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Lab Studies of Stirring by Small-Scale Geostrophic Motions
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| PIs: |
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M. A. Sundermeyer and D. L. Hebert |
| Grad Students: |
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G. A. Stuart (Masters Degree June 2007) |
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A.-M. Suzuki-Brunner (Ph.D. expected June 2010) |
| Grant Title: |
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Laboratory Studies of Stirring
by Small-Scale Geostrophic Motions |
| Funding Agency: |
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The National Science Foundation
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Objectives
We use laboratory experiments to study lateral stirring by small-scale
geostrophic motions formed by the adjustment of diapycnal mixing events.
Experiments build on analytical and numerical studies by Sundermeyer
et al. (2005) and Sundermeyer and Lelong (in press), which predict
the amount of lateral dispersion caused by vortical mode stirring.
A major advantage of the laboratory studies over previous
analytical and numerical studies, however, is that here diapycnal
mixing events will ultimately be driven by internal wave breaking
rather than artificially imposed mixing.
Two major goals of this work are 1) to test theoretical predictions
for vortical mode stirring when internal wave forcing and breaking
are present, and 2) to provide a basis for parameterizing horizontal
dispersion rates by vortical mode stirring in the ocean.
The proposed work will help provide a quantitative description of
vortical mode stirring on scales of 1-10 km in the ocean.
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Rotating tank facility at the University of
Rhode Island's Graduate School of Occeanography.
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Description of Lab Experiments
Experiments are conducted at the University of Rhode Island's
Graduate School of Oceanography rotating tank facility. A 1 m diameter,
30 cm deep uniformly stratified rotating tank is used to model
conditions in the ocean's stratified interior. Two methods will be
used to generate diapycnal mixing events: 1) mechanical stirring in
the form of localized grid-forced turbulence, and 2) a quasi-random
field of internal waves and wave breaking generated by near resonant
forcing of a mode-1 internal wave, and wave-wave interactions to
scatter energy into higher modes. The formation of vortical modes and
their effects on lateral stirring of a passive fluorescent dye will
be examined using a combination of Particle Imaging Velocimetry (PIV),
Laser Induced Fluorescence (LIF), and digital video analysis. Results
will be compared with theoretical and numerical predictions from
previous studies.
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Results to Date
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(Left) Laboratory setup for single mixer experiments.
(Middle) Side (above) and top (below) views of a single grid mixer.
(Right) Side (above) and top (below) views after mixing dye within
the mixed patch.
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Single Mixer Experiments
- In the first phase of our study we analyze the case of a
single eddy in order to confirm the dynamics of the geostrophic
adjustment problem, and to obtain relevant time and space scales for
the multi-eddy case. For these experiments, isolated mixed patches
are generated mechanically using grid-forced turbulence. A schematic
of the laboratory configuration for the single mixed patch case is
shown below. Also shown is a pair of photographs of the tank before
and after a mixed patch is generated. The mixed patch is created by
vertically oscillating a small disk-shaped grid for a brief time, and
allowing the resulting mixed patch to adjust under the influence of
rotation. In the right-most image, a green dye is injected into the
center of the mixed patch as it is being generated. The dye clearly
shows both the vertical and horizontal extent of the mixed patch.
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The same single mixer experiments can also be visualized using PIV.
The sequence of images below show the adjustment and gradual decay of
the vortex that ensues from the mixed patch adjustment. These images
provide a means of quantitatively assessing the strength of the resulting
eddy, its size, and its decay time, all of which have significant
implacations to the overall lateral dispersion that results.
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A series of PIV images (horizontal velocity shown
by colored arrows)
of the adjustment of a single mixed patch. Times are shown in each
image in terms of number of seconds since the cessation of mixing,
and in terms of the number of inertial periods. Noteworthy is the
rapid organization of the adjustment into a coherent eddy after
approximately 1 inertial period, and the subsequent persistance of
the eddy.
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Schematic of laboratory setup for multi-mixer
experiments. Configuration is similar to single mixer case, except
that multiple mixers are activated in turn at quasi-random locations
in the tank.
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Multi-Mixer Experiments
- Next we analyze the case of multiple eddies and their effect on
lateral dispersion. Again we begin by generating isolated mixed
patches, this time at regular time intervals, but at random locations
in the tank. A schematic of the multi-eddy laboratory set-up
is shown to the right.
Dye is released at the center of the tank, and tracked for
many tens of inertial periods in order to visualize the dispersion.
The sequence of images below shows an example of one of these
experiments. Times in seconds and inertial periods are given in each
frame.
Still images of the dye are analyzed to estimate the second moment of
the dye patch as it evolves in time. The second moment of the patch is
then used to infer the effective eddy diffusivity of the patch.
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Sequence of images from multi-eddy experiment showing
eddy dispersion of a dye released at the center of the tank.
Times are shown in each image in terms of number of seconds since
the cessation of mixing, and in terms of the number of inertial
periods.
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(Left) Horizontal second moments inferred at a
single snapshot in time from
one of the tracer tracer images shown above, and (Right) growth
of the second moments in each direction over the course of the
experiment.
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Ongoing Analysis
As a next step to the above analysis, we will repeat the above
experiments for varying experimental parameters, including the Coriolis
frequency, time between mixed patches, and stratification.
For the single mixer experiments, this will enable us to verify the
dynamics of the geostrophic adjustment problem, while for the multi-eddy
case, it will enable us to begin to test the theoretical scaling
prediction of Sundermeyer et al. (2005).
Once we have completed this initial phase of the experiments, we will
turn to phase two of this project in which the mixed patches will be
generated by internal wave breaking forced by large-scale internal
waves. This will be done using a large-scale wave generator, again on
a rotating tank. Here we will explicitly explore the dynamics of the
wave breaking itself, and how the wave field effects the subsequent
development of, and stirring by, small-scale eddies.
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... Stay tuned for more results to follow ...
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Presentations
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Stuart, G. A., M. A. Sundermeyer, and D. L. Hebert.
Lab Studies of Small-Scale Geostrophic Eddies.
Middle Atlantic Bight Physical Oceanography and Meteorology
Meeting, November, 2005, Stony Brook, NY.
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