Dynamics of planetary polar vortices: Barotropic instability and quasistable

Dynamics of planetary polar vortices: Barotropic instability and quasi-stable modes NTNU Coriolis NTNU Coriolis Polar Vortices EC contract no. 261520 Status: final Date: Jun 2008 Infrastructure Project Campaign Title NTNU Coriolis Dynamics of planetary polar vortices: Barotropic instability and quasistable modes HyIII-NTNU-16 NTNU Coriolis Polar Vortices Lead Author Luca Montabone Email montabone@atm.ox.ac.uk Contributors Tom Jacoby Email jacoby@atm.ox.ac.uk Date Campaign Start Date Final Completion 16/06/2008 29/09/2008 Date Campaign End 16/06/2008

Contents: Heading: Contents: 1 Scientific aim and background 2 User-Project Achievements and difficulties encountered (max 250 words) 3 Highlights important research results (max 250 words) 4 Publications, reports from the project 5 Description 5.1 General description, including sketch 5.2 Definition of the coordinate systems used 5.3 Instruments used 5.4 Definition of time origin and instrument synchronisation 6 Definition and notation of the experimental parameters 6.1 Fixed parameters 6.2 Variable independent parameters 6.3 Derived parameters and relevant non-dimensional numbers 7 Description of the experimental campaign, list of experiments 8 Data processing 9 Organisation of data files 10 Remarks about the experimental campaign, problems and things to improve 1. Scientific aim and background: This project was intended to investigate the dynamics of the planetary polar vortices in the laboratory, with particular emphasis on analogues of Venus polar vortex and possibly Saturn s. The overall objective of the project was the study of the possible transitions between different quasi-stable modes of a polar vortex structure, induced by barotropic (i.e., shear) instabilities. In the case of Venus, for instance, the possibility of barotropic instabilities in the polar jets is supported by calculations made using radio occultation observations from Pioneer Venus, and by results from linearized numerical models. The principal aims of the laboratory experiments were the following: To establish the formation of a central olar vortex by sole means of a dynamical forcing produced by mass sources and sinks. To quantify the dependence of the shape and strength of the vortex on the experimental parameters: rotation rate, volume flux and distribution of sources and sinks. To verify the onset of barotropic instabilities originating around the inflexion points of the radial profile of tangential velocity around the vortex. To study the effects of such instabilities for selected parameter ranges in approximate dynamic similitude with planetary cases (Venus in particular, possibly Saturn). In particular, we wanted to test the existence of a quasi-stable wavenumber-2 mode and possibly verify the transition between different quasi-stable modes.

2. User-Project Achievements and difficulties encountered: 38 experimental runs were completed during the three-week period of our project. A central vortex was formed by using the planned source-sink set-up, starting from initial conditions corresponding to solid body rotation. Such a vortex has proved to follow the expected dynamics according to the used parameters. We have been able to span a vast range of dynamical parameters, varying the rotation rate of the tank, the source-to-sink flux, the configuration of the central sink and the configuration of the source, as planned. In all experiments we have used blue dye to visualize the dynamics in the central vortex, allowing us to establish the presence of instabilities at its edge, the number of satellite vortices (modes) which formed around the center, their stability or the transition between consecutive modes. Measurements of the azimuthal velocity of the vortex at different radial positions and depths were made by using a velocity probe. These measurements are extremely important to test the theory behind the experiment and compare with predictions and numerical simulations. We also tried to use the particle tracking technique in selected experimental runs in order to obtain instantaneous velocity measurements with sufficient resolution. The major difficulty we encountered was obtaining global velocity measurements with sufficiently high resolution in order to resolve the structures which formed by barotropic instability. Unfortunately the particle tracking technique failed to provide a resolution which was high enough for our purposes. Particle image velocimetry is important to our experiment. 3. Highlights important research results: The presence of barotropic instabilities at the edge of a polar vortex were confirmed by means of the source-sink technique. These instabilities grow to create stable satellite vortices orbiting around the central 'polar' vortex. The number of vortices is a function of the experimental parameters, namely the local Rossby number, the Ekman number and the experimental initial conditions. Hysteresis plays a major role in determining the final stable number of satellite vortices, after a transient period during which transitions between different modes are likely observed. In all our less turbulent experiments we have observed that the barotropic instabilities form structures characterized by either mode 2 (dipole), mode 3 (tripole), mode 4 (quadrupole) or mode 6 (hexagon), according to the experimental parameters. Highly turbulent experiments (using the highest available experimental flux rate, i.e. 2 l/s) didn't show the presence of stable vortices during the experimental time (~2 hours). In these cases the shear is too strong to allow the stabilization of the satellite vortices, which are strained as soon as they form. Our experiments suggest the hypothesis that barotropic instability is the physical phenomenon at the origin of the multi-modal coherent structures observed around the poles of several planetary atmospheres. It is essential to further study in detail the growth of such instabilities and the initial competition between different modes until the moment when the strongest one dominates. Such a study would require the use of a global Eulerian visualization technique such as the Particle Image Velocimetry. 4. Publications, reports from the project:

1. L. Montabone, R. Wordsworth, A. Aguiar, T. Jacoby, T. McClimans, P. L. Read, C. Wilson, "Coherent structures in Planetary Polar Vortices: A Laboratory View". International Conference on Comparative Planetology: Venus Earth Mars, ESA/ESTEC, Noordwijk (The Netherlands), May 2009. 2. L. Montabone, R. Wordsworth, A. Aguiar, P. L. Read, T. Jacoby, T. McClimans, I. Ellingsen, "Barotropic Instability of Planetary Polar Vortices: Concept, Experimental Set-up and Parameter Space Analysis", Proceeding of the Hydralab III Joint Transnational Access User Meeting, February 2010, Hannover (Germany), ISBN-978-3-00-030141-4, p. 135 5. Description: 5.1. Description: Figure 5.1.1 The 5-m diameter "Coriolis" tank of the University of Science and Technology in Trondheim (Norway), with our experimental set-up. The colander-like sink is visible in the centre of the tank. The ring of point sources is visible at the periphery. In this experiment, we used a source-sink technique to create a central vortex in homogeneous water with fixed depth (H = 0.4 m). Water was pumped out of a source ring (radius = 2 m) at a given flux rate Q, and was sucked from a central, circular sink region (maximum radius = 0.46 m). See Fig. 2 for a sketch of the experimental set-up. This colander-like sink region had a parabolic shape to account for the γ effect at the pole of a planet, i.e. the quadratic term of the expansion of the Coriolis parameter f = 2Ωsinφ near the

pole. The parabolic sink plate was mounted on a circular frame 0.04 m wide, which sloped down linearly to the level of the tank (false) floor. We were able to use different configurations of the sink region by covering selective portions with four specifically designed annular masks (Fig. 3), each of them 0.09 m across, and a central, circular mask of 0.18 m diameter. Figure 5.1.2 Sketch of the experimental setup.

Figure 5.1.3 Sketch of the masks used to cover portions of the parabolic sink region. 5.2. Definition of the coordinate systems used: There are two types of coordinate systems, one for the velocity probe and one for the cameras. The coordinate system for the cameras is a system co-rotating with the tank, where the centre of the colander approximately coincides with the centre of the camera image. Calibration images were taken to calibrate the three cameras used for 3D particle tracking. The coordinate system for the velocity probe is a radial line from the centre of the tank (i.e. the centre of the parabolic sink plate) to the outermost position, at two depths. 5.3. Instruments used: Dye injection at the surface of the water to visualize the coherent structures at the edge of the central vortex. We used a time-lapse camera as well as a Firewire camera to record its evolution. Doppler velocity probe to measure the three components of the velocity field at 25 radial locations, each separated by 0.05 m, starting from a distance of 0.09 m from the centre (The probe measured at depths of 0.05 and 0.17 m below the surface of water at rest). Particle tracking with 1 cm diameter surface tracers. We used three dedicated cameras to follow the tracers. 5.4. Definition of time origin and instrument synchronisation:

Time was measured with a clock, and every event refers to the local time in Trondheim as absolute reference. Times are detailed in the appendix table. Local time was embedded in camera images used to record the dye evolution. 6. Definition and notation of the experimental parameters: 6.1. Fixed parameters: Depth of water at rest above the false bottom of the rotating tank: H = 0.4 m Maximum height of the sink plate above the false bottom of the rotating tank: 0.86 m Full diameter of the parabolic sink plate: 0.46 m Full diameter of the parabolic + linear sink plate: 0.50 m Distance of the source ring from the centre of the rotating tank: 2.0 m 6.2. Variable independent parameters: Notation Name Unit Definition Remarks Table 6.2.1

6.3. Derived parameters and relevant non-dimensional numbers: Notation Name Unit Definition Remarks Table 6.3.1

7. Description of the experimental campaign, list of experiments: Experiment Name Experiment Date Remarks

Table 7.1 Run No. Date Flow Rate Rotation Period Source Sink Spinup Configuration Configuration Started Pump Rate Changed Velocity Probe Started PTV Started Dye Firewire Firewire camera Notes Visualisation Index started L/s s 5 19 juni 2008 2 80 Full 1 12:00:00 12:57:00 N/A 14:03:00 N/A N/A Wobbly monopole 6 19 juni 2008 1 80 Full 1 12:00:00 14:28:00 N/A 14:58:00 N/A N/A Irregular m = 2-5. 7 19 juni 2008 0.5 80 Full 1 12:00:00 15:28:00 N/A 15:51:00 16:04:00 N/A N/A 8 20 juni 2008 2 30 Full 1 08:30:00 09:46:00 N/A 9 20 juni 2008 1 30 Full 1 08:30:00 11:14:00 N/A 10:36:00 10:48:00 10:59:00 11:10:00 12:00:00 12:16:00 12:06:00 13:30:00 13:30:00 Irregular. Unstable hexagon goes to dipole. N/A N/A Very fast flow. Turbulent. N/A N/A Messy vortex. Turbulent. 10 20 juni 2008 0.5 30 Full 1 08:30:00 13:51:00 N/A 14:50:00 N/A N/A Experiment finished 15:09 11 20 juni 2008 0.5 14.6 Full 1 15:35:00 13:51:00 N/A 16:15:00 N/A N/A 12 I 23 juni 2008 2 15 Full 3 14:06:00 15:00:00 15:35:00 None 15:50? N/A N/A 12 II 23 juni 2008 2 15 Full 3 17:05:00 17:50:00 18:08:00 None 15:57 N/A N/A 12 II 23 juni 2008 1 15 Full 3 17:05:00 18:49:00 13 24 juni 2008 0.5 15 Full 3 09:05:00 09:55:00 13 24 juni 2008 0.388 15 Full 3 09:05:00 11:50:00 19:05:00 19:40:00 10:10:00 10:52:00 12:05:00 12:40:00 14 24 juni 2008 2 15 Full 3,4,5 13:38:00 14:29:00 14:44:00 None 14 24 juni 2008 1 15 Full 3,4,5 13:38:00 15:38:00 15:53:00 16:38:00 None None N/A N/A None 11:31:00 N/A N/A m = 3-4? None 13:16-13:27 N/A N/A 15:17:00 15:32:00 N/A N/A None 16:29:00 N/A N/A 14 24 juni 2008 0.5 15 Full 3,4,5 13:38:00 17:14:00 17:29:00 17:52:00 N/A N/A In going from run 10 to 11 we change rotation rate without altering the flux. Flow unstable. Experiment stopped due to probe control program problem, polar cap moving out of place Velocity probe out of water for last 3 measurements at higher level

14 24 juni 2008 0.388 15 Full 3,4,5 13:38:00 18:38:00 15 25 juni 2008 1 15 Half 3,4,5 10:37:00 11:20:00 15 25 juni 2008 0.5 15 Half 3,4,5 10:37:00 12:54:00 15 25 juni 2008 0.388 15 Half 3,4,5 10:37:00 14:40:00 18:03:00 None 18:53:00 19:27:00 11:35:00 12:20:00 13:11:00 14:05:00 None 19:24:00 N/A N/A None 12:10:00 N/A N/A None 13:48:00 N/A N/A Asymetric m = 2. Two vortices have different strength 14:55:00 15:34-15:54 None N/A N/A Regular dipole 15:53:00 16:35:00 Table 7.2 16 26 juni 2008 0.375 15 Half 3,4,5 09:50:00 10:35:00 16 26 juni 2008 0.2 15 Half 3,4,5 09:50:00 13:05:00 10:50:00 12:16:00 16 26 juni 2008 0.1 15 Half 3,4,5 09:50:00 15:15:00 15:50:00 16 26 juni 2008 0.15 15 Half 3,4,5 09:50:00 16:42:00 17 27 juni 2008 0.388 15 Half 5 09:52:00 10:35:00 17 27 juni 2008 0.2 15 Half 5 09:52:00 12:13:00?? N/A N/A 13:23:00 N/A N/A? 14:23:00 14:34:00 N/A N/A 16:57:00 17:36:00 10:52:00 11:38:00 12:28:00 13:13:00 16:? 16:20:00 16:32:00 N/A N/A 17:27:00 18:12-18:38 N/A N/A m = 4 Flowmeter buoy stopped at bottom: unable to verify whether there was flow or not. Void experiment.? 11:30:00 N/A N/A Looks turbulent 13:03:00 13:07:00 N/A N/A 18 27 juni 2008 0.388 15 Half 1,2,3,4,5 14:00:00 14:32:00 14:48:00 15:22:00 15:25-15:45 N/A N/A Irregular/unsteady m = 3-4 18 27 juni 2008 0.2 15 Half 1,2,3,4,5 14:00:00 15:46:00 16:01:00 16:36:00 16:40-17:00 N/A N/A Unstable/unteady 19 30 juni 2008 0.5 14.8 Full 3,4,5 16:04:00 17:31:00 Not Done 18:15:00 18:31:00 1 18:39:00 Tripole 20 30 juni 2008 0.388 14.8 Full 3,4,5 16:04:00 18:51:00 Not Done 18:36:00 21 30 juni 2008 0.2 14.5 Full 3,4,5 16:04:00 20:15:00 20:25:00 21:05:00 N/A 2 19:54:00 Tripole N/A 3 20:10:00 21:22:00 4 21:32:00 Wobbly tripole N/A 5 21:39:00 N/A 6 22:09:00 Quad/pentapole Probe entered 21:41

22 01 juli 2008 0.9 29.7 Full 3,4,5 10:05:00 11:18:00 23 01 juli 2008 0.5 29.7 Full 3,4,5 10:05:00 13:48:00 21:34:00 11:34:00 N/A 7 22:19:00 12:53:00 1 12:55:00 Irregular/wobbly dipole 12:32:00 Extra dye added outside 13:07:00 13:00:00 2 13:01:00 central vortex region. Vortex broke apart 14:06:00 3 15:16:00 14:52:00 15:10:00 15:26:00 4 15:21:00 24 01 juni 2008 0.388 29.6 Full 3,4,5 10:05:00 16:05:00 17:44:00 17:05:00 6 17:31:00 Dipole-ish ~17:36 7 Extra dye added outside 17:39:00 central vortex region 25 01 juli 2008 0.2 29.6 Full 3,4,5 10:05:00 18:23:00 19:36:00 19:00:00 19:17:00 8 m = 3, making way for a 4th 19:26:00 vortex? 9 19:31:00 Back to stable m = 3 26 02 juli 2008 0.388 10.0 Full 3,4,5 10:10:00 10:49:00 16:20:00 27 02 juli 2008 0.2 10.0 Full 3,4,5 10:10:00 13:22:00 15:02:00 14:25:00 28 02 juli 2008 0.5 10.0 Full 3,4,5 10:10:00 15:44:00 17:06:00 16:42:00 16:57:00 17:22:00 5 17:26:00 Irregular tripole 11:04:00 1 12:28:00 11:59:00 12:24:00 PTV aborted: didn't work 12:39:00 2 12:34:00 14:43:00 3 14:49:00 Hexagon! Velocity probe broke up hexagon, but then 14:55:00 4 14:56:00 it reformed within minutes when probe left jet region. 5 16:06:00 6 17:01:00 Accidentally pressed. Discard. 29 02 juli 2008 0.9 10.0 Full 3,4,5 10:10:00 17:47:00 18:27:00 18:05:00 18:18:00 7 18:20:00 Turbulent tripole. 30 03 juli 2008 0.9 29.9 Full 3,4,5 10:09:00 11:03:00 11:27:00 None 11:03:00 1 11:05:00 Firewire 1 just to see spinup. 11:18:00 2 11:22:00 m = 2 -> m = 4 -> m = 3... 31 03 juli 2008 0.5 29.9 Full 3,4,5 10:09:00 12:03:00 12:40:00 None 12:33:00 3 12:35:00 Vacillating m = 2 3. 32 03 juli 2008 0.388 29.8 Full 3,4,5 10:09:00 13:18:00 14:01:00 None 13:48:00 33 03 juli 2008 0.2 29.8 Full 3,4,5 10:09:00 14:36:00 15:21:00 None 4 13:50:00 Vacillating m = 2 3. 5 13:55:00 15:06:00 6 15:08:00 Dipole 15:16:00 7 15:16:00 Asymetric dipole. 34 03 juli 2008 0.9 14.7 Full 3,4,5 15:57:00 16:28:00 17:01:00 None 16:53:00 8 16:54:00 Dipole

N/A 04 juli 2008 N/A N/A N/A N/A N/A N/A 09:42:00 N/A N/A N/A N/A 35 04 juli 2008 0.388 14.8 Half 3,4,5 10:20:00 10:52:00 12:38:00 12:15:00 36 04 juli 2008 0.39 14.8 Full 3,4,5 13:14:00 10:52:00 13:59:00 None 13:46:00 Test done in air to test new probe settings. New settings such that velocity recorded every second, rather than averaged over a minute at each position. 11:52:00 1 11:54:00 Particles thrown in 12:01 to see how they perturb flow. 12:31:00 2 12:00:00 Bleach thrown in prior to PTV measurement at 12:40:00 3 12:33:00 12:12. PTV not working. Vortex patern is a tripole. 4 13:48:00 5 13:53:00 6 14:04:00 37 04 juli 2008 0.2 14.8 Full 3,4,5 13:14:00 14:36:00 15:17:00 None 15:07:00 7 15:08:00 38 04 juli 2008 0.5 14.8 Full 3,4,5 13:14:00 15:54:00 16:30:00 None Run No. Date Flow Rate Rotation Period Source Sink Spinup Configuration Configuration Started Pump Rate Changed Velocity Probe Started PTV Started 16:22:00 16:31:00 8 16:24:00 Tripole Dye Firewire Firewire camera Notes Visualisation Index started Tape removed 13:10. Tripole. Very even, stable, pretty tripole. Luca did this just to annoy Tom. Probe voids result. Continuously creating and destroying vortices.

8. Data processing: Images of the dye taken by the cameras do not need processing. The images of the PT tracers taken with the three devoted cameras need the PT processing software in order to produce Lagrangian velocities. This software is provided by NTNU. Calibration images were produced by taking an image of a known calibration frame at the level of the focal plane when the tank was empty. Measurements from the Doppler velocity probe require data processing to separate single experiments from the daily records. Software is provided upon request to address to the project leader (see email in the heading). 9. Organisation of data files: 10. Remarks about the experimental campaign, problems and things to improve: The major difficulty we encountered was to obtain velocity field measurements with sufficiently high resolution in order to resolve the coherent structures which formed by barotropic instability. Unfortunately the particle tracking technique proved to not be able to provide a high enough resolution for our purposes. Particle image velocimetry would have been very much desirable in our experiment.

It will be extremely interesting to study in detail the growth of such instabilities and the initial competition between different modes until the moment when the strongest one prevails. Such a study would require the use of an Eulerian visualization technique such as PIV. Window size: x Viewport size: x