18110.2.4 High Frequency Measurements
and Quantification of Dissipation
and Vertical Diffusivity in the Water
Column of Lake Pavin
When the water column of a lake is turbulent, the turbulent
kinetic energy is transmitted from big scales to smaller struc-
tures and scales. When the scale reaches the one of viscous
forces, the kinetic energy is transformed into heat and the
temperature of the fluid rises. It is possible to calculate the
dissipation in the water column from the fluctuations of tem-
perature profiles with the Batchelor method (Batchelor
1959 ). This method relies on the fit between a theoretical and
an experimental spectra around the length scale of viscous
forces.
Nevertheless, both turbulent and diffusive processes cause
micro-fluctuations of temperature in lakes. Time-series of a
depth averaged “effective dissipation rate” (εμ) can be com-
puted by assuming that all fluctuations are due to mechanical
turbulence. This approximation is only valid when the turbu-
lent diffusion coefficient exceeds molecular diffusivity.
When the dissipation falls below or close to molecular dif-
fusivity, this approach under-evaluates the diffusivity. It hap-
pens in Lake Pavin around the chemocline and therefore the
vertical diffusivity has a lower bound which is molecular
diffusivity.
For steady conditions and neglecting the divergence
terms, the production of turbulent kinetic energy (by the
Reynolds stress working on the mean shear) is balanced by
the dissipation rate ε and the buoyancy flux b. The turbulent
kinetic energy balance becomes:
−∂
∂uu =+U
x
ij i b
jε
(10.1)where Uj is the mean velocity and uj is the fluctuating
velocity.
Temperature fluctuations are measured through tempera-
ture microstructure surveys (SCAMP – Self-Contained
Autonomous Micro-Profiler designed by PME) in 2006 and
2007 completed by CTD profiles (Seabird, SBE 19). The
microprofiler is used in falling mode, at a speed of ca. 0.1
m/s, with a 100 Hz sampling rate for temperature and 40 Hz
for conductivity. The resolution of the device is 0.005 °C and
the relative error for conductivity is 5 %.10.2.5 Determination of the Dissipation Rate ε
from Microstructure MeasurementsSeveral profiles were performed at a central position in Lake
Pavin from April to June 2007, with a time step of about 15’
(this time step is the minimum delay to acquire successive
measurements with the SCAMP because the falling speed is
set). Based on SCAMP profiles, histograms of measured dis-
sipation rates with different boundaries (from 10−12 W/kg to
10 −9 W/kg, from black to white) as a function of depth are
plotted on Fig. 10.3. From Fig. 10.3, it can be observed that
the dissipation rate ε is highly intermittent in space and time
in the water column of Lake Pavin.
The water column of Lake Pavin spends most of time at
low dissipation rates (below the detection threshold of the
instrument). Making the assumption that the measured pro-Fig. 10.3 Histograms
representing the intermittency
of the dissipation rate
(in W/kg) in the whole water
column in July–September–
November 2006
10 Lake Pavin Mixing: New Insights from High Resolution Continuous Measurements