Project Name:

Laboratory Model Of The Antarctic Circumpolar Current

Joel Sommeria
Keshav Raja
Adekunle Opeoluwa Ajayi

see ExpDiary.

0 - Publications, reports from the project:

1 - Objectives

The Antarctic Circumpolar current is recognized as the main source of ocean mixing with strong impact on Earth climate. This current is driven by the dominant Eastward wind around Antarctica. This surface forcing is balanced in average by a bottom drag, which determines the flow activity. Drag is controlled by the wake of bottom topography which takes the form of internal gravity waves propagating upward, in combination with horizontal eddies. Instabilities of these waves and vortices lead to turbulence and determine the drag friction and mixing.

The aim of the project is to reproduce these processes in the laboratory on the ‘Coriolis’ rotating platform. The circular current will be obtained by a small change of tank rotation speed while a linearly stratified density profile will be produced by salinity. A pavement of circular caps will be used to produce the bottom topography. Dynamical similarity with the ocean will be obtained by appropriate choice of rotation speed and density stratification. The flow will be measured by Particle Imaging Velocimetry, which will provide information on instability processes and momentum flux. The vertical mixing will be monitored by profilers using local conductivity probes. Data analysis will involve comparisons with numerical and theoretical studies, as well as in situ measurements in the Antarctic circumpolar current.

2 - Experimental Setup

The experiment is schedule to take place in different modules with different setups. The details of each experiment is given below. The values of necessary dimensional parameters is tabulated in the table below. The position of the laser sheet, density profilers and cameras is indicated on the diagram of the experimental setup.

2.1 - Modules of experiments

2.1.1 - Module One : Single Cap (Without rotation)

The experimental setup for this module is shown in the figure above. At this stage we include a single cap to represent a system with just one mountain then take note of wave and wake developments, formation of vortex and eddies and other needed informations. A case of rotation and NO rotation is considered for this experiment, variable mean flow is generated in either case by carefully changing the rotation of the tank. The horizontal laser is applied in two strategy, (i) Fixed: at the top and also at the bottom. (2) Multilevel: with height corresponding to z=5, 10, 15,20,25,30,50,70 cm, amounting to eight (8) levels.

At velocity 3 cm/s, dt = 0,5 s between images, displacement 1,5 cm=6 pixels for PIV (1000 pixels for 2,5 m).

2.1.2 - Module Two : Single Cap (With rotation)

Same with Module one

2.1.3 - Module Three : 18 Cap clustered in a section of the Tank (Without rotation)

This module is an extension of module two but with 18 caps representing bottom topography. We expect to have superposition of wave and eddies produced by the topographies and it will be of interest to see our this happens, also to observe the strength of instability and mixing as a result of many mountains.

2.1.4 - Module Four : 18 Cap clustered in a section of the Tank (With rotation)

Same as in Module Three

2.2 - Generation of Mean flow

2.2.1 - Without Rotation (f = 0)

The tank is filled with stratified water without rotation. To get the desired mean flow , the tank is rotated from rest while the water in the tank is assumed stationary with respect to the rotating tank and the cap. In the frame of reference of the Tank, the water is in motion with respect to the stationary cap and we those generate the desired mean flow.

2.2.2 - With Rotation

The tank is filled with stratified water while been rotated. After filling the tank, the desired mean flow is generated by inducing a change in the rotation rate. the magnitude of the speed is calculated from the product of the change in rotation rate and the radius of the tank.

2.3 - Definition of the coordinate system

$x$, along tank azimuth, clockwise direction, $y$ radial, see sketch. Origin at the cap centre.

$z$ vertical upward, origin at the tank bottom.

3. Relevant Parameters

3.1 - Fixed parameters:

Notation DefinitionValueRemarks
$R_T$Tank radius$R$=650 cm.....
$R_c$Radial position
of the cap centre
$R_c$=450 cm
$H$total water height90cmtaken at reference radius R/srqrt(2)=460 cm
$h$Cap height$h$=20cm
$D$Cap diameter at its base$D$=69 cmwhole sphere diameter =80 cm
$N$Buoyancy frequency$N$=0.47 s-1drho/rho=4%
$h/D$Aspect Ratio0.029

3.2 - Derived parameters and Non-Dimensional numbers

Notation DefinitionFormulaUnitRemarks
$\Omega$Rotation rateTurn/min
$f$Coriolis parameter$f=4\pi\Omega_0 /60 $$1/s$
$U_0$Velocity at cap centre$U=\Delta \Omega R_c$$cm/s$
$Fr$Froude Number$Fr = U/Nh$-
$Ro$Rossby Number$Ro = U/fD$-
$R_d$Rossby Radius of Deformation$R_d = Nh/f$-
$Bu$Burgers Number$Bu = (Nh/fD)^{2}$ -

3.3 - Table of Coriolis parameter

$f$Value of $f$$\Omega$ /seconds$\Omega$ turn/minPeriod

3.4 - Derived variable speed values and Froude Number

Change of rotation $\Delta \Omega$ $ (s^{-1})$$\Delta \Omega$ $ (/min)$Derived Speed : $U (cm/s) $ Froude Number Remarks

4 - Instrumentation and data acquisition

4.1 - Instruments

In this projects velocity measurements is performed using PIV method on images taking by four different cameras. Horizontal laser sheets is generated by laser arranged in the horizontal top view and The density is measured by the conductivity probes.

4.1.1 - Camera calibration

This project uses four camera namely Delsa1, Desla2, Falcon and PCO with three different perspective view where Falcon and PCO are overlapping each order. The calibration is done on UVMAT by appending five 3D images of the grid (different views of the same grid observed at different angles) with a flat image taken at height 53.5cm. This calibrated image is then used to calibrate the image taken simultaneously by the cameras each indicating the exact position of the grid. This final calibrated image is then merge to give a single view of the grid.

Each experiments is expected to last 10 minutes. The time interval for image acquisition is 0.5 seconds for all experiments amounting to 1200 images for each experiment.

4.1.2 - Laser Sheet

The laser sheet is horizontal with two different acquisition method (a) Fixed: The laser sheet is fixed at a particular height in the tank. (b) Multilevel: z=5, 10, 15, 20, 25, 30, 50, 70 cm, amounting to 8 levels. For the multilevel method, each level is scanned for 15 seconds amounting to 2 minutes time to scan the entire column. This is done repetitively through out the period of the experiment.

The laser sheet is calibrated using the table of values of fluid height and laser sheet control.

Laser valuesFluid Height from ground

4.1.3 - Density Profilers

Density profile of the flow at a point is acquired using two density probs stationed at strategic position from cap. Their positions are well indicated in the experimental setup figure above.

4.2 - Definition of time origin and instrument synchronization

4.3 - Requested final output and statistics

4.4 - Methods of calibration and data processing:

Geometric calibration:

The intrinsic camera parameters are obtained by images of the calibration grid with different angles, stored in folders 0_REF_FILES/3DCalib... for each camera.

Next the external parameters of the different cameras are adjusted by translation and rotation of the calibration points to get coincidence. This is done in 0_REF_FILES/Calib_24_02 for the final camera position. The coincidence is finally checked by making a composite image using series/merge_proj on a common grid  in phys coordinates. The result is in 0_REF_FILES/Four-cameras.mproj.

The calibration parameters are then exported to EXP1, setting z=11 with free surface at z=90 to take into account refraction. We observe that the images of Falcon and Dalsa1 are then shifted by about 10 cm, while Dalsa1 and dalsa2 coincide within  about one cm.

7 - Organization of data files:

All data related to the project are in Coriolis /.fsnet/project/coriolis/2016/'16CIRCUMPOLAR'

  • 0_DOC: miscellaneous documentation and reports
  • 0_MATLAB_FCT: specific matlab functions
  • 0_PHOTOS: photos of set-up
  • 0_REF_FILES: files of general use (calibration data, grids ...)
  • 0_RESULTS: processed data (time series, statistics...) and figures.
  • EXP1, EXP2, folder for each experiment with names given in the table below. The names refer to the FJORD, ESTUARY or GULF(effect of rotation) cases.
    • Within each experiments, images from successive runs are put in subdirectories labelled by a, b, c... Probes data are put in a folder 'PROBES'. Data from the acoustic anemometer are in a folder ADV.
      • Each folder of Images contains subfolders DeviceFolder named after the camera name, 'DALSA1', 'DALSA2', 'NIKON' (used only for a few experiments).
      • Results from data processing are stored in a folder DeviceFolder.ext where ext is set by the processing program.
      • An xml file DeviceFolder.xml specifies information from the devices, for instance timing and calibration parameters for an image series.
    • Probe data are put in the folder PROBES, in files with names labelled with a, b , c corresponding to the run. The original text format .lvm is translated into netcdf (extension .nc) for faster reading and standardisation.