1 JongJin Park Woods Hole Oceanographic Institution Decay Time Scale of Mixed Layer Inertial Motions in the World Ocean (Observations from Satellite Tracked Drifters) Internal Wave Workshop, 3-4 October 2008, Applied Physics Laboratory-University of Washington, Seattle
23
Embed
1 JongJin Park Woods Hole Oceanographic Institution Decay Time Scale of Mixed Layer Inertial Motions in the World Ocean (Observations from Satellite Tracked.
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
11
JongJin ParkWoods Hole Oceanographic Institution
Decay Time Scale ofMixed Layer Inertial Motions in the
World Ocean
(Observations from Satellite Tracked Drifters)
Internal Wave Workshop, 3-4 October 2008, Applied Physics Laboratory-University of Washington, Seattle
22
Inertial energy budget in the mixed layer
Mix
ed L
ayer
Inertial kinetic energy( )Global Inertial Kinetic Energy ( EI )
Park et al. [2005]: Mixed layer KE
Alford and Whitmont [2007]: Depth integrated
IE
Previous Studies
Inertial energy flux from wind ( ) Inertial energy flux from wind ( )Alford [2001; 2003]
Watanabe and Hibiya [2001]
Jiang et al. [2005]
~ based on a slab ocean model Plueddemann and Farrar [2007]
windwind
Long-Term Goal :Global inertial energy budget in the oceanic mixed layer
Global distributionof decay time scale
~Deep e IE
Inertial energy efflux out of the mixed layer ~( )Ideep eE
Parameterization of decaying inertial motion in the mixed layer
Inertial motion decays exponentially
Q: How is the decay time scale distributed in the
global ocean ?
Dynamics of inertial motion decay
44
Two ways of decaying inertial motion in the mixed layer
- Propagation of inertial-internal wave (Non-Turbulent process) : [Gill, 1984; D’Asaro, 1989; Zervakis and Levine, 1995; Meurs, 1999; etc…]
- Turbulent mixing at the base of the mixed layer (Turbulent process) : [D’Asaro, 1995; Eriksen, 1991; Hebert and Moum, 1994]
• Most of the previous studies focused on the wave propagation as a major decaying process.
• The wave propagation may be primarily responsible for the fast decay of mixed layer inertial energy [Balmforth and Young, 1999; Moehlis and Smith, 2001].
- Buoyancy Frequency - Forcing scale : Gill [1984], D’Asaro [1995]- Wave number change by Beta effect : D’Asaro [1989]- Mixed layer depth : Zervakis and Levine [1995]
- Flow convergence : Weller [1982] - Relative vorticity : Kunze [1985], Balmforth and Young [1999] - Relative vorticity gradient : Van Meurs [1999] - Etc : Advection by background flow Vertical shear of the flow
Without background flow With background flow
Q: Which factor can play more important role to control the global distribution of inertial decay timescale?
Method to estimate inertial amplitude from Satellite Tracked Drifter
Weighted Function Fitting Method
-4 -2 0 2 4 6Z o n a l D ista n ce (k m )
-2
0
2
4
6
8
Mer
idio
nal
Dis
tan
ce (
km
)
P 5m o
P 4m o
P 3m o
P 2m o
P 1m o
P 6m o
P 1m f
P 2m f
P 3m f
P 4m f
P 5m f
P 6m f
m : cycle number
( , )
;
( , )
;
o o ok k k
f f fk k k
P x y
observed
P x y
estimated
rectilinear inertialu u u e
(Park et al., 2004)
1, ( 1, , )k kt t t k N
( )*cos( ) ( )*sin( )
( )*sin( ) ( )*cos( )
fk L k o r o k r o k
fk L k o r o k r o k
x u t x x x f t y y f t
y v t y x x f t y y f t
Inertial Recti-linear 1
exp[ ( )]kt
rtU i ft dt P
Trajectory segment length : > 0.7 * local inertial period Number of fixes : > 5Data latitude : 60oS~60oN except 29o~31o Rectilinear velocity : < 50 cm/s
Data Criteria
r oinertial oU u P P f
Inertial amplitude
Distribution of inertial amplitudes (U) estimated from Satellite tracked drifters (1990~2004)
Global distribution of inertial amplitude (U)
66
Mean Inertial amplitude(2ox2o) 1990~2004
(cm/s)Drifter measurement of U
Inertial energy fluxestimated by a slab model andNCEP wind
77
( , )
1( ) ( ( , ) )( ( , ) ),
( ) 40
k
k
N
k i i k j j ki jk
i j k k i j o
U x t U U x t UN
t t t and x x km
Assumption : Homogeneous amplitude within (Uncorrelated observation error, homogeneity of error, homogeneity of variance)
Why are the meridional structures of the buoyancy effect so different?
2 2
log( / )
2 log( / )
2 log( / )
m
cm
c
cm m m
b N H
b b b N H
N N N
H H H
b
mH
N
2 2
2 1
5.9
2.2 10
~ 110
c
c
cm
b m s
N s
H m
Buoyancy structure
180oW 120
oW 60
oW 0
o 60
oE 120
oE 180
oW
60oS
45oS
30oS
15oS
0o
15oN
30oN
45oN
60oN
-3
-2
-1
0
1
2
3
180oW 120
oW 60
oW 0
o 60
oE 120
oE 180
oW
60oS
45oS
30oS
15oS
0o
15oN
30oN
45oN
60oN
-3
-2
-1
0
1
2
3
180oW 120
oW 60
oW 0
o 60
oE 120
oE 180
oW
60oS
45oS
30oS
15oS
0o
15oN
30oN
45oN
60oN
-3
-2
-1
0
1
2
3
• N and Hm seem to be canceled out in terms of spatial distribution.
• Shallow Hm in the high latitude of the North Pacific is responsible for the longer decay time scale.
• Weaker stratification in the Southern Ocean makes the time scale longer.
• In the North Atlantic, deep mixed layer and yet strong buoyancy may be the major cause of the shortest decay time scale in the high latitudes.
longer δ
longer δ
longer δ
1919
Understanding Dynamics
From Kunze [1985]’s dispersion relation2 2 2
2
( ) 1[ ( )]
2 2o o
N k l U Vf y l k
fm m z z
Group velocity of inertial-internal wave ignoring vertical shear of low frequency background current
2 2
3o
gz
N lC
m fm
N2 fo
2 2
3gz
N lC
fm
or
0k assuming
0 0( ) ( 0)l t l t consider l [D’Asaro, 1989]
exp( ( )) exp( ( ))I oZ U i ft ly U if t iy l t
l gzC
Stratification and Local inertial frequency
Beta Effect and Forcing Scale
2020
Understanding Dynamics : MLD
2 2
3o
gz
N lC
m fm
With a continuously varying density structure, a perturbation is separated into several modes (normal modes). Large MLD induces lower modes to have larger energy [Zervakis and Levine, 1995]
mH
m gzC
[Zervakis and Levine, 1995]
Deep MLD
Shallow MLDLowMode
HighMode
Mixed Layer Depth
2121
Summary & Conclusion
Global distribution of inertial decay timescale from the drifter observation : Increasing with latitudes in all the basins except in the North Atlantic
The analytical model with beta dispersion dynamics reproduces global distribution of the decay timescale fairly comparable to the observation.
Dephasing process by beta effect is primarily responsible for the meridional variation of the decay timescale in the North Pacific and the Southern Ocean.
In the North Atlantic, buoyancy effect seems to compensate the beta effect which leads to a lack of meridional variation.
Temporal correlation function
Theoretical solution Shape of exponential function
AcceptableRayleigh damping
The decay time scale distribution shown in this study suggested that the mixed layer inertial energy budget may have basin-dependency.
2222
Special thanks : Ray Schmitt, Young-Oh Kwon, Chris Garrett, Stefan Smith, Kurt Polzin, Tom Farrar, Julie Deshayes
2323
Special thanks : Ray Schmitt, Young-Oh Kwon, Chris Garrett, Stefan Smith, Kurt Polzin, Tom Farrar, Julie Deshayes