Cyclones and Anticyclones in Rotating stratified flows

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1 Cyclones and Anticyclones in Rotating stratified flows Oriane Aubert Patrice Le Gal Michael Le Bars Pedram Hassanzadeh Philip Marcus

Shetty, Asay-Davis & Marcus (2010) The Great Red Spot was discovered by

2 25000 km Credit: NASA/JPL-CaltechClose-up of Jupiter's Great Red Spot as seen by a Voyager spacecraft. Shetty, Asay-Davis & Marcus (2010) The Great Red Spot was discovered by Hooke (1664) and Cassini (1665) : Enormous Anticyclone: winds ~ 100 m/s 90 % of Jovian large vortices (> 2000 km) are anticyclonic

3 Several attempts to reproduce and model the GRS: first understood as a Taylor column (Hide, 1961)

4 Geostrophic balance in a rotating fluid : Taylor-Proudman theorem Balance between Coriolis force and pression gradient that is perpendicular to the axis of rotation: - Taking curl of equation :Taylor-Proudman theorem: If v z = 0 somewhere, perturbations generate Taylor columns From Greenspan (1976)

5 Generation of vortices through baroclinic instability Cold pole Hot equator Jupiter seen form its south pole Read & Hide (1983, 1984) Merging of vortices to form a unique anticyclone Rhines (youtube, 2011)

Generation of vortices by forcing a shallow water

- Rotating anulus: generation of a zonal flow in a

instability : ring of vortices (cyclones or

6 Generation of vortices by forcing a shallow water layer Antipov, Nezlin, Snezhkin & Trubnikov (1986) - Rotating anulus: generation of a zonal flow in a shallow water parabolic -Kelvin-Helmholtz instability : ring of vortices (cyclones or anticyclones) Merging of vortices to form a unique large anticyclone

ans succions from the wall Merging of vortices to form a unique

7 Generation of vortices by forcing radial jets Sommeria, Meyers, Swinney (1988) Generation of a zonal flow through the injection ans succions from the wall Merging of vortices to form a unique large cyclone (the experiment cannot generate «easily» anticyclones)

What is fine in the different cases: -A single vortex can be selected: it is stable, (longlived because of forcing) Anticyclonic and «it eats» the others.

8 What is fine in the different cases: -A single vortex can be selected: it is stable, (longlived because of forcing) Anticyclonic and «it eats» the others. What is not fine: - barotropic vortex : column all along the depth of the layer - Real stratification should limit the vertical extension of vortices Jupiter Atmosphere p ~ p 0 e -z/h h = 27 km (23 km Cho et al.) Rossby deformation radius: L R = Nh/f ~ 2500 km Cloud layer 0.7 b ~50 km

9 Generation in the laboratory of the 2 main ingredients rotation and stratification

10 Salt Stratification (rad/s) Brunt-Väisälä frequency N g z Coriolis parameter f 2 s i n Statified salted water on a rotating table Generation of an anticyclone

11 Injection of a small volume of homogeneous dyed water From the top From the side PIV Measurements v θ t/t=15 v r V = - v r Rossby number R o v f

12 Stationary Euler equations with solid body rotation vortex ~ ~ ~ Geostrophic balance Hydrostatic balance Mechanism: density anomaly keeps the anticyclone alive Self-similar elliptic shape P P L P H P 0 0 = - 0 f v D = - 0 2H 2L Aspect ratio: = H/D

13 Extension of the model to take into account the centrifugal term and the internal stratification of vortices Solid body rotation or Gaussian vortex Aspect ratio

14 Rossby number evolution through time Transient to reach geostrophic regime Transient to reach Full circularization regime (viscous time) Longlived anticyclones (Salt diffusion time) f/n=4,25 f/n=1

15 Elliptic self-similar shape: p 00 is measured at initial time by a best fit of the vertical section. Volume is conserved after the transients. Temporal evolution parametrized by the Rossby number measured in horizontal planes by PIV Time

16 Freely decaying vortices Continuous injection: rate Q = 10 ml/min

10-4 rad/s N 10-3 rad/s H 1km L 100 km Ro 0,3 Ω 10-5 rad/s v max 0,1 m/s V.

17 Oceanic Anticyclones: «meddies» Life time: 4 years (1600 périods) Simulation PAM year 2000: salinity at 870 m, Yann Drillet (2000) Tychensky et Carton, 1998 f 10-4 rad/s N 10-3 rad/s H 1km L 100 km Ro 0,3 Ω 10-5 rad/s v max 0,1 m/s V. Thierry, X. Carton et J. Paillet, 1999 Internal stratification can be taken into account N Nc

18 Experimental analysis of pancake anticyclones in rotating stratified flows (salted water): Aubert JFM 2012 Jupiter vortices Experiments ( Ro (1+Ro) ) Meddies

21 Numerical analysis of pancake vortices in rotating stratified flows (DNS): Hassanzadeh JFM 2012 Cyclones (suction, instability of colomnar vortices) Anticyclones

Cyclone - Anticyclone asymmetry: Long standing debate in stratified rotating flows if away from QG hypotheses Anticyclones are predominent: Linden et al.

22 Cyclone - Anticyclone asymmetry: Long standing debate in stratified rotating flows if away from QG hypotheses Anticyclones are predominent: Linden et al. JFM 1995 Polvani & Cho PoF 1996 Because of generation mechanisms McWilliams Rev. Geophys Perret et al. JPO 2011 Or anticyclones more stable Stegner & Dritschel JPO 2000 Graves et al. GAFD 2006 Cyclones are favored Hakim et al. J. Atm; Sci Praud et al. JFM 2006 Roullet & Klein PRL2010 Credit: NASA

23 Numerical simulation of cyclones induced by suction: DNS under Boussinesq equations and sink in sphere radius R Spectral method (256 3 Fourier modes)

24 Generation of vorticity field: shielded 3D vortices Shield : closed vortex lines

25 Rossby number evolution in time During suction After suction stops Fast damping compared to anticyclones Blue: strong rotation with stratification, high suction rate Red: weak rotation with stratification, high suction rate Black: strong rotation with stratification, low suction rate

26 Brünt-Vässäliä frequency evolution in time During suction After suction stops Super-stratification Blue: strong rotation with stratification, high suction rate Red: weak rotation with stratification, high suction rate Black: strong rotation with stratification, low suction rate

27 Density and velocity fields Super-stratification Secondary flow streamlines Blue: strong rotation with stratification, high suction rate Red: weak rotation with stratification, high suction rate Black: strong rotation with stratification, low suction rate

28 Experiments on cyclones induced by suction No dye for visualization, instead Synthetic Schlieren

29 Observation of super-stratification by synthetic Schlieren Modified Gaussian vortex (solution of thermal wind equation) With «caps» Nguyen et al. 2012

30 b is estimated from a best fit of the vertical density gradient and then maintained constant through time K is given by the vertical density anomaly gradient at origin

31 Experiment Gaussian model with best H t/t =30 t/t =30 t/t =180 t/t =180 H (and L) are obtained by best fit of the Gaussian vortex

32 Note: errors come from 2D approximation of Schlieren images which are axisymmetric and Would require an inverse Abbel Transform. Values for L are checked by PIV. ~ 0.25 on

33 Rossby number evolution in time Fast damping compared to anticyclones

34 Superstratification difficult to create : fast damping Lifetime is increased by Small suction rates for longer durations Damping 5 times faster than anticyclones

35 Conclusions: -Cyclones and Anti-cyclones are observed in natural systems. -Anticyclonic and Cyclonic long-lived pancakes are reproduced in stratified rotating flows. Differences experiments/numerics for cyclones (shield vs. caps) - Cyclonic long-lived pancakes require super-stratification to be sustained. Possible but much more difficult to create and to sustain in numerical simulations and in laboratory experiments. -Both Cyclones and Anticyclones aspect ratio are in excellent agreement with our aspect ratio scaling theory. -Our claim is that Cyclones should be less predominent in Nature because of this requirement to be superstratified.

37 Perpetual Ocean This visualization shows ocean surface currents around the world during the period from June 2005 through December The visualization does not include a narration or annotations; the goal was to use ocean flow data to create a simple, visceral experience. This visualization was produced using model output from the joint MIT/JPL project: Estimating the Circulation and Climate of the Ocean, Phase II or ECCO2. ECCO2 uses the MIT general circulation model (MITgcm) to synthesize satellite and in-situ data of the global ocean and sea-ice at resolutions that begin to resolve ocean eddies and other narrow current systems, which transport heat and carbon in the oceans. ECCO2 provides ocean flows at all depths, but only surface flows are used in this visualization. The dark patterns under the ocean represent the undersea bathymetry. Topographic land exaggeration is 20x and bathymetric exaggeration is 40x. This visualization was submitted to the SIGGRAPH 2011 Computer Animation Festival, but it wasn't selected by the jury.

38 Floatting lenses in the ocean : with Raùl C. Cruz, Anne Cros, Hector De la Rosa, Guadalajara University, Mexico Upper surface solid body rotation core: Lower surface solid body rotation core : Unstable solution Parabolic interfaces

40 Calculation of the anticyclone aspect ratio = (f+ ) R 4 g m a - m That can be written as : = - Ro (1+Ro) f 2 with N 2 = 4 g ( - ) m a??? N 2 R m Or the alternative form respecting the meddy scaling law: = - Ro (1+Ro) f 2 with N2 = 16 g 2 ( m - a ) 2??? (f+ ) R 2 2 a N 2 Neither of these N is the frequency of the vertical oscillations of a floatting body... 4 g 2 ( m - a ) F 2 = (f+ ) R 2 a Need more physical modelling and experiments

44 PIV measurements on floatting particles: Rossby number Angular velocity vorticity

45 N 2 /f 2 with N 2 = 4 g ( m - a ) R m Ro (1+Ro )

ATMS 310 Tropical Dynamics

ATMS 310 Tropical Dynamics Introduction Throughout the semester we have focused on mid-latitude dynamics. This is not to say that the dynamics of other parts of the world, such as the tropics, are any