Tracer transport in a sea of vortices

Transcription

1 Tracer transport in a sea of vortices A. Provenzale ISAC-CNR, Torino and CIMA, Savona, Italy Work done with: Annalisa Bracco, Jost von Hardenberg, Claudia Pasquero A. Babiano, E. Chassignet, Z. Garraffo, J. Lacasce, A. Martin, C. Mockett, K. Richards J.C. Mc Williams, J.B. Weiss

2 Rapidly rotating environmental flows are characterized by the presence of coherent vortices: Mesoscale eddies, Gulf Stream Rings, Meddies Rotating convective plumes Hurricanes, the polar vortex, mid-latitude cyclones Spots on giant gaseous planets

3 Effects of coherent vortices on Lagrangian transport: Vortices are transport barriers and trap Lagrangian tracers for long times

4 Effects of coherent vortices on Lagrangian transport: Surface 1500 m Velocity pdfs in the North Atlantic Bracco, LaCasce, AP, JPO (2000) Bracco, LaCasce, Pasquero, AP, Phys. Fluids (2000) Pasquero, AP, Babiano, JFM (2001) Bracco, Chassignet, Garraffo, AP, JAOT (2003) Vortices induce characteristic signatures on Lagrangian statistics

5 Effects of coherent vortices on Lagrangian transport: Vortices act as one component of the marine ecosystem

6 A simplified model: A layer of homogeneous flow, f-plane or β-plane: Barotropic quasigeostrophic (2D) turbulence u = ψ y, v = ψ x ζ = 2 ψ 1 R 2 ψ + β y ζ t + ψ,ζ [ ] = F + D

7 A two-component view of mesoscale turbulence: Vortices and background

8 Particle transport ( X j ( t), Y j ( t)) is the position of the j th particle at time t dx dt j = u( X j, Y j, t) = ψ y dy dt j = v( X j, Y j, t) = ψ x Formally, a non-autonomous Hamiltonian system with one degree of freedom

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10 Before going on: What happens for stratified, baroclinic rotating flows?

11 Baroclinic quasi-geostrophic flow (3D-QG) Dq Dt q t + u q x + v q y q t + ψ,q [ ] = Diss u = ψ y, v = ψ x q = 2 ψ + f 2 ψ z N 2 (z) z N 2 (z) = g ρ ρ z Bracco, von Hardenberg, McWilliams, Provenzale, Weiss, PRL (2004)

12 Lagrangian dynamics in 3D-QG A 2 (t,t 0 ) = 1 N Single-particle dispersion N { [X j (t) X j (t 0 )] 2 + [Y j (t) Y j (t 0 )] 2 } j=1 R 2 (t) = 2 N(N 1) Relative dispersion { [X j (t) X k (t)] 2 + [Y j (t) Y k (t)] 2 } j k Bracco, von Hardenberg, McWilliams, Provenzale, Weiss, PRL (2004)

13 Bracco, von Hardenberg, McWilliams, Provenzale, Weiss, PRL (2004)

14 Back to barotropic turbulence

15 Strong impermeability of the vortex edges to inward and outward particle exchanges

16 How important are the trapping properties of coherent vortices? Particle dispersion Reaction rates

17 Different effects of coherent vortices on particle dispersion on f-plane or on β-plane Particle motion on the β-plane (Bracco, Mockett, Provenzale, in preparation)

18 Vortices and plankton (i.e. dynamics of reactive tracers) Bracco, Provenzale, Scheuring, Proc. R. Soc. B (2000) Martin, Richards, Bracco, AP, Global Biogeochem. Cycles (2002) Pasquero, Bracco, Provenzale, in Shallow Flows (2004) Pasquero, Bracco, Provenzale, Weiss, LAPCOD book (2004)

19 e.g. Dynamics of reactive tracers

20 Eulerian method Semi-Lagrangian method

21 The principle of competitive exclusion and the paradox of the plankton

22 In equilibrium conditions, when two species compete for the same resource only the most favoured species survives. The Paradox of the Plankton: phytoplankton compete for a few resources (light, nutrients), still there are many coexisting planktonic species.

23 Ways out: Temporal variability (non-equilibrium) Spatial or temporal segregation

24 Segregation by incomplete mixing: Vortices act as transport barriers and shelter the (temporally) less favoured species from competition with other species

25 Horizontal advection by 1) A Langevin stochastic process (with no coherent flow structure) 2) 2D Turbulence (with vortices)

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27 Vortices provide a shelter that allows temporary survival of the less-favoured species Bracco, Provenzale, Scheuring, Proc. R. Soc. B (2000) Pasquero, Bracco, Provenzale, in Shallow Flows (2004)

28 The presence of vortices significantly affects (chemical and biological) reaction rates Bracco, Provenzale, Scheuring, Proc. R. Soc. B (2000) Pasquero, Bracco, Provenzale, in Shallow Flows (2004)

29 Do coherent vortices affect primary productivity in the open ocean? Martin, Richards, Bracco, AP, Global Biogeochem. Cycles (2002) Pasquero, Bracco, Provenzale, submitted (2004)

30 y v x u t dt d H w D D Z P Z P g P g dt dd Z Z Z P g P g dt dz P Z P g P g P N k N dt dp Z D P N k N N N s dt dn s D Z P Z Z P Z D + + = = + = + + = = / ) (1 ) ( µ µ µ ε ε γ µ γ ε ε γ µ ε ε α γ µ α Oschlies and Garcon, Nature, 1999

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32 Three cases with fixed A (12%) and I=100: Control : NO velocity field (u=v=0) (no mixing) Case A: horizontal mixing by turbulence, upwelling in a single region Case B: horizontal mixing by turbulence, upwelling in mesoscale eddies

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34 29% more than in the no-mixing control case

35 139% more than in the no-mixing control case

36 Effect of the size of the upwelling regions DN Dt = s(x, y,t)(n 0 N) β DP Dt = β N k N + N P + µ N (1 γ) aεp 2 a + εp Z + µ P + µ Z 2 2 P Z N k N + N P aεp 2 a + εp Z µ P 2 P DZ Dt = γ aεp 2 a + εp 2 Z µ Z Z 2 D Dt = t + u x + v y s = s p = day 1 s = s a = day 1 Pasquero, Bracco, Provenzale, submitted (2004)

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38 The increase in primary productivity is due to the alternance between active and quiescent regions and to the asymmetry between growth and decay

39 Homogeneous system: Effect of the duration of upwelling events

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41 The spatial and temporal distribution of the nutrient input plays a crucial role, due to the presence of mesoscale (and submesoscale) structures and the associated mixing processes Models that do not resolve mesoscale features can severely underestimate primary production

42 An interesting challenge: parameterising the effect of mesoscale structures on biogeochemical reactions

43 Future work: A study of the interaction between mesoscale structures and marine ecosystem dynamics Use of primitive-equation models (POM, ROMS) in simplified configurations to study the effects of fronts and vortices The ISHMAEL initiative: an Integrated Simulator of the Hydrodynamics and the MArine Ecosystem in the Ligurian sea