inviscid dissipation catalyzed by topography ini, oct. 18, 2010 wk dewar fsu collaborators: prof. p....
TRANSCRIPT
Inviscid Dissipation Catalyzed by Topography
INI, Oct. 18, 2010
WK DewarFSU
Collaborators: Prof. P. Berloff, Prof. A. Mc. Hogg, Prof. JC McWilliams
Work offered in the memory of PD Killworth
An analysis of ocean power, after Wunsch and Ferrari, 2004.
And there is a related potential vorticity budget question.
Connection to themeof School: Are theseprocesses that can berepresented as a stochastic process?
Numerical Evidence in Support
An ultra-fine embedded solution for Monterey Bay
(Simpler)NumericalEvidence inSupport
Temperature at western wall
Next obvious question
Experiment used vertical walls, which don’t exist, really, in the open ocean.
What happens for, say, a seamount.
Some danger here, as topography is difficult to represent numerically.
Summary:
Something very interesting happens at topography when balanced flow interactions with it.
Question:
What the hell is it?
Focus of the rest of the talk.
Theory of Wall Interactions
ut uux vuy fv M x
vt uvx vvy fu M y
M p gz
qt uqx vqy 0; q ( f vx uy ) / z
EOMs in density coordinates
zt (uz )x (vz )y 0
At the wall, normal flow vanishesand consider inviscid, adiabatic flow
u=0
M xx f2M
M 0
M gz
Decompose v into geostrophic imprint and wall response
M 'xx f2M 'M
0
SETEICST
Hydrostatic?
fv ' M x
v 'tv '2
2
y
vgv ' yM 'y vgt vgvgy M gy
Solutions:
MITgcm
Anticyclone/Cyclone Asymmetry captured, as are amplitudes, density overturnings, rates of development
M xx f2M
M 0
fv M x
vt v2
2
y
(vgv)y M y vgt vgvgy M gy
M nt (vg fRdn )M ny vgyM n
V
Asymmetry?
Source of Instability?• Linearize and
M xx f2M
M 0
fv M x
vt vgvy M y 0
vg vg ()
(vg c)M xŽ f MŽ 0
(vg c)2MŽ M MŽ 0
(vg cr )| (vg c)2 |2
|MŽ |2 d 0
Instability is not baroclinic
Source of Instability?• Linearize and
M xx f2M
M 0
fv M x
vt vgvy M y vgyv
vg vg (y)
M nt (vg fRdn )M ny vgyM n
V
Y
What does nonlinearity do?go to reduced gravity frame
M xx f2 M
Rd0
fv M x
vt v2
2
y
(vgv)y M y vgt vgvgy M gy
!
Temperature at western wall
4. How fast does the shock go?
csvy v2
2
y
(vgv)y M y (F(vg ))y
cs
M
M
cs M M
2 fR vg c fR
Non-hydrostatic dynamics arrest the shock
(zq)t (uqz )x vqz y(Yx Xy ) (uH )y (vH )x
uzq 'dyd vH o dyd O( fR)2
(Simpler)NumericalEvidence inSupport
Summary and to do list
Simple, surprisingly accurate local theory for wall interactions can be written
• predict anisotropy• steepening and breaking• can be parameterized• stochastic parameterization?
Extend this to non-wall topography?(Yes?)
Introduce into models to control boundary dissipation