Intrusions


Vertical mixing is inhibited in the stratified interior of lakes and the ocean.  Field observations suggest that turbulence created at the boundaries is responsible for the majority of the mixing that occurs. Much work has been done investigating mixing at boundaries; less attention has been paid to the fate of this mixed fluid. Intrusion generation may provide one path of transport.
Schematic of physical processes leading to boundary mixing and intrusions in a lake. The wind acts on a density stratified lake (a representative density (ρ) profile is shown), creating seiches with a dominant frequency ω1 and critical internal waves with a frequency ωc.

Importance of Intrusions

  • They can transport mixed fluid away from boundaries.
    • Boundary-interior communication
    • Increased efficiency of boundary mixing
  • They can create thin layers where the density gradient is sharp.

Laboratory view of intrusions from internal waves breaking on a slope in a linearly stratified fluid (D.F. Hill, pers. comm.).

EXPERIMENTS

We have conducted two dye studies to track fluid from the boundary of the south basin of Ada
Hayden Lake where a 10 m long streak of Rhodamine WT was injected at the northeast shore at a
target isopycnal.  In Summer 2008, we plan on doing four more dye injections.  Preliminary results are
discussed here.

July 2005: The dye cloud was mapped with a fluorometer for one day after the injection, with
temperature microstructure profiles measured concurrently with a Self-Contained Microstructure
Profiler (SCAMP).
   
August 2007: The dye cloud was mapped for three days following the injection.  A Lake Diagnostic
System (LDS) and two 29 node thermistor chains were deployed.  CTD casts were done along the
transect shown.  Additionally a high resolution acoustic current profiler (an Aquadopp) was
deployed facing downward into the bottom boundary layer on the slope.  An ADCP was placed
uplooking near one of the T-chains to measure the entire water column.


Bathymetric map of south basin of Ada Hayden Lake. This also summarizes the measurements
and their locations.

Topographic transect along the dashed line above shown with the thermal structure (in C).

RESULTS FROM 2005

Dye was injected immediately following a storm event in July 2005 (black arrow).  The Lake
number (LN) is a ratio of the wind strength to the stratification strength. When LN = 1, upwelling is
expected to occur; for LN < 10, seiching motions should be generated. A second wind event
occurred one day after the injection (purple arrow).
Horn et al. (2001) use the Wedderburn number (similar to the Lake number) to classify the lake response. Ada Hayden Lake falls mainly in the damped linear wave regime, although under certain conditions solitary waves might form.  Wind conditions were unsuitable for generating critical internal waves, given the wind direction.  Elevated turbulence observed on the slope after the first wind event indicates that seiching motions were generated.

Log of the critical internal wave frequencies (in cph) on the lake slopes.  The arrows in the corner indicate the wind direction of the three wind events described here in 2005 and 2007.
  • T profiles show constant density layer at the intrusion depth.
  • C profiles indicate seiching is likely.
  • K profiles show elevated mixing onshore at the slope.

Vertical profiles of temperature, dye concentration, and vertical eddy diffusivity.  The y-axis is depth (in m).  The dashed lines indicate onshore profiles and the solid lines indicate offshore profiles.  The eddy diffusivity was computed from quantities averaged over the ten profiles at each site.  There is no data in the upper 4 m because FP07s were not calibrated above 27°C.
The dye moved approximately 250 m offshore in one day in a coherent tongue extending to the southwest, a movement perpendicular to the wind.  Because of the observed mixing at the boundary and the step like thermal structure, we propose that the boundary mixed fluid collapsed into an intrusion.

Map of dye in Ada Hayden Lake one day after dye injection.  Concentrations in ppb.
Dye moved 250 m offshore in 1 day: front velocity ~ 0.3 cm/s

Gloor et al. (2000):


From lab experiments, front position vs. time follows power law:

 

n

DeSilva et al (1997)

0.83

McPhee-Shaw & Kunze (2002)

0.7 – 1.1

Present Data

1.2

Vertical profiles one day after injection.  Profiles are offset by 10 ppb. Numbers above each curve are the distances (in m) from the injection site.

RESULTS FROM 2007

The day before the planned dye injection in August 2007, a large wind     event was observed; on
the day of the dye release, the wind was calm. With the exception of a small wind event 12 hours
after the dye injection (the blue arrow), the wind forcing remained weak for the five days of the study.



Map of dye in Ada Hayden Lake six hours, one day, and two days after the dye injection.
 Because of weak wind forcing during the experiment and the wind direction during the single wind event, we do not expect much mixing to be generated at the dye injection site.

At the lake bottom we saw a vertical eddy diffusivity slightly enhanced over the molecular value both onshore and offshore.
The eddy diffusivity only exceeds 10-5 m2/s offshore during the second and third sets of measurements, possible due to the seiching motions generated by the wind event passing over the rough topography at the offshore site.

Between the first and second dye mapping, there was a brief wind event that excited internal waves in lake and the dye moved offshore.

Along the steep eastern wall, only a very small region is adjacent to the stratified metalimnion and only very high frequency waves will break. 

Spectral analysis of the internal wave field shows that such waves do exist, but the breaking region was below the lower extent of the dye cloud. 

Friction from the internal waves moving along the wall could have created a turbulent layer that intruded.

Alternatively, seiche induced horizontal velocities may have carried the dye inshore. 
From modal analysis, we see that the horizontal velocity induced by the V2H1 seiche at the depth of the dye is approximately 1.5 cm/s.

Between the second and third day, the winds were calm and the dye cloud did not spread in any coherent manner. Horizontal diffusion is the most likely mechanism for spreading of the dye during this time.