Lake Water Body in the Ice Season - Freezing of Lakes and the Evolution of their Ice Cover - page 223

Rahm (1985) constructed a horizontally-integrated one-dimensional circulation model
in an idealized lake with constant heat input from sediments and stably strati

ed water
column. The model produced a two-cell circulation pattern in the vertical direction in the
lake. In the upper layer, downward currents flowed along the bottom slope, and a com-

pensating upwelling resulted in the middle of the lake. In the lower layer, there were
upward boundary currents compensated by downwelling in the lake interior. The depth of
the dividing level of no motion depended on the strati

fl

cation and the angle of the bottom
slope, but roughly speaking it was at the half-depth of the lake. Upward boundary currents
were produced by diffusion-generated density gradients along the bottom slope — a

mechanism described before in the deep ocean dynamics (Phillips 1970; Wunsch 1970) —

and counteracted the downward currents produced by the sediment heat release. Likens
and Ragotskie (1965) observed a similar two-cell structure in Tub Lake in 1961, but in the
preceding year they found a simple one-cell circulation, with downward boundary cur-
rents and mid-lake upwelling throughout the entire lake. Hence, the circulation pattern can
differ from year to year depending on the amount of heat stored in the sediment and on the
strati cation in the lake, both affected strongly by the conditions prior to ice coverage.

The effect of the Earth

ux driven circulation has been largely
neglected in most investigations of small and medium-size lakes. These effects were

' s rotation on the bottom- fl

rst

discussed brie y by Likens and Ragotskie (1966). Recently, Huttula et al. (2010) applied

a 3-dimensional model to simulate rotation-in

fl

ux
from sediment of constant temperature (Fig. 7.10 ). An idealized cylindrical lake and Lake
P

fl uenced density currents forced by heat fl

rvi, southern Finland acted as the study basins. The results demonstrated the for-
mation of two vertically superimposed lake-wide gyres, coinciding roughly with the
circulation cells in the model of Rahm (1985), and rotating in opposite directions.

ää j ä

Example 7.6 . Consider a cylindrical basin with radius r and depth H. The geostrophic

balance is written in polar coordinates (r,

ʸ )as

fu h ¼ q @ p fu r ¼ q @ p

@ r ;

r @h

@ p
@ z ¼ g q

An axisymmetric solution has zero radial velocity, while the azimuthal component
comes from the radial pressure gradient. High water in the middle produces clockwise
gyre and vice versa. If there is a pressure compensation depth, the circulation would
change sign. The 1st order correction to this balance gives a radial vertical circulation

-

pattern.