LAKES AND RESERVOIRS - Water Quality Engineering in Natural Systems - page 245

Wind Wind

(a) (b)

Figure 7.2. Wind-induced circulation in lakes: (a) shallow lake; (b) deep lake.

affects biological productivity and the biota. Lake cur-
rents are driven primarily by wind, inflow/outflow, and
the Coriolis force. For small shallow lakes, particularly
long and narrow lakes, inflow/outflow characteristics are
most important, and the predominant current is a
steady-state flow through the lake. For very large lakes,
wind is the primary generator of currents, and except
for local effects, inflow/outflow have a relatively minor
effect on lake circulation. The Coriolis effect, a deflect-
ing force that is a function of the Earth's rotation, also
plays a role in circulation in large lakes, such as the
Great Lakes.
Typical wind-induced circulation regimes in shallow
and deep lakes are illustrated in Figure 7.2, where the
main difference is that shallow lakes tend to have a
single circulation cell, whereas deeper lakes tend to
have more than one circulation cell. Lakes are typically
classified as shallow if they are less than 7-10 m (20-
30 ft) in depth, and deep if they are more than 10 m
(30 ft) in depth; in some cases, deep lakes are defined as
those with depths greater than 5 m (15 ft) (e.g., Novotny,
2003). Depth and wind have significant influences on the
thermal structure of lakes, with shallow lakes (<10 m
[30 ft]) rarely stratifying for long periods, and very deep
lakes (>30 m [100 ft]) remaining stratified for long
periods of time, either permanently in tropical climates
or seasonally outside the tropics (James, 1993). The cir-
culation pattern in a lake depends significantly on the
surface area of the lake, since lakes with larger surface
areas experience greater wind force and have a greater
tendency to form a single (vertical) circulation cell.
Consequently, it is more appropriately the ratio of the
water body surface area to its depth that dictates
whether a water body is shallow or deep. In cases where
lake circulation is to be estimated in detail, the use of
hydrodynamic circulation models are appropriate.
The magnitudes of wind-induced surface currents,
called wind drift , depend on the characteristics of the
lake, and these wind-induced surface currents are typi-
cally on the order of 2-3% of the wind speed. The wind
stress on the surface of a lake is given by

where τ is the wind stress (FL −3 ), C D is the drag coeffi-
cient (dimensionless), ρ a is the density of air (ML −3 ), and
U is the wind speed (LT −1 ). The density of air depends
on the ambient temperature, pressure, and humidity,
and is usually in the range 1.2-1.3 kg/m 3 , and C D can be
taken as 1.0 × 10 −3 for wind speeds up to 5 m/s (11 mph),
with a linear increase to 1.5 × 10 −3 for wind speeds of
15 m/s (33 mph) (Hicks, 1972).
Lake Okeechobee in Florida is an example of a large
shallow lake where the currents are primarily wind
driven. Lake Okeechobee is the third largest lake con-
tained entirely in the United States, after Lake Michi-
gan and Iliamna Lake (in Alaska), and has a surface
area of approximately 1900 km 2 (730 mi 2 ) and an
average depth of about 3 m (10 ft). Chen and Sheng
(2005) have demonstrated that wind-generated flows in
the lake are sometimes sufficient to stir up a significant
amount of bottom sediment. The phosphorus desorbed
from the increased suspended sediment in the water
column contributes significantly to phosphorus concen-
trations in the lake, which is typically in the range of
50-100 µ g/L. This implication of this result is that ade-
quate prediction of the phosphorus concentrations in
Lake Okeechobee requires a circulation (hydrody-
namic) model combined with both a sediment transport
model to describe the sediment fluidization and resus-
pension process, and a water-quality model to describe
the relationship between adsorbed and dissolved
phosphorus. If Lake Okeechobee were a deep lake,
wind-induced currents would probably not cause signifi-
cant sediment suspension, and a simpler description
of the fate and transport of phosphorus would be
possible.

EXAMPLE 7.3

Sediment resuspension is observed to occur in a lake
when the average wind speed is 20 mph. What is the
corresponding shear stress on the surface of the lake?
Based on this shear stress, estimate the order of magni-
tude of the turbulent velocity fluctuations that would be
induced in the surface layer of the lake.

2

τ = C U

D a

ρ (7.4)