182
files are representative of the state of intermittency in the water
column, the dissipation is below 10−11 W/kg more than 50 % of
the time. Similar observations were performed in the ocean
interior in the California Current in the eastern North Pacific
Ocean where (Gregg et al. 2003 ) observed that over a large
proportion of the water column, ε is less than the instrumental
noise level about 60 % of the time. Strikingly, lakes and ocean
behave similarly on this point and no significant difference
appears concerning the turbulent weather of the water
column.
The conditions for a significant buoyancy flux to occur is
ε > 19υN^2 and for isotropic condition to be fulfilled is
ε > 200υN^2 (Itsweire, 1993 ). In the hypolimnion in 2006, the
condition is satisfied when ε > 10−11 W/kg. At the chemo-
cline, when ε > 10−9 W/kg and at the thermocline, when
ε > 10−8 W/kg. The conditions are increased by one order of
magnitude for the isotropic condition. In the case of Lake
Pavin, it means that significant buoyancy flux is generated
30–40 % of the time in the hypolimnion and less than 10 % of
the time at the thermocline and chemocline. As far as the
isotropy condition is concerned, rarely the turbulence is iso-
tropic at the density interface and about 10 % of the time in
the hypolimnion. Comparing to the ocean, the data set avail-
able here on Lake Pavin shows that the mixed layer is far less
mixed than in the ocean. Because of small hills around the
lake surface, Lake Pavin surface is protected from strong
winds.
General trend of the dissipation rate shows more intense
dissipation where the generated shear by internal wave
motions is the highest. Internal waves occur in stratified
water bodies after the wind stops. In fact, the wind tilts the
lake surface when it blows. When the wind stops, the gravity
brings the surface back to its equilibrium position and the
lake surface oscillates several times. At the thermocline, this
observation was obvious from profiles collected in 2006
(data not shown) and 2007 (see Fig. 10.3). At the chemo-
cline, an enhanced dissipation is only noticeable in 2007 (see
Fig. 10.3), which is marked by a higher density gradient
around 60 m depth as shown in Fig. 10.1.
In 2007, the dissipation rate at the thermocline is higher
than 5 × 10−10 W/kg about 70 % of the time. On the contrary,
dissipation in the hypolimnion is very low: below the mixed
layer, the water column presented turbulence levels below
1 × 10−11 m^2 s−1 more than 50 % of the time. But high values
of dissipation (above 1 × 10−9 m^2 s−1) may occur about 15 %
of the time. At the chemocline, dissipation levels are close to
dissipation levels at the thermocline.
10.2.6 Estimates of Vertical Diffusivity (Kz)
Kz is an important parameter used by different geochemical
models to simulate the transport of solutes in a water body.
An example applied to Lake Pavin is given in the next
section.
Knowing ε, the vertical diffusivity (Kz) can be calculated
by the Osborn method (Osborn 1980 ).K
z N
=γεmix
2 (10.2)with γmix the mixing efficiency,and N2 the buyoancy or
Brunt-Väisälä frequency. γmix = 0.2 is the usual value given
for the mixing efficiency (Ellison 1957 ) that was used in this
study.
Computed Kz are geometrically averaged (Baker and
Gibson 1987 ) to calculate the averaged value of Kz. The error
bars (Fig. 10.4) represent the standard deviation of log(Kz)
on each monthly series of Kz, at each meter. They relate the
intermittency of the mixing in the water column. The inter-
mittency of turbulence is caused by the intermittency of forc-
ings (wind for example) and by the sporadic and statistic
occurrence of turbulent bursts.
Averaged profiles are reported in Fig. 10.4. In black, aver-
aged Kz of May 2006 lays slightly below averaged Kz of July
(in green) and November 2006 (in red). The vertical diffusiv-
ity presents two minima at the thermocline and at the chemo-
cline except in July: at these locations, the diffusivity is
below heat molecular diffusivity. Outside of strong density
gradient regions, vertical diffusivity is higher in the hypolim-
nion and in the monimolimnion. The stratification is higher0
10
20
30
40
50
Depth (m)
60
70
80
90
-11 -10 -9 -8 -7 -6 -5 -4 -3 -2
log (Kz)
Fig. 10.4 Kz (in m^2 /s) with error bars calculated from microstructure
measurements by the Batchelor fitting method on the whole water col-
umn. Black: May 2006, Red: July 2006, Green: November 2006C. Bonhomme et al.