How the ocean`s mean structure conspires to generate - eur

Transcription

How the ocean's mean
state generates submesoscale turbulence
EUR-Oceans Hot Topics Conference
Gran Canaria
6-8 November 2013
Shafer Smith
CAOS/Courant/NYU
Monday, November 25, 2013
Outline
• Eddies, baroclinic instability and the
oceanic energy cycle
• The structure of the eddy field:
geostrophic turbulence and SQG
• How the eddies stir tracers
Sea Surface Height anomaly
... eddies everywhere
Chelton,
Schlax
&
Samelson
(2011)
SSH on 28 August 1996 constructed from TOPEX/Poseidon (T/P) data only (top) and from the m
What’s the source?
Energy cycle
Ferrari & Wunsch ’10
Blue: Geostrophic
Green: Ageostrophic
Transfers in TW = 106 W
Resevoirs in EJ = 1018 J
Energy cycle
Wind work on
interior ocean:
0.8TW
Blue: Geostrophic
Green: Ageostrophic
Energy cycle
Wind work on
interior ocean:
0.8TW
Baroclinic instability APE to EKE (eddies):
0.9TW
Blue: Geostrophic
Green: Ageostrophic
The stratified ocean
The stratified ocean
Gill, Green and Simmons (1974):
APE ~ (Basin scale/Deformation scale)2 ~ 1000
2
~ (3000 km/100 km)
...enormous resevoir of energy available for
conversion...
Thermal wind balance with
two density layers
94
Lectures on Geophysical Fluid Dynamics
Figure 2.12 The mean westerly flow in a system healed near the equator (where the upper,
warmer layer is thickest) and cooled near the pole.
isopycnal displacements that contain a relatively large amount of available potential energy. In the Earth's atmosphere, the sun creates available potential energy
by net heating in the tropics and net cooling in the polar regions. If the Earth
Thermal wind balance with
two density layers
94
Lectures on Geophysical Fluid Dynamics
Figure 2.12 The mean westerly flow in a system healed near the equator (where the upper,
warmer layer is thickest) and cooled near the pole.
Sloping isopycnals store APE. When steep
enough, baroclinic instability occurs,
converting
APE
eddy
KE large amount of available potenisopycnal
displacements
thatto
contain
a relatively
tial energy. In the Earth's atmosphere, the sun creates available potential energy
by net heating in the tropics and net cooling in the polar regions. If the Earth
The classic eddy cycle
Wind work on
gyres
Large scale
Small scale
Deformation
scale
of energy transfer in a two-layer fluid. The
gure 6.6 Schematic diagram
upper leve
presents baroclinic energy (vertical wave number 1) and the lower level represent
arotropic energy (vertical wave number 0). Horizontal wave number increases to th
ght. Solid arrows indicate the direction of energy transfer; dashed arrows indicate poten
al enstrophy transfer.
Salmon (1980)
The classic eddy cycle
Wind work on
gyres
Large scale
Small scale
Deformation
scale
gure 6.6 Schematic diagram of energy transfer in a two-layer fluid. The upper leve
presents
baroclinic
energy eddies
(vertical wave
1) and the lower
Classic
picture:
grownumber
in horizontal
and level represent
arotropic energy (vertical wave number 0). Horizontal wave number increases to th
vertical
scale >>>
big, smooth
structures,
ght. Solid
arrows indicate
the direction
of energy transfer;
dashed arrows indicate poten
al enstrophy
transfer. with ‘blurry’ SSH image
consistent
Salmon (1980)
Idealized evolution of BCI
Simulation by J. Taylor
Ro = 0.125
Boussinesq
Vertical vorticity (color), Isopycnal surface (white)
10km
10km
1km
Deformation scale: ld = N H/2πf � 320km
Idealized evolution of BCI
Simulation by J. Taylor
Ro = 0.125
Boussinesq
Vertical vorticity (color), Isopycnal surface (white)
10km
10km
1km
Deformation scale: ld = N H/2πf � 320km
APE in the ocean
JOURNAL OF PHYSICAL OCEANOGRAPHY
1/2
APE
(Eady time scale)
Eddies form mostly in high APE areas,
consistent with BCI
Tulloch et al. (2011)
Eddy kinetic energy
60°N
0°N
60°N
120°E
(cm/s)2
180°E
25
50
240°E
75
100
125
300°E
150
175
200
360°E
225
250
275
60°E
300
325
350
120°E
375
KE × sin2 φ
Eddies form mostly in high APE areas,
consistent with BCI
Stammer & Wunsch (1998)
Figure 4
Estimate of the geostrophic kinetic energy (KE) (cm s−1 )2 of oceanic variability at the sea surface, here multiplied by sin2 φ, where φ is
the latitude, to avoid the equatorial singularity in noisy data. Note the very large spatial changes of kinetic energy. Figure taken from
Wunsch & Stammer 1998.
intense currents such as the Gulf Stream along the Eastern U.S. coast or the Agulhas Current
What about submesoscales?
(e.g. turbulence below the
deformation scale)
Sea Surface Height anomaly
... eddies everywhere
Blow up
this region
Chelton,
Schlax
&
Samelson
(2011)
SSH on 28 August 1996 constructed from TOPEX/Poseidon (T/P) data only (top) and from the m
Sea Surface Temperature
SST provides a
‘blow up’ of a
region,
exposing finer
detail of eddies.
Sea Surface Temperature
SST provides a
‘blow up’ of a
region,
exposing finer
detail of eddies.
Energetic vortices
and fronts range
down to
resolution of
instrument
(Sea Surface Roughness
contrast .. .glitter analysis
shows even finer scales)
10 km
Thanks to B. Chapron
Shcherbina et al (2013)
eW
su at
pp er
ed or re
is ting gio
d m in n i
on ar fo n
th M ked rm win
e s od in ati te
ra urv era Fi on r. (a
di ey te gu fo )
en , R re r m Se
Ad ts sh es 1 o a
m at a ow olu a. ( del sur
f
in
is re ing tio c) de ac
od
NA
BI
ER
ET
.:
AL
OS
CA
LE
ES
BM
SU
UL
E
TU
RB
NC
E
ST
AT
IS
TI
CS
Simulation
provides
further blow
up...
Vorticity: shows
continuous range of
finer scale turbulence
Velocity spectrum
SHCHERBINA ET AL.: SUBMESOSCALE TUR
(a)
shallower than -3
slope: energetic
submesoscales
Shcherbina et al (2013)
(c)
AUGUST 2008
Submesoscales in BCI sim
1757
KLEIN ET AL.
1754
KE z=0
VOLUME 38
KE z=-150
KE from U,V
KE from SSH
KE z=-400
VOLUME 38
Surface vorticity
Upper Ocean Turbulence from High-Resolution 1748
3D Simulations
PATRICE KLEIN
AND
KE from U,V
KE from BT
BACH LIEN HUA
Laboratoire de Physique des Océans, IFREMER/CNRS, Brest, France
GUILLAUME LAPEYRE
Laboratoire de Météorologie Dynamique/IPSL, Ecole Normale Supérieure/CNRS, Paris, France
XAVIER CAPET
Institute of Geophysics and Planetary Physics, University of California, Los Angleles, Los Angeles, California
SYLVIE LE GENTIL
Laboratoire de Physique des Océans, IFREMER/CNRS, Brest, France
1748
HIDEHARU SASAKI
Earth Simulator Center, JAMSTEC, Yokohama, Japan
(Manuscript received 29 January 2007, in final form 17 December 2007)
Monday, November
25, 2013
KE z=-800
FIG. 5. Velocity spectra estimated from u and ! (red curve) at (a) z " #2 m, (b) #150 m, (c) #400 m, and (d) #800 m. The black
curve in (a) and (b) is the surface velocity spectrum estimated from the SSH. The blue curve in (c) and (d) is the velocity spectrum
estimated from the barotropic velocity. The green curve in each panel is the density spectrum. Surface density spectrum is scaled by
a factor of g2/(N 20&20) " 7.1 using N0 /f0 " 37 to match the surface velocity spectrum (see text). Other density spectra are scaled to match
the velocity spectra at k " 15. The horizontal axis displays the nondimensional wavenumber k. The value k " 10 corresponds to a
wavelength of 300 km. Units on the vertical axis are m3 s#2.
Upper Ocean Turbulence from High-Resolution 3D Simulations
J O U R N A L O F PPHATRICE
YSICA
L OC
E AB
NACH
O GL
R A PH
HUA
Y
KLEIN
spectralIEN
range. This
confirms
locity spectrum, suggesting that the energy
there AND
is whole
the geostrophic
equilibrium mentioned
examining
captured by this mode.
Aprincipally
UGUST 2008
K L before
E Brest,
I Nwhen
EFrance
T
A L . the graLaboratoire
de
Physique
des
Océans,
IFREMER/CNRS,
To quantify the degree of ageostrophy of the flow in dient wind balance, that is, the velocity field near the
the upper layers (where the Rossby number is large) surface almost equilibrates the pressure field. Then we
V
KLEIN ET AL.: VERTICAL
Submesoscales
in VELOCITIES
BCI simFROM
Note vertical velocities associated with fine-scale
vorticity features: submesoscale fronts and filaments
are sites of intense upwelling (Raf’s talk)
How can BCI generate
submesoscales at surface?
Conditions for BCI
ng-force to zonal PV perturbations (Pedlosky 1987; Walker and Pedlosky 2002). M
nic instabilities
generated
by criteria
non-zonal
Charney Stern
Pedlosky
formean
BCI - flows
need:are very effective at generatin
in the
(Phillips
• Q
y changes
urbulence
(Spall
2000;sign
Arbic
andinterior
Flierl 2004),
duemodel)
to a strong nonlinear feedback
• Uz has the same sign at the upper and lower boundaries (Eady
eneration problem)
and eddy scale and anisotropy (Smith 2007a). That said, such instabiliti
• near
Uz atmeridional
the lowercontinental
boundary has
the sameand
signhere
as Q
the interior
y in
rimarily
boundaries,
we
focus
on flows that
(original Charney problem)
onal, such
ACC,
boundary
current
extensions
and
theofsubtropical
• Uasatthe
the
upper
boundary
has the
opposite
sign
Q in the counter cu
z
y
interior (‘oceanic Charney problem’)
e large-scale meridional QGPV gradient, generalized as in Bretherton (1966) to
For ocean-relevant
cases need
sign function
change ofsheets,
singleisfunction (a la
nd lower
boundary conditions
via delta
Bretherton ’66):
∂s
f 2 dU
∂ Q̃
=β−f
+ 2
δupper , where s=By/N2
∂y
∂z N dz
erturbations (Pedlosky 1987; Walker and Pedlosky 2002). Moreover,
Mean PV structure from hydrography
ated by non-zonal mean flows are very effective at generating baroZonally-averaged Qy/β from OCCA atlas
Uz
; Arbic and Flierl 2004), due to a strong nonlinear feedback between
> 1.5#
a)
(50m)
0
ale and anisotropy (Smith 2007a).
!n=27That said, such instabilities# likely
1km
Depth
nal continental boundaries,
n
=27.5 we
!
and here
.5#
focus on flows that are rela0
Qy
C, 2km
boundary current extensions and the subtropical counter currents.
".5#
nal QGPV gradient, generalizedn as in Bretherton (1966) to include
! =28
3km
"#
nditions via delta function sheets, is
−60
−40
−20
0
Latitude
∂s
f 2 dU
∂ Q̃
=
β
−
f
+
δ
,
upper
2
b) ∂y
∂z N dz
20
40
60
< "1.5#
2
where s(z) = By/N2 = -fUz/N(1)
Tulloch, Marshall, Hill and Smith (JPO 2011)
gradient, s = −by /N 2 the meridional isopycnal slope, f the Coriolis
erturbations
3km
n
!
=28and Pedlosky 2002).
(Pedlosky 1987; Walker
"#
Moreover,
< "1.5#
ated by −60
non-zonal
flows are 0very effective
at40generating
−40mean −20
20
60 baroLatitude
Schematic QGPV
gradient
Uz
; Arbic and Flierl 2004), due to a strong nonlinear feedback between
(50m)
b)
ale and anisotropy (Smith 2007a). That said, such instabilities likely
nal continental boundaries, and here we focus on flows that are rela-
Qy/β
C, boundary current extensions and the subtropical counter currents.
nal QGPV gradient, generalized as in Bretherton (1966) to include
nditions via delta function sheets, is
∂s
f 2 dU
∂ Q̃
β − f cross-section
+ 2
δof
upper
) Zonally=
averaged
the, meridional QGPV gradient (in (1)
units of β), from
∂y
∂z N dz
tlas. The upper surface gradient Uz is shown
aboveMarshall,
the dashed
at a2011)
depth
Tulloch,
Hillline
andevaluated
Smith (JPO
2
Monday, Novembers
25, =
2013 −by /N
gradient,
the meridional isopycnal slope, f the Coriolis
ated by non-zonal mean flows are very effective at generating baroMoreover,
baroclinic instabilities generated by nonzonal
Hydrography...
mean flows are very effective at generating baroclinic tur; Arbic and Flierl 2004), due to a strong nonlinear feedback between
ulence (Spall 2000; Arbic and Flierl 2004) because of
strong nonlinear feedback between eddy generation and
ddy scale and anisotropy (Smith 2007a). Here we focus on
ows
that
are
relatively
zonal,
such
as
the
ACC,
boundary
nal continental boundaries, and here we focus on flows that are relaurrent extensions, and subtropical return flows.
large-scale
gradient, generalC,The
boundary
currentmeridional
extensions QGPV
and the subtropical
counter currents.
zed as in Bretherton (1966) to include upper and lower
oundary
via delta function
sheets, is (1966) to include
nal
QGPVconditions
gradient, generalized
as in Bretherton
2
~
›
Q
›s
f
dU
nditions via delta
function
sheets,
5b ! f
1 2 is dupper ,
›y
›z
N dz
(1)
igure 3: Schematic of typical2zonal velocity profiles in westerly, mixed and easterly sheared me
∂s
f dU
∂ Q̃
2
=
β
−
f
+
δ
,
(1)
where b is the planetary PV
gradient,
s 5 2by/N is the
upper
2
∂y
∂z UN(z) dz
ows.
The
curve
indicates
the Coriolis
horizontalparameter,
dashed line indicates
approximately the heig
meridional isopycnal slope, fand
is the
N2
Tulloch,
Marshall,
Hill and Smith (JPO 2011)
s the stratification, and dupper is a delta
function
at the
2 is zero assuming negligible planetary PV gradient. The surface she
t which thesQGPV
gradient,
= −bgradient
/N
y
Hydrography...
ows
that
are
relatively
zonal,
such
as
the
ACC,
boundary
large-scale
boundary
currentmeridional
extensions QGPV
and the subtropical
counter currents.
oundary
via delta function
nal
QGPVconditions
as in Bretherton
2
~
›
Q
›s
f
dU
These sheets,
types efficiently
generate surface b...
nditions via delta
function
is
(1)
5b ! f
1 2
dupper ,
›y
›z
N dz
igure 3: Schematic of typical2zonal velocity profiles in westerly, mixed and easterly sheared me
∂s
f dU
∂ Q̃
2
=
β
−
f
+
δ
,
(1)
gradient,
s 5 2by/N is the
upper
2
∂y
∂z UN(z) dz
ows.
The
curve
indicates
the Coriolis
is the
N2
Tulloch,
Marshall,
function
at the
t which thesQGPV
gradient,
= −bgradient
/N
y
Hydrography...
ows
that
are
relatively
zonal,
such
as
the
ACC,
boundary
large-scale
boundary
currentmeridional
extensions QGPV
and the subtropical
counter currents.
oundary
via delta function
nal
QGPVconditions
as in Bretherton
2
~
›
Q
›s
f
dU
These sheets,
types efficiently
generate surface b...
nditions via delta
function
is
(1)
5b ! f
1 2
dupper ,
›y
›z
N dz
Why
and
igure 3: Schematic of typical2zonal velocity profiles in westerly,
mixed
andhow?
easterly sheared me
∂s
f dU
∂ Q̃
2
=
β
−
f
+
δ
,
(1)
gradient,
s 5 2by/N is the
upper
2
∂y
∂z UN(z) dz
ows.
The
curve
indicates
the Coriolis
is the
N2
Tulloch,
Marshall,
function
at the
t which thesQGPV
gradient,
= −bgradient
/N
y
The spectra
Regimes
characterization
Eddy PV
from
Phillips vs. Charney BCI
Charney
(w/ Bsurf
gradient)
Oceanic tracer
Phillips
stirred by a turbu
(no Bsurf
gradient)
Roullet, McWilliams, Capet & Molemaker (JPO 2012)
The spectra
Regimes
characterization
Eddy PV
from
Phillips vs. Charney BCI
Charney
(w/ Bsurf
gradient)
Oceanic tracer
Phillips
stirred by a turbu
(no Bsurf
gradient)
Note small
eddies and
filaments
Roullet, McWilliams, Capet & Molemaker (JPO 2012)
Simple model for Charney BCI
Consider simple model for the oceanic version of Charney-type
baroclinic instability that Shane showed earlier...
N = N0
U(z) = Γ(z + z2/(2H) - H/3)
so By = -f Uz(0) = -fΓ
Uzz(z) = Γ/H
and Qy = β - Γf2/HN2
= constant
Have BCI when Qy and By
have same sign.
If Γ>0 possible to have By with no BCI...
Γ =-1
H=1
Linear instability of simple Charney
Growth rates
Amplitudes
Note:
1. Growth at all scales, as in original problem
2. Growth focused at upper surface -- instability excites buoyancy
anomalies at surface => SQG behavior
Baroclinic instability & SQG
1. Surface ∇B opp sign
from interior ∇Q
=> Charney instability,
with amplitude sharply
peaked at surface
from interior ∇Q
peaked at surface
2. Eddy velocity u grows fastest at
surface
from interior ∇Q
peaked at surface
surface
3. Surface buoyancy conservation
(because w=0 at z=0) is
∂tb + (u+U)⋅∇(b+B) = 0
so variance is generated:
d/dt〈½b2〉=〈-bu〉⋅∇B > 0
for down-gradient flux.
from interior ∇Q
peaked at surface
surface
3. Surface buoyancy conservation
(because w=0 at z=0) is
∂tb + (u+U)⋅∇(b+B) = 0
so variance is generated:
d/dt〈½b2〉=〈-bu〉⋅∇B > 0
for down-gradient flux.
4. Eddy buoyancy b dominates interior
PV q, so inversion to get
streamfunction is SQG-like
Nonlinear Charney:
Horizontal slices
hC/H = -1
Thanks to Shane Keating
Surface PV
PV at z=-.3
Nonlinear Charney: PV(x,z)
hC/H = -1
hC/H = -1/3
hC/H = -1/7
hC/H = -1/11
Submesoscale structures
from interior stirring
NATRE
and
SFTRE
experiments
North
Atlantic
Tracer
Release
Experiment
NATRE
data set
NATRE
North Atlantic Tracer Release Experiment data set
•
High Resolution Profiler provided 127 vertical profiles of T, S, and
shear (0-4000m depth)
•
Moored current meters provided U, V velocities for one year (200 !
3500m depth)
T-S Profiles in NATRE
T-S relationship is tight
in thermocline
At MS level, T-S relationship
characterized by 0.2 psu
thermohaline fluctuations
S (psu)
in thermocline
Vertical mixing by internal wave breaking
or double diffusion?
S (psu)
in thermocline
S (psu)
in thermocline
or stirring along isopycnals?
S (psu)
in thermocline
S (psu)
in thermocline
S (psu)
Thermohaline fluctations have little signature on density:
compensated fronts of 1-5km in horizontal, 10-100m in vertical.
=> Stirring along isopycnals will effectively stir tracers inclined to
isopycnals, not density (McVean and Woods1980)
Lateral structure in
simulation
‣ T, S passive tracers => filamentation
compensated in effect on density
‣ Interior: little density gradient, ample
tracer variance along isopycnals
K
0
Spice
10
PSD
‣ Spectra: Tracer ~ K-1, density ~ K-5
K-1
−1
2
10
−2
Density
10
K-5
−5
K
−4
10
Dens & Spice spectra
−6
10
0
10
1
10
K (nondimensional)
2
10
Vertical structure in
simulation
‣ 3D cascade => ample strain and shear at
submesoscales
‣ Shear/Strain ~ N/f (independent of scale)
‣ Tracer (T & S) filaments are 3D, with
2490 ratios followingJ O
URNAL OF PHYSICAL
aspect
shear/strain
~N/f
z
(N/f)2
(S aspect ratio)2
OCEANOGRAPHY
FIG. 10. (left) Horizontal and (right) vertical slice
central simulation. The dashed black line in each p
panel. The white contours in the vertical slice are th
and the white line is a reference line with slope f/N,
is centered. The line is situated next to a filamen
filaments are easily found in any snapshot slice.
Slope f/N
the right panel follows a 21 power law (the thin solid
line has a 21 slope for comparison), also consistent
with isotropy. Notice that the spectra become very
noisy at the largest vertical wavenumbers. This hap-
b
Conclusions
• Oceanic APE resevoir generates
ample eddies through BCI
• At surface, eddy stirring of buoyancy
gradients readily generates
submesoscale motions
• At depth, eddy stirring leads to
compensated fine-scale T/S fronts
But .. don’t really need Charney BCI
Consider two runs with N constant and
U1(z) = U0 cos(πz)
U2(z) = U0 cos(πz) + Γ(z2/2 + z - 1/3), Γ>0, hC>0
Qy(z)
U2(z)
U1(z)
Surface component does not contribute to BCI (no Charneytype instability), yet have surface buoyancy gradient
Linear BCI is nearly the same in both cases
Growth rates
Amplitude (max)
Slices of PV
U1(z)
U2(z)
Patches of surface buoyancy field
U1(z)
U2(z)
Note secondary vortex formation
Surface KE spectra
U2(z)
U1(z)
-2
-3

How the ocean`s mean structure conspires to generate - eur

Transcription

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