Instability in the STCC region

Instability in the STCC region

20111014alu

Background

Qiu and Chen 2010 JPO

Res=0.1deg (~10km)Domain:130E~179.9W(180.1),3N~33.1NGrid size:502x302x71 Flat bottom: 2000m

135E 140E

WOA2001 monthly Temp & Saln

Flow Relaxation Scheme and sponge zone

Flow Relaxation Scheme and sponge zone

33N ←

3N ←↓130E

↓180E

Periodic BC

Periodic BC

27N ←

9N ←

Zero transport(u, v=0) & free-slip BC

Zero transport(u, v=0) & free-slip BC

1st 360 days: strong relaxation for spinup2nd 360 days: no relaxation except northern and southern boundaries for instability growing

Set up monthly runs for the region 135E~140E

0-relax Snapshots(t=0)Mar Sep

elevation

u & temp section@137E

2'2' vuEKE

Eddy kinetic Energy (averaged from 18N~25N)

tEKEEKELEKE

eEKEEKE t

0

0

ln

1ln)(0

t

EKEEKEtLEKEDay foldinge

EKE0=eke at day 5

RifGrowthRateEady 22

2

zv

zuNRi

Unit: 1/days

Mar May Sep

Nov

Averaged in upper 100m

Kobashi et al. fig3a

Averaged from 20N~25N

Fig 3

JPO,2011

Fig 4

Kobashi et al. fig6

Thermal wind relationKobashi et al. fig15

Mar Aug

z

fyx

PV yxErtel

Initial state(t=0)

PV profile@137E

dPV/dy @137E

Integrated from z0 to z200

dzyzyPVIIyIndexInstabilit ),()(

If II is close to 0, means it reaches the most necessary condition for instability.

Color: u shear in unit cm/s (u=u_surf – u_300) Contours: u_surf (positive region indicates the STCC)

The pink region indicates the large u shear occurs in May, June, July. In these months, the strength of u shear is mainly contributed by upper layer STCC. However, the NEC starts retreating in these months, and the EKE analysis also shows the more stable conditions. So, the strengthening of STCC does not contribute to the instability

Qiu,1999

Solid: u shearDash: eke

Qiu, 1999. fig10


1 2 3 4 5 6 7 8 9 10

10 regions x 12 months=120 cases

u_shear (u0-u300)


STCC_135140

STCC_140145

STCC_145150

STCC_150155

STCC_155160

STCC_160165

STCC_165170

STCC_170175

STCC_175180

STCC_130135u_shear VS mean growth rate

Instability analysis

2

12

12 0

LL

S

zS

zyQ

zS

zy

dtd

bcD

),,,(,,,, tzyxzytzyx

從準地轉位渦平衡方程式出發

zUf

ygM

zgNgb

dydzNMbv

yUvu

t

EKEdydz

refrefref

00202

2

20

,,

''''

令總流場＝初始 (背景 ) 流場 +perturbed 流場 , 代入上式整理

zS

zy

y

yqJq

xU

t x

12

2

0

00 0,

得

zS

zyyq

yxqU

tq

x

12

2

2

2

00 0

假設 ||<<1, drop J(,q)項 , 考慮邊界條件 w*=w0+w1+O(^2) at surf and bott,整理得到：

000

dVyx

qUtq

x

BT BC

Instability analysis

dydzyUvuBT 0''

dydzNMbvBC 2

2

''

BCBTdydzEKEt

u_shear VS mean growth rate

Kobashi,2006,JGR

BT VS BCY_integ: 18N:25NZ_integ:-400:0


Order analysis (in first 100 days)

dydzyUvuBT 0''

dydzNMbvBC 2

2

''

Order of BT=1*2*3= 1e-14

1. order of u’: 1e-3 2. v’: 1e-4 3. dU0dy:1e-7

Order of BC=1*2*3/4=1e-12

1. order of v’: 1e-4 2. b’: 1e-4 3. M2: 1e-8 Approach A:M2=f*dU0dz a.1 f: 1e-5 a.2 dU0/dz: 1e-3 Approach B:M2=g*d(rho0/rhoref)dy b.1 g: 1e1 b.2 d(rho0/rhoref)dy:1e-9 4. N2: 1e-4

Z=0-400mY=18-25N

Jan Feb Mar APR

May Jun Jul Aug

Sep Oct Nov Dec

dLEKE/dt (color), LEKE(black contours), EKE(red contours)case: stcc_135140, new def., upper 100m

EKE(average Upper 100m, 18N~25N, zonally)

LEKE=log(EKE/EKE0), EKE0=eke at day 5

dudy_uprof(11pt-smooth), stcc_135140

Literatures• Qiu, 1999 JPO: Seasonal Eddy Field Modulation of the North Pacific

Subtropical Countercurrent: TOPEX/Poseidon Observations and Theory. • Kobashi et al, 2006 JGR: Three subtropical fronts in the North Pacific:

Observational evidence for mode water-induced subsurface frontogenesis

• Yamanaka et al, 2008 JGR: Decadal variability of the Subtropical Front of the western North Pacific in an eddy-resolving ocean general circulation model

• Qiu and Chen, 2010 JPO: Interannual Variability of the North Pacific Subtropical Countercurrent and Its Associated Mesoscale Eddy Field

• Xie et al,2011 JC: Dynamical Role of Mode Water Ventilation in Decadal Variability in the Central Subtropical Gyre of the North Pacific.

2

12

12 0

LL

S

zS

zyQ

zS

zy

dtd

bcD

),,,(,,,, tzyxzytzyx

從準地轉位渦平衡方程式出發

zUf

ygM

zgNgb

dydzNMbv

yUvu

t

EKEdydz

refrefref

00202

2

20

,,

''''

令總流場＝ (背景 )初始流場 +perturbed 流場 , 代入上式整理

zS

zy

y

yqJq

xU

t x

12

2

0

00 0,

得

zS

zyyq

yxqU

tq

x

12

2

2

2

00 0

假設 ||<<1, drop J(,q)項 , 考慮邊界條件 w*=w0+w1+O(^2) at surf and bott,整理得到：

000

dVyx

qUtq

x

zUf

ygM

zgNgb

dydzNMbv

yUvu

t

EKEdydz

zS

zyyq

yxqU

tq

yq

xU

t

zS

zy

y

yqJq

xU

t

tzyxzytzyx

LL

S

zS

zyQ

zS

zy

dtd

refrefref

x

x

x

Dbc

00202

2

20

12

2

2

2

00

00

12

2

0

00

2

12

12

,,

''''

0

0

0,

),,,(,,,,

0

Color: map of the max growth rate in the first year (1/days)Contours: when the max growth rate occur (days), thick contour indicates 100

The NEC tail extends to the northmost in Jan and retreat to the southmost in Sep

Quantification of the movement of NEC (tail)

Color: zonal averaged u at 200m (t=0), in unit cm/s. Contours: u = -5.5cm/sRed dot line: the exact position in latitude of the movement of the NEC(tail) in each month

The NEC tail extends to the northmost in Jan and retreat to the southmost in Sep

Color: u shear in unit cm/s (u=u_surf – u_300) Contours: u_surf (positive region indicates the STCC)

The pink region indicates the large u shear occurs in May, June, July. In these months, the strength of u shear is mainly contributed by upper layer STCC. However, the NEC starts retreating in these months, and the EKE analysis also shows the more stable conditions. So, the strengthening of STCC does not contribute to the instability

Bo Qiu,1999

Jan Feb Mar APR

May Jun Jul Aug

Sep Oct Nov Dec

d/dy(PV) , u, and temp

Jan Feb Mar APR

May Jun Jul Aug

Sep Oct Nov Dec

d(LEKE)/dt yt-plots

Jan Feb Mar APR

May Jun Jul Aug

Sep Oct Nov Dec

RifGrowthRateEady

u shear VS u surface(130E~180E 10 cases)

Color:u shear [u0-u300] (cm/s)Contour:u surface (cm/s)

u shear VS max_growth_rate(130E~180E 10 cases)

Color: u shear[u0-u300] (cm/s)Conotur: max_growth_rate (z=0-100avg)(0.05,0.1,0.15,0.2 [1/days])



Documents

Instability in the STCC region