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Outline of the presentation: - Tools : equations - potential vorticity anomalie (PVA)

Erosion of a surface vortex by a seamount on the beta plane Steven Herbette (PhD-SHOM), Yves Morel (SHOM), Michel Arhan (IFREMER). Outline of the presentation: - Tools : equations - potential vorticity anomalie (PVA) - Presentation of the problem - configuration - Erosion - one example

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Outline of the presentation: - Tools : equations - potential vorticity anomalie (PVA)

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  1. Erosion of a surface vortex by a seamount on the beta planeSteven Herbette (PhD-SHOM), Yves Morel (SHOM), Michel Arhan (IFREMER)

  2. Outline of the presentation: - Tools : equations - potential vorticity anomalie (PVA) - Presentation of the problem - configuration - Erosion - one example - Sensitivity study - Conclusion

  3. Tools – Equations : Shallow Water equations : Potential Vorticities 0 PVA = PV – f0/H PVAd = PV – PV(at rest) NOT conserved if f = f0 + b y H = Htopo(x,y)

  4. Tools : POTENTIAL VORTICITY “thinking” The velocity field can be reconstructed from the knowledge of PVAd (if geostrophic balance is assumed) INVERSION PRINCIPLE z= rot (U) important quantity BUT NOT CONSERVED PV = (z+f) . r (= (z+f)/h ) is conserved for each particles if adiabatic motion PV = TRACER z d PVAd > 0 => cyclonic d PVAd < 0 => anticyclonic d PV

  5. Configuration : Top view side view f = f0 + b y Rd = 34 km - 16 km

  6. h PVA (t) dx dy Rfc (t) = h PVA (t=0) dx dy Problem : FOCUS ON EROSION (how much of the vortex remains) COMPARE WITH F-PLANE (WHAT IS NEW)

  7. Result from f-plane (Herbette et al, JPO, 2003) PVA 1 PVA 2 PVA 3 Rv = 100 km Q = -1.5 f0 s (Vmax ~ 0.8 m/s) Lf = 100 km (Umax ~ 0.25 m/s) -1

  8. Including BETA : PVA 1 PVA 2 PVA 3

  9. Results : • Same processes still exist (splitting, filamentation), • Propagation induced by b => no pole remains trapped above topo, • Splitting seems even more vertical (reduced impact on PVA 1), • Additional PVAd poles emerge because of advection of particles • especially in the third layer in our case

  10. Effect of the formation of PVAd poles (in the lower layer) : PVA 2 PVA 3 PVAd 3 Evolution without topography • Erosion • Masking (weaker velocity field)

  11. Sensitivity to initial vortex position : • Hypersensitivity

  12. Erosion for different seamount positions (along trajectory) : Minimum Distance reached (opt = 100 km) Erosion rate (20% for opt. On F-plane)

  13. Conclusion : • Same processes still exist (splitting, filamentation), • Propagation induced by b => no pole remains trapped above topo, • Splitting seems even more vertical (reduced impact on PVA 1), • Additional PVAd poles emerge because of advection of particles especially in the third layer in our case : • masks vortex in lower layer (lower erosion rates) • hypersensitivity PVAd 3 Circulation layer 3 • Flat bottom exp. • PVAd and circul. • Trapping of fluid parcels

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