Lake Water Body in the Ice Season - Freezing of Lakes and the Evolution of their Ice Cover - page 229

where is the thickness of the surface boundary layer, and H is the

depth of the convective layer. Accordingly, the velocity scale w* is a measure of the
kinetic energy of the convective motions and is representative for both the root-mean-
square (rms) velocity u rms of vertical convective water motions and the rate of the mixed
layer deepening. The rms velocity was estimated from large eddy simulations as 0.7w*by
Mironov et al. (2002). Typical reported u rms physical values are 2

ʒ is the buoyancy fl ux, ʴ

3mms − 1

(Farmer

-

1975; Kelley 1997) and support the above scaling.
The rate of deepening of a convective mixed layer is approximately given by (see
Kirillin et al. 2012b)

dt ¼ 0 : 2 w 3

dH

ð 7 : 31 Þ

H D b

where b is the buoyancy jump at the bottom of the mixed layer. The reported rates of the

mixed layer deepening are typically

ʔ

0.5 m day − 1 and increase up to several meters per
day in deeper lakes. The background strati

*

cation enters into Eq. ( 7.31 ) through the

ʔ

buoyancy jump uences on the convective layer

development. A case with very fast development was registered in Lake P

b. Therefore the past winter history in fl

ää ä

rvi, Finland,
in sunny weather in April 2011 after relatively long snowy winter (Fig. 7.12 ). As a result,
a large amount of radiation penetrating into a weakly stratified water column deepened the
mixed layer at the rate of more than 3 m day − 1 . Then, a sharp temperature gradient at the
bottom of the mixed layer was then produced, increasing the term (H ʔ b) in Eq. ( 7.31 ), and
the deepening rate reduced to about 1 m day − 1 .

j

Fig. 7.12 Convective
temperature profiles in the
central part of Lake P ää j ä rvi,
spring 2011 (Kirillin et al.
2012a). Dots mark approximate
locations of the convectively
mixed layer