Erosion of a surface vortex by a seamount on the beta plane

Steven Herbette (PhD-SHOM), Yves Morel (SHOM), Michel Arhan (IFREMER)

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Outline of the presentation:

- Tools : equations - potential vorticity anomalie (PVA)

- Presentation of the problem - configuration

- Erosion - one example

- Sensitivity study

- Conclusion

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Tools – Equations :

Shallow Water equations :

Potential Vorticities

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NOT conserved if f = f0 + y H = Htopo(x,y)

PVA = PV – f0/HPVAd = PV – PV(at rest)

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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 bereconstructed from theknowledge of PVAd (if geostrophicbalance is assumed)

INVERSION PRINCIPLEz

PVAd > 0 => cyclonic

PVAd < 0 => anticyclonic

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Configuration :

f = f0 + yRd = 34 km - 16 km

Top view side view

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FOCUS ON EROSION

(how much of the vortex remains)

COMPARE WITH F-PLANE (WHAT IS NEW)

Problem :

Rfc (t) = h PVA (t) dx dy

h PVA (t=0) dx dy

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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)

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PVA 1 PVA 2 PVA 3

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PVA 1 PVA 2 PVA 3

Including BETA :

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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

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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

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Sensitivity to initial vortex position :

Hypersensitivity

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Minimum Distance reached(opt = 100 km)

Erosion rate(20% for opt. OnF-plane)

Erosion for different seamount positions (along trajectory) :

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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