LAKES AND RESERVOIRS - Water Quality Engineering in Natural Systems - page 258

phosphates are released from the sediments during con-
ditions of anoxia in the hypolimnion and in the sedi-
ments. Decomposition in the hypolimnion produces
gasses such as hydrogen sulfide (H 2 S), methane (CH 4 ),
and carbon dioxide (CO 2 ), which tend to remain dis-
solved in the bottom waters, particularly if the lake is
deep and the bottom pressure is high.
Water flowing into a lake will travel through the lake
at a depth having the same density as the inflow until it
becomes mixed. If the incoming water has a lower tem-
perature and higher density than the lake water, when
the incoming velocity subsides, the incoming water will
“plunge” beneath the surface, with extensive mixing
possible. If the incoming water is nutrient laden, these
nutrients will be mixed with the lake water. If it is high
in organic matter, which would settle in the hypolim-
nion, the microbial metabolism could deplete the oxygen
supply. In addition to inflow influences, the discharge of
the lake, whether from a surface spillway or outlet pipe
at the bottom of the lake, will have a major influence on
the temperature of the lake, the depth of the metalim-
nion, the water temperature of the discharge, and the
receiving stream. Such lake discharges can significantly
affect water quality and oxygen content, and, in turn, the
aquatic species makeup of the receiving stream. Releases
of cold, low DO hypolimnetic water downstream cause
reductions of BOD removal rates and decreases in
reaeration rates, resulting in reduced oxygen levels and
an overall reduction in the waste assimilative capacity.
In addition, the release of cold hypolimnetic water may
affect primary contact recreation, such as swimming. To
avoid these negative consequences, some large dams
store discharged water in a second downstream reser-
voir in order to raise the temperature and DO levels
prior to subsequent release of the water downstream
(Jung, 2009).
Extreme depletion of DO in lakes may occur in ice-
and snow-covered lakes, in which light is insufficient for
photosynthesis. If depletion of DO is great enough, fish
kills may result.

column must be overcome by velocity shear within the
water column. The relative magnitudes of these effects
are measured by the Richardson number , Ri (dimen-
sionless), which gives the ratio of the buoyancy to shear
forces as

g ∂

∂

ρ

−

buoyancy
shear

ρ z

Ri = = (7.28)

2

∂
∂

u
z

where g is gravity (LT −2 ), ρ is the density of water (ML −3 ),
z is the vertical coordinate (L), and u is the horizontal
velocity of the water in the reservoir (LT −1 ). The nega-
tive sign in the numerator of Equation (7.28) accounts
for the fact that in stable environments, ρ decreases with
increasing values of z , and hence the negative sign
assures that values of Ri are positive. In cases where
Ri >> 0.25 the stratification is sufficient to inhibit mixing,
while for Ri << 0.25 significant mixing can occur to over-
come the stratification.
Stratification is commonly characterized by the buoy-
ancy frequency , N , defined as

g ∂

∂

ρ

N = − (7.29)

ρ z

The buoyancy frequency, N , defined by Equation (7.29),
is also called the Brunt-Väisälä frequency , and typical
values are on the order of 10 −3 Hz. The buoyancy fre-
quency, N , is the frequency at which a vertically dis-
placed parcel of fluid will oscillate within a statically
stable environment. Combining Equations (7.28) and
(7.29) yields the following alternate form of the
Richardson number in terms of the buoyancy

frequency,

N
u
z

2

Ri = (7.30)

2

∂
∂

7.4.4 Measures of Mixing Potential

The Richardson number is a widely used metric of
the likelihood of vertical mixing in both limnology
and oceanography, where stratified conditions are
commonplace.

During stratification, the steep temperature gradient
(i.e., thermocline) in the metalimnion suppresses many
of the mass-transport phenomena that are otherwise
responsible for the vertical transport of water-quality
constituents within a lake. In strongly stratified lakes,
the exchange of water and dissolved constituents
between the epilimnion and hypolimnion can be reduced
to molecular diffusion rates.

EXAMPLE 7.11

A lake is 10.0 m deep, has an average temperature of
13.5°C, and the temperature difference between the top
and bottom of the lake indicates that the corresponding
density difference is 0.500 kg/m 3 . If wind induces a

7.4.4.1 Richardson Number. For macroscopic mixing
to occur, the gravitational stability of a stratified water