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

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

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

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

1 Configuration : f = f0 +  y Rd = 34 km - 16 km Top view side view

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

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

1

1 Including BETA :

1 Results : -Same processes still exist (splitting, filamentation), -Propagation induced by  => 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

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

1 Sensitivity to initial vortex position :  Hypersensitivity

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

1 Conclusion : PVAd 3 Circulation layer 3 Flat bottom exp. PVAd and circul.  Trapping of fluid parcels -Same processes still exist (splitting, filamentation), -Propagation induced by  => 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