Erosion of a surface vortex by a seamount on the beta plane Steven Herbette (PhD-SHOM), Yves Morel...
-
Upload
owen-chandler -
Category
Documents
-
view
217 -
download
0
description
Transcript of Erosion of a surface vortex by a seamount on the beta plane Steven Herbette (PhD-SHOM), Yves Morel...
![Page 1: Erosion of a surface vortex by a seamount on the beta plane Steven Herbette (PhD-SHOM), Yves Morel (SHOM), Michel Arhan (IFREMER)](https://reader036.fdocuments.in/reader036/viewer/2022062503/5a4d1aec7f8b9ab05997b5a3/html5/thumbnails/1.jpg)
Erosion of a surface vortex by a seamount on the beta plane
Steven Herbette (PhD-SHOM), Yves Morel (SHOM), Michel Arhan (IFREMER)
![Page 2: Erosion of a surface vortex by a seamount on the beta plane Steven Herbette (PhD-SHOM), Yves Morel (SHOM), Michel Arhan (IFREMER)](https://reader036.fdocuments.in/reader036/viewer/2022062503/5a4d1aec7f8b9ab05997b5a3/html5/thumbnails/2.jpg)
1
Outline of the presentation:
- Tools : equations - potential vorticity anomalie (PVA)
- Presentation of the problem - configuration
- Erosion - one example
- Sensitivity study
- Conclusion
![Page 3: Erosion of a surface vortex by a seamount on the beta plane Steven Herbette (PhD-SHOM), Yves Morel (SHOM), Michel Arhan (IFREMER)](https://reader036.fdocuments.in/reader036/viewer/2022062503/5a4d1aec7f8b9ab05997b5a3/html5/thumbnails/3.jpg)
1
Tools – Equations :
Shallow Water equations :
Potential Vorticities
0
NOT conserved if f = f0 + y H = Htopo(x,y)
PVA = PV – f0/HPVAd = PV – PV(at rest)
![Page 4: Erosion of a surface vortex by a seamount on the beta plane Steven Herbette (PhD-SHOM), Yves Morel (SHOM), Michel Arhan (IFREMER)](https://reader036.fdocuments.in/reader036/viewer/2022062503/5a4d1aec7f8b9ab05997b5a3/html5/thumbnails/4.jpg)
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 bereconstructed from theknowledge of PVAd (if geostrophicbalance is assumed)
INVERSION PRINCIPLEz
PVAd > 0 => cyclonic
PVAd < 0 => anticyclonic
![Page 5: Erosion of a surface vortex by a seamount on the beta plane Steven Herbette (PhD-SHOM), Yves Morel (SHOM), Michel Arhan (IFREMER)](https://reader036.fdocuments.in/reader036/viewer/2022062503/5a4d1aec7f8b9ab05997b5a3/html5/thumbnails/5.jpg)
1
Configuration :
f = f0 + yRd = 34 km - 16 km
Top view side view
![Page 6: Erosion of a surface vortex by a seamount on the beta plane Steven Herbette (PhD-SHOM), Yves Morel (SHOM), Michel Arhan (IFREMER)](https://reader036.fdocuments.in/reader036/viewer/2022062503/5a4d1aec7f8b9ab05997b5a3/html5/thumbnails/6.jpg)
1
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
![Page 7: Erosion of a surface vortex by a seamount on the beta plane Steven Herbette (PhD-SHOM), Yves Morel (SHOM), Michel Arhan (IFREMER)](https://reader036.fdocuments.in/reader036/viewer/2022062503/5a4d1aec7f8b9ab05997b5a3/html5/thumbnails/7.jpg)
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)
-1
PVA 1 PVA 2 PVA 3
![Page 8: Erosion of a surface vortex by a seamount on the beta plane Steven Herbette (PhD-SHOM), Yves Morel (SHOM), Michel Arhan (IFREMER)](https://reader036.fdocuments.in/reader036/viewer/2022062503/5a4d1aec7f8b9ab05997b5a3/html5/thumbnails/8.jpg)
1
![Page 9: Erosion of a surface vortex by a seamount on the beta plane Steven Herbette (PhD-SHOM), Yves Morel (SHOM), Michel Arhan (IFREMER)](https://reader036.fdocuments.in/reader036/viewer/2022062503/5a4d1aec7f8b9ab05997b5a3/html5/thumbnails/9.jpg)
1
PVA 1 PVA 2 PVA 3
Including BETA :
![Page 10: Erosion of a surface vortex by a seamount on the beta plane Steven Herbette (PhD-SHOM), Yves Morel (SHOM), Michel Arhan (IFREMER)](https://reader036.fdocuments.in/reader036/viewer/2022062503/5a4d1aec7f8b9ab05997b5a3/html5/thumbnails/10.jpg)
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
![Page 11: Erosion of a surface vortex by a seamount on the beta plane Steven Herbette (PhD-SHOM), Yves Morel (SHOM), Michel Arhan (IFREMER)](https://reader036.fdocuments.in/reader036/viewer/2022062503/5a4d1aec7f8b9ab05997b5a3/html5/thumbnails/11.jpg)
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
![Page 12: Erosion of a surface vortex by a seamount on the beta plane Steven Herbette (PhD-SHOM), Yves Morel (SHOM), Michel Arhan (IFREMER)](https://reader036.fdocuments.in/reader036/viewer/2022062503/5a4d1aec7f8b9ab05997b5a3/html5/thumbnails/12.jpg)
1
Sensitivity to initial vortex position :
Hypersensitivity
![Page 13: Erosion of a surface vortex by a seamount on the beta plane Steven Herbette (PhD-SHOM), Yves Morel (SHOM), Michel Arhan (IFREMER)](https://reader036.fdocuments.in/reader036/viewer/2022062503/5a4d1aec7f8b9ab05997b5a3/html5/thumbnails/13.jpg)
1
Minimum Distance reached(opt = 100 km)
Erosion rate(20% for opt. OnF-plane)
Erosion for different seamount positions (along trajectory) :
![Page 14: Erosion of a surface vortex by a seamount on the beta plane Steven Herbette (PhD-SHOM), Yves Morel (SHOM), Michel Arhan (IFREMER)](https://reader036.fdocuments.in/reader036/viewer/2022062503/5a4d1aec7f8b9ab05997b5a3/html5/thumbnails/14.jpg)
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