind event.
Fig. 3: Progressive vector diagram showing inertial oscillations.
Fig. 4: Total and two components of current spectra.