Comparison between vertical shear mixing and surface wave-induced mixing in the global ocean Fangli Qiao and Chuanjiang Huang Key Laboratory of Marine Science and Numerical Modeling First Institute of Oceanography, SOA, China PICES-212, Oct 16, Hiroshima, Japan qiaofl@fio.org.cn
Outline 1. Introduction of Bv and its applications 2. Vertical shear mixing vs Bv 3. Summary
1. Introduction of Bv and its applications
Some related work: 1. Phillips, O. M., 1961: Although the use of potential theory has been very successful in describing certain aspects of the dynamics of gravity waves, it is known that in a real fluid the motion can not be truly irrotational. And Phillips (1974): Wave is proved to be too feeble for any dynamic consequence 2. Wave enhanced turbulence (Craig & Banner,1994; Terray, E.A. et al, 1996; Le Ngoc LY 2; Burchard &Karsten, 21; Mellor & Blumberg, 24): Wave-breaking 3. Wave-current interaction (Xie et al 22, 23): 2-D 4. Mellor et al, 23JPO, and 28 J. Atmos. Ocean. Technol [wave breaking] While these studies (wave-breaking) have shown some improvements in simulation, the surface wave effects are mostly limited to the top few meters, and too weak
Some related work: 5. We wave-induced vertical mixing, Bv, as the function of wave number spectrum(yuan, Qiao et al, 1999; Qiao et al, 24,21). 6. In 25 and 26 (GRL), Alex Babanin: There is accumulating evidence that in absence of wave breaking, and even wind stress, turbulence still persists through the water column and not only the boundary layers. 7. The non-breaking wave-induced mixing was measured in Lab (Babanin et al, 29, JPO; Dai et al, 21, JPO; Savalyev et al, 212, JGR) and in the ocean (Huang et al, 21, 212). 8. We have done interesting numerical experiments to close the shear-related mixing, ocean circulation model can work quite well (Qiao et al, 212, JGR).
E(K) is the wave number spectrum which can be calculated from a wave numerical model. It will change with (x, y, t), so Bv is the function of (x, y, z, t). Qiao et al, GRL, 24; OD, 21 v v v ( ) v v 2 B exp{ 2 } ( ) V = α E k kz dk ω E k exp{ 2kz} dk v z k v k If we regard surface wave as a monochramatic wave, B = αa kω e = αa u e 3 ( 3 kz) ( 3 kz) s Bv is wave motion related vertical mixing instead of wave breaking. Although the horizontal scale of surface wave, 1m, is much smaller than that of circulation, however, the wave-induced vertical velocity in the upper ocean could be stronger than vertical current turbulence velocity., 1 2 Stokes Drift
The distribution of the 2m-averaged Bv (cm 2 /s) in Feb.
Hs Bv The vertical distribution of the Bv (cm 2 /s) along dateline in Feb. (In fact,.1 cm 2 /s means a lot for circulation processes)
Wave-circulation coupled model: How to use Bv (1) To include current effects into a wave model is another story, but not so important. (2) To include wave effects into a circulation model is so simple, just add Bv U U ( KM ) [( KM + BV) ] z z z z V V ( KM ) [( KM + BV) ] z z z z T T ( KH ) [( KH + BV) ] z z z z S S ( KH ) [( KH + BV) ] z z z z
Laboratory experiments: Wave tank: 5m in length with height of.4m and width of.2m. To generate temperature gradient through bottom cooling of refrigeration tubes, and temperature sensors are selfrecorded with sampling frequency of 1Hz. (1) Temperature evolution in natural condition (2) Temperature evolution with wave Top of wave tank Temperature sensor Refrigeration tube Dai and Qiao et al, JPO, 21 Bottom of wave tank
Experiment results without and with waves T T = kz t z z kz=k+bv Evolution of water temperature without waves. (a) Observation; (b) simulation.
Simulation results with waves Evolution of water temperature with waves. Left: observation; right: simulation; (a,b) 1.cm, 3cm; (c,d) 1.cm, 52cm;
In-situ observation evidences 1 S1 S2 S3 S4 Depth (m) 2 3 4 5 1 1 1 9 1 8 1 7 1 6 1 1 1 9 1 8 1 7 1 6 1 S5 S6 S7 S8 Depth (m) 2 3 4 5 1 1 1 9 1 8 1 7 1 6 1 S9 S1 S11 S12 Depth (m) 2 3 4 5 1 1 1 9 1 8 1 7 1 6 ε (m 2 s 3 ) 1 1 1 9 1 8 1 7 1 6 ε (m 2 s 3 ) Vertical profiles of the measured dissipation rates ε m (dots), and those predicted by wave ε wave (black lines) and the law of the wall ε wall (pink lines) at Station S1~S12 (in m 2 s 3 ). Observation is conducted in SCS during October 29 to November 1, 21. Huang and Qiao et al, 212,
Applications in ocean models
1-D numerical models Time-depth sections of temperatures for ocean weather station (OWS) Papa (a) simulated by one-dimensional KPP scheme, (b) observed and (c) simulated by one-dimensional KPP scheme with B v. The the red contour line indicates 9ºC isotherm. Shu and Qiao et al, 211, OM
1.5 2.5 3.5 3.5 2.5 KPP-OBS -2 1.5 z(m) -4-1.5-1.5-1.5-1.5-2.5 1.5 KPP -6.5.5.5.5-8 Jun Jul Aug Sep Oct Nov Dec time(month).5 1.5-2 -.5 -.5 z(m) -4.5.5 KPP+Bv -6.5-8 Jun Jul Agu Sep Oct Nov Dec time(month) The simulation deviation for Papa Station in 27 (Li and Qiao, 212, AOS)
depth (m) 2 4 6 (a) Temperature anomaly: P1 4 3 2 1 Simulated daily mean temperature deviations from the observation ( o C) MY 8 J J A S O N D J (b) Temperature anomaly: P2 depth (m) 2 4 6 3 2 1 MY+ wave breaking by Mellor 8 J J A S O N D J (c) Temperature anomaly:p3 depth (m) 2 4 6 1 1 MY+ Bv 8 J J A S O N D J Huang and Qiao, 211, JGR
3D coastal circulation models We apply Bv into: Bohai Sea Yellow Sea East China Sea And South China Sea Xia et al, JGR,26
Model results (POM) Wave-tide-circulation coupled model Multi-year observed Temperature along 35N in August Qiao et al, Ocean Dynamics, 21
T_Bohai section 26 H(m) -5-1 -15-2 -25 385 39 395 4 Latitude(1/1 N) 26 25.5 25 24.5 24 23.5 23 22.5 22 21.5 21 2.5 2 19.5 19 18.5 18 17.5-5 -1-15 -2-25 POM+Bv -3 38 38.5 39 39.5 4 4.5 25.5 25 24.5 24 23.5 23 22.5 22 21.5 21 2.5 2 19.5 19 18.5 18-5 -1-15 -2-25 -3 (a) POM 38.5 39 39.5 4 26 25 24 23 22 21 2 19 18 17 16 15 14 13 12 11 Observation in summer Lin et al, 26 JGR
Applications in the global ocean SST, mixed layer, circulation POM: Qiao et al, 21, OD MOM4: Shu and Qiao et al, 211, OM ROMS: Wang and Qiao et al, 21, JGR HIM: Huang and Qiao, 212, AOS POP: Huang and Qiao, 212, JGR
Apply Bv into different ocean circulation models POM: Mellor-Yamada turbulence closure model (1982) and new scheme (24, JPO) Circulation model linkage: (1) Topography from ETOPO5; (2)78 S-65 N, -36 E, Solid Boundary along 65 N; (3)Horizontal resolution of.5 by.5 (4) 16 vertical sigma layers (5) Wind stress and heat flux from COADS. Case 1: Original POM Cold start and run for 1 years Case 2: POM+Bv
MLD in summer (Qiao et al, OD, 21) MLD of the Southern Pacific in Feb. MLD of the Northern Atlantic in Aug. With waveinduce mixing Without waveinduce mixing World Ocean Atlas
With Bv Mean Correlation Coefficient:.68-.93 (35N) Without Bv
The two lines represent the whole upper ocean: Zonal (x-direction) and upper 1m (z-direction) averaged correlation coefficient (t). Based on POM28. Bleck, POM28 without wave effects; Green: with wave breaking (and IW) suggested by Mellor (24, JPO); Red: with Bv suggested by Qiao et al (24)
2. Comparison between vertical shear and surface waves mixing Bv vs Shear Mixing
(Mellor and Yamada, 1982) Numerical experiments for closing the shear-related vertical mixing POM covering 72 o S -65 o N is selected; Zonal resolution 1 o, while meridional resolution is 1/3 o between 1 o S- 1 o N, and gradually increases to 1 o by 2 o N and 2 o S; 32 sigma levels; The background mixing of 1 1-4 m 2 s -1 (K m ) for viscosity and 1 1-5 m 2 s -1 (K h ) for diffusivity. Experiment A: MY(Ps) + MY(Pb) + Bv + BG Experiment B: MY(Ps) + MY(Pb) + BG Experiment C: MY(Pb) + Bv + BG
Depth (m) Depth (m) Depth (m) 25 5 75 1 125 15 25 5 75 1 125 15 25 5 75 1 125 1 1 1 2 3 2 4 2 3 4 4 (a) Exp A (b) Exp B (c) Exp C 15 J F M A M J J A S O N D Month Monthly-mean vertical diffusivity (in m 2 s -1 ) as a function of depth and time at 3 o N, 18 o E. The diffusivities have been taken by denary logarithm
Too shallow and too strong thermocline in Exp B Thermocline in Exp C is very similar as that in Exp A Depth (m) 25 5 75 1 18 (a) Exp A 2 26 24 (b) Exp B 2 18 16 26 24 125 15 (c) Exp C (d) WOA1 At 3 o N, 18 o E Depth (m) 25 5 75 1 18 2 26 24 18 2 26 24 125 15 J F M A M J J A S O N D Month J F M A M J J A S O N D Month Monthly-mean temperature as a function of depth and time at 3 o N, 18 o E from (a) Exp A, (b) Exp B, (c) Exp C, and (d) the climatology. Contour interval is 1 o C.
18 17.8 Temperature ( o C) 17.6 17.4 17.2 Exp A Exp B Exp C 17 1 2 3 4 5 6 7 8 9 1 Year Time evolutions of annual-mean temperature within the upper 2 m averaged between 65 o S and 65 o N
Too shallow and too strong thermocline in Exp B Thermocline in Exp C is very similar as that in Exp A Depth (m) 5 1 26 24 2 (a) Exp A 28 24 2 28 (b) Exp B 24 2 16 28 24 2 15 2 5 28 24 16 2 (c) Exp C 28 18 24 28 24 2 (d) WOA1 28 18 24 Along 3 o N Depth (m) 1 2 2 15 16 16 2 15E 18E 15W 12W 9W 6W 3W Lontitude 15E 18E 15W 12W 9W 6W 3W Lontitude Temperature distribution along 3 o N in August from (a) Exp A, (b) Exp B, (c) Exp C, and (d) the climatology. Contour interval is 2 o C.
Too cold subsurface temperature in Exp B Temperature difference in Exp C is very similar as that in Exp A MY+Bv Depth (m) 5 1 15 1 (a) Exp A 1 1 2 Depth (m) 5 1 15 1 2 1 (a) Exp A 1 MY Depth (m) 2 5 1 15 (b) Exp B 3 2 1 1 2 Depth (m) 2 5 1 15 1 3 2 1 (b) Exp B 2 1 1 Bv Depth (m) 2 5 1 15 1 (c) Exp C 1 1 2 Depth (m) 2 5 1 15 1 1 (c) Exp C 1 2 2N 3N 4N 5N 6N Latitude Temperature deviations from the climatology averaged in August along the dateline 2 15E 18E 15W 12W 9W 6W 3W Longitude Temperature deviationss from the climatology averaged in August along 3 o N
Too shallow mixed layer depth (MLD) in Exp B MLD in Exp C is very similar as that in Exp A Simulated MLD (in m) in August from (a) Exp A, (b) Exp B, (c) Exp C, and (d) that from the climatology.
In the extra-tropical region: correlation coefficient in Exp B is smaller than those in Exps A and C In the tropical region: correlation coefficient in Exp B is similar as those in Exps A and C Latitude 5N 4N 3N 2N 1N 1S 2S 3S 4S 5S Exp A Exp B Exp C.4.5.6.7.8 Correlation coefficient Zonally averaged correlation coefficients in the upper 2 m between the simulated and monthly-mean climatological temperature.
Conclusions Surface wave is quite import for ocean circulation models through vertical mixing. 1. The non-breaking surface wave-induced vertical mixing (Bv) plays a key role in improving ocean circulation models, so it may be a low-lying fruit for improving forecasting ability of ocean, and then climate. 2. Bv is nearly not model dependent, it can be easily included into coastal circulation models and global ocean circulation models, and more important, Bv is effective. 3. Even excluding shear-induced mixing, POM can work quite well, which suggests that Bv plays much more important role than that of shear-induced mixing.
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