Lake Water Body in the Ice Season - Freezing of Lakes and the Evolution of their Ice Cover - page 225

7.3.2 Shallow Water Waves

Free oscillations of the entire water body, or barotropic seiches, are intrinsic features of
lakes, observed also in the ice season (e.g., Falkenmark 1973). The wave speed is obtained
from the shallow water theory as

p

gH c ¼ ð 7 : 23 Þ

first tilting the lake surface level by wind or atmospheric
pressure over the lake. When the wind or pressure force ceases, oscillation starts up and
continues as a standing wave. In a narrow linear lake with depth H and length L, the
period of uninodal (

Seiches are initiated by

is formula. In
uninodal oscillation there is a node at the centre and antinodes at the ends of the lake.
In ice-covered lakes, seiches are induced by oscillation of the

(first mode) oscillation is t S =2L/c, known as the Merian '

floating ice sheet
(Bengtsson 1996; Malm et al. 1998; Petrov et al. 2006; Zdorovennova 2009; Kirillin et al.
2012b). The ice cover does not damp these oscillations (Sturova 2007; Zyryanov 2011),
but the amplitudes are lower than in open water season because the seiches are excited by
oscillations of the ice surface rather than by the wind-driven inclination of the lake
surface.
The one-dimensional model can be also employed for seiches in two-dimensional
lakes, with L as the length of the basin in the direction of the oscillation. In larger lakes the
Coriolis acceleration starts to in

fl

fl uence the direction of the wave motion. The scale of this

in uence is expressed by the ratio of the characteristic lake size to the Rossby radius of

deformation, which is de

fl

ned as

L R ¼ cf 1 ð 7 : 24 Þ

Barotropic motions in lakes with horizontal dimensions smaller than L R are unaffected
by the Earth 20 m s − 1 , ' s rotation. For H 40 m and latitude 60 ° , we have c

* *

10 − 4 s − 1 and L R * f =0.63 × 300 km; for H =10m,L R * 150 km. Therefore only in very

large lakes Earth uences barotropic seiches. Exceptions are shallow lakes

with large horizontal dimensions, e.g. Lake Erie and Lake Balkhash.
One of the

' s rotation in fl

first systematic observations of barotropic seiches was performed in ice-
covered Swedish lakes by Bengtsson (1996). He reported of oscillating currents with
periods of the first mode seiches and average magnitudes of 0.4 cm s − 1 . Parallel esti-

mations of horizontal dispersion revealed up to 10-fold increase in horizontal mixing
associated with strong wind events, which were ascribed to the mixing intensi

cation by

seiches. In small, flow velocity

oscillations of several millimetres per second, driven by the longitudinal seiche, were
found to exist during the entire ice-covered period (Malm et al. 1998; Malm 1999)
accompanied by vertical oscillations of the ice cover. Atmospheric pressure variations
have been identi

ice-covered Lake Vendyurskoe in Russian Karelia, fl

ed as the main mechanism providing the kinetic energy to the