Transcript Internal wave generation and propagation: analytical and numerical computations

Internal wave generation and
propagation: analytical and numerical
computations
Flavien Gouillon
and Eric Chassignet
Center for Ocean-Atmospheric Prediction Studies
November 13th, 2008
Flavien Gouillon (COAPS)
Internal waves matter!
• Internal waves occur in stably stratified fluid when a water
parcel is displaced by external forces and restored by
buoyancy forces.
• Knowledge of internal wave generation and propagation is
crucial to understand ocean mixing and the large scale
ocean circulation (Munk and Wunsch, 98).
Spain
Internal wave surface
signature at the strait
of Gibraltar
Flavien Gouillon (COAPS)
From J. Nash
• Maintain the strength of the thermohaline circulation
• Half of the energy to vertically mix the abyssal ocean
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Internal wave modeling background
• Their spatial scales (m to few km) are not resolved in
Oceanic General Circulation Models that are 1° to 1/12°
horizontal resolution at best.
• The dynamic of internal wave is non-hydrostatic and
thus cannot be well resolved in Oceanic General
Circulation Models that usually make the hydrostatic
approximation.
• 3 types of model vertical discretization (z-, σ- and ρ-)
• Numerical models that use fixed vertical coordinate (zand σ- levels) have a spurious diapycnal mixing
associated with the transport of density.
z
ρ
σ
Flavien Gouillon (COAPS)
Internal Wave Modeling
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Internal wave mixing parameterization
• To represent the internal wave breaking mixing in models we need to use a sub grid
scale parameterization.
• Numerical models assume a quasi-uniform internal wave mixing in the deep interior.
• Unrealistic since it depends mostly on the geography (topography) and the dynamic
of the internal wave.
In Oceanic General Circulation Models we need, first, to well understand:
Internal-Tide Generation
Garrett and Kunze 07
Processes that transfer energy into small scale turbulence mixing
Flavien Gouillon (COAPS)
Internal Wave Modeling
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My PhD Objectives
1) To investigate the internal wave
representation in Oceanic General
Circulation Models as a function of model
grid spacing.
2) To document and quantify the numerically
induced mixing in the fixed coordinate
ocean model.
Flavien Gouillon (COAPS)
Internal Wave Modeling
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My PhD Objectives
1) To investigate the internal wave
representation in Oceanic General
Circulation Models as a function of model
grid spacing.
2) To document and quantify the numerically
induced mixing in the fixed coordinate
ocean model.
Flavien Gouillon (COAPS)
Internal Wave Modeling
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Approach
We compare the results for the same simple problem
• From an analytical point of view.
• From 2 numerical models: The HYbrid Coordinate
Ocean Model (HYCOM, ρ-level) and the Regional
Ocean Model System (ROMS, σ-level).
Schematic of the situation being modeled
Flavien Gouillon (COAPS)
Internal Wave Modeling
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The only slide with equations…
• Analytical solution derived by Khatiwala (2003).
• Conditions: the baroclinic response needs to be
weaker than the barotropic forcing.
The vertical velocities:
Wave mode structure
Moving frame
Topography
System Properties
with
Flavien Gouillon (COAPS)
Internal Wave Modeling
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Analytic vs. Numeric (snapshot, linear regime)
m.s-1
m.s-1
m.s-1
Δx =1.5km
25 layers
U0=0.02 m.s-1
N=Constant
f=0
No mixing
No bottom friction
1h Output
m.s-1
Flavien Gouillon (COAPS)
Internal Wave Modeling
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The impact of the model horizontal resolution (animation)
Cross vertical section of the zonal baroclinic velocities using ROMS
Δx = 1.5 km
Δx = 30 km
Depth (m)
0
m.s-1
2000
-600 km
0 km
600 km
• Low modes (fastest) are well represented (carry ~70% of the energy away).
• Higher modes (slowest) at the tip of the ridge are not (responsible for the
turbulent mixing).
Flavien Gouillon (COAPS)
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Conclusions
• Internal wave modeling matters for the global
ocean circulation.
• From the barotropic tide to the turbulent
processes, steps are not well understood.
• Numerical models seem to well represent the
internal wave if the horizontal resolution is high
enough (what is high enough?).
• If the grid is too coarse, higher modes are not
well represented.
• “The Graal”: Can we derived a physically based
internal wave breaking mixing parameterization
to implement in numerical models?
Flavien Gouillon (COAPS)
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