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Impact of channel geometry and rotation on the trapping of internal - - PowerPoint PPT Presentation
Impact of channel geometry and rotation on the trapping of internal - - PowerPoint PPT Presentation
Impact of channel geometry and rotation on the trapping of internal tides Sybren Drijfhout and Leo Maas The internal wave drag due to oscillating flow over topography: 1 = 2 D N h u b tide 2 The energy flux per unit area out of
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The internal wave drag due to oscillating flow over topography: The energy flux per unit area out of barotropic tides:
〉 〈 =
2 2
2 1 ) , (
tide b
u h N y x E κ ρ
tide b
u h N D
2
2 1 κ =
The turbulent dissipation:
) ( ) , ( ) / ( z F y x E q ρ ε =
The relation of dissipation to diffusion:
2
N k k v ε Γ + =
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- 60 to 90% of the energy flux from barotropic to internal tides is
contained in low-mode internal waves that are able to propagate large distances from the generation site
- Dissipation of these low-modes waves gives rise to a canonical
background mixing of k0= 10-5 m2/s
- The remaining portion, denoted as the “tidal dissipation
efficiency” (q), dissipates as locally enhanced turbulent mixing
- Three questions remain:
(1) How important is the energy flux from the wind? (2) does q vary from site to site? (3) can the radiating low-mode waves be trapped, giving rise to sites of enhanced mixing, unrelated to local generation?
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Three-dimensional effects
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Top view Focusing
- n wave
attractor ‘Edge wave’ type trapping 3D view Circle: critical depth N=const
x0
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Research Question
- Does geometrical trapping of internal waves exist in 3D?
- Can trapping be predicted by the nondimensional parameter
L H f N
2 2 2 2
− − = ω ω τ
0.87 < < 1
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Methodology
- MICOM’s 3D isopycnic model
- Horizontal resolution: 3.75 km; Vertical resolution: 100 m
- Channel geometry: 1200 x 191.25 km
- Sponge layer in west, continental slope in east
- Barotropic velocity in sponge layer forced
- Bottom either flat or parabolic
- f = 0, N = 3.0 10-3 ; or, f = 10-4, N = 2.2 10-3
94 . = τ
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Channel model
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W E
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S N S N
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W S N E E W S S N
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Conclusions
- A cross-channel bottom slope constrains the
penetration of the internal tidal energy due to trapping upon multiple refractions.
- Near the critical depth edge-waves carry part of
the energy much further away from the slope.
- In case of rotation, near the shelf-slope the
trapped “Poincaré wave” and southern boundary-edge wave interact, destroying the characteristics of the attractor.
- The Kelvin wave along the northern slope acts