Review of Lynne s last lecture: What makes the ocean move?

Transcription

1 Review of Lynne s last lecture: What makes the ocean move?

2 Force = mass acceleration F = m a a = dv / dt = rate of change in velocity acceleration = [Sum of Forces] / mass

3 acceleration = [Sum of Forces] / mass Force 1 + Force 2 =?? Net force, so accelerate to the right

4 acceleration = [Sum of Forces] / mass Force 1 + Force 2 =?? X NO net force, so no acceleration But still could be velocity, it s just that velocity isn t CHANGING

5 Forces acting on the earth overall 1) Gravity 2) Centrifugal force Ω F=Ω 2 r

6 Zooming in Centrifugal force real gravity effective gravity Q: why doesn t all the ocean water flow towards the equator?

7 Answer: it does! Or rather the whole earth has reshaped itself real gravity Centrifugal force effective gravity With a squashed earth, the surface is perpendicular to the effective gravity

8 Sideways step - rate of change of temperature dt dt =? 1) Advection Currents (U) cooler dt dx > 0 warmer

9 Sideways step - rate of change of temperature dt dt = - U dt dx 1) Advection Currents (U) cooler dt dx > 0 warmer

10 Sideways step - rate of change of temperature dt dt =? 2) Diffusion cooler dt dx > 0 warmer

11 Sideways step - rate of change of temperature dt dt =? 2) Diffusion cooler dt dx > 0 warmer

12 Sideways step - rate of change of temperature Flux = apple dt dx 2) Diffusion Flux goes DOWN GRADIENT cooler dt dx > 0 warmer

13 Sideways step - rate of change of temperature Convergence or divergence of fluxes dt dt = d(flux) dx Flux = apple dt dx dt dt = apple d2 T dx 2 cooler dt dx > 0 warmer

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15 Sideways step - rate of change of temperature dt dt = u dt dx + appled2 T dx 2 1) Advection Currents 2) Diffusion cooler dt dx > 0 warmer

16 Sideways step - rate of change of temperature Expanding to all directions dt dt = udt dx v dt dy w dt dz + apple(d2 T dx 2 + d2 T dy 2 + d2 T dz 2 ) dt dt = ~u rt + appler2 T dt dt + ~u rt = appler2 T DT Dt = appler2 T +Source/ Sink Following a parcel of fluid, the only things that can change it are diffusion. True?

17 What about salinity? DT Dt = appler2 T +Source/Sink Should the equation be the same for salt? cooler warmer saltier fresher

18 What about salinity? DT Dt = apple T r 2 T +Source/Sink Should the equation be the same for salt? No! Salt diffuses MUCH more slowly. DS Dt = apple Sr 2 S +Source/Sink apple T ~10-7 m 2 /s apple S ~10-9 m 2 /s (book, chapter S7)

19 Net lessons for temperature/salinity equations DT Dt = apple T r 2 T +Source/ Sink DS Dt = apple Sr 2 S +Source/ Sink At any one place (d/dt), the change in temperature is due to 1) advection (movement) of water when there is a temperature gradient, 2) diffusion to/from your cooler/warmer neighbors, and 3) sources/ sinks (solar heating, etc) If you are following along with a water parcel (D/DT) the advection term is gone, and only diffusion and sources/sinks change your temperature.

20 Now moving on to momentum equations Force = mass acceleration F = m a a = dv / dt = rate of change in velocity In the ocean we don t consider total mass (it s not a discrete thing), but density = mass per unit volume du dt = Sum of forces acting on that bit of volume, or parcel of water du dt = 1 (Sum of forces acting on that bit of volume, or parcel of water )

21 Momentum equation: advective terms dt dt = u dt dx + appled2 T dx 2 The first couple terms look similar to those for temperature du dt = udu dx +.. What does advection mean here?

22 Momentum equation: advective terms du dt = udu dx v du dy w du dz +.. Du Dt = +..

23 Momentum equation: viscous terms DT Dt = apple T r 2 T +Source/Sink What s the equivalent term here? How do you diffuse velocity or momentum? L U FLOW U Du Dt = r2 u +.. is the kinematic viscosity ~ m 2 /s

24 Momentum equation: Stress / drag At the surface or bottom of the ocean, instead of viscous stress (the ocean dragging on itself), you have Bottom drag: friction with the sea-floor slows down the flow. The strength of this effect increases with the current speed. Du Dt = r2 u +.. Du Dt = C Du at the ocean bottom! Wind Stress: the wind drags the ocean along with it. This speeds up the ocean currents, in the direction of the wind. Du Dt = r2 u +.. Du Dt = at the ocean surface!

25 think about some numbers DT Dt = apple T r 2 T +Source/ Sink A good way to get a basic feel for the answer is to look at the rough size and units of different terms [Temperature] [Time] = apple T [Temperature] [Length] 2 Think about how long it takes temperature in the profiles on the right to diffuse about 10 meters downwards from the ocean surface, by rearranging the rough equation above, and using apple T ~10-7 m 2 /s

26 Stirring and mixing Vertical stirring and ultimately mixing: (Bill Smyth) Internal waves on an interface stir fluid, break and mix Horizontal stirring and ultimately mixing: Gulf Stream (top): meanders and makes rings (closed eddies) that transport properties to a new location

27 Eddy viscosity and diffusivity Molecular diffusivity and viscosity κ T = cm 2 /sec (temperature) κ S = cm 2 /sec (salinity) ν = cm 2 /sec at 0 C (0.010 at 20 C) Eddy diffusivity and viscosity values for heat, salt, properties are the same size (same eddies carry momentum as carry heat and salt, etc) But eddy diffusivities and viscosities differ in the horizontal and vertical Eddy diffusivity and viscosity A H = 10 4 to 10 8 cm 2 /sec (horizontal) = 1 to 10 4 m 2 /sec A V = 0.01 to 10 cm 2 /sec (vertical) = 10-6 to 10-3 m 2 /sec

28 Momentum equation: total Du Dt = 1 dp dx + A H( d2 u dx 2 + d2 u dy 2 )+A v d 2 u dz 2 Dv Dt = 1 dp dy + A H( d2 v dx 2 + d2 v dy 2 )+A v d 2 v dz 2 Dw Dt = Acceleration following a fluid parcel Pressure differences push 1 water dp dz + A H( d2 w dx 2 + d2 w dy 2 )+A v Redistribution of momentum within the ocean, tends to act gradually, sometimes ignored for some problems. But the surface/ bottom stress versions are not!! d 2 w dz 2 +g

29 More on the mixing term: let s look at the largescale, smooth ocean circulation Atlantic θ km 60 S 40 ts 20 S 0 20 N 40 N 60 N Atlantic Salinity km 60 S 40 ts 20 S 0 20 N 40 N 60 N (Talley et al, 2011)

30 World Ocean Circulation Experiment reveals more complex, global conveyor belt patterns (b) 80 N 80 W 40 W 0 40 E E N E 160 W 120 W 80 N Mass transports (Sv) Surface Intermediate Deep Bottom 60 N 40 N 120 E N N N S S S S 40 S 60 S 80 S 80 W 40 W 0 40 E 80 E 120 E 160 E 160 W 120 W 80 S (Talley etfigure al, 2011) 14.6 Net transports (Sv) in isopycnal layers across closed hydrographic sections (1 Sv ¼ 1 " 10 6 m3/sec). (a)

31 [Hallberg & Gnanadesikan, JPO 2006]

32 [Gula et al 14] 1 deg 150 m 1.5 km [Saba et al 2016] 500 m 5 1/3 deg 1 l ta e e v a r sg 1/10 deg Mu (J. Klymak) With increasing resolution comes increasing complexity 1/10 deg

33 Why care about diapycnal turbulent mixing? 1. Deep and abyssal mixing set deep circulation patterns and energetically drive the MOC. 2. Mixing in the upper ocean controls SST and hence strongly affects air-sea fluxes, in both directions. 3. Mixing at all depths influences the distributions of tracers, dissolved gasses, nutrients.

34 Large-scale, smooth ocean circulation Atlantic θ km 60 S 40 ts 20 S 0 20 N 40 N 60 N Atlantic Salinity km 60 S 40 ts 20 S 0 20 N 40 N 60 N (Talley et al, 2011)

35 l resolution data centered between (a) m, (b) 500 1,000 m, and (c) 1,000 2,000 m are averaged over 1.5 squ s and plotted if they contain more than three dissipation rate estimates. The underlying bathymetry is from the Smith dwell dataset [Smith and Sandwell, 1997] version Global patterns of turbulence The strength of small-scale turbulence varies by a factor of 1000! It has systematic patterns related to physical processes we are starting to understand Whalen, Talley and MacKinnon, 2012 Whalen, MacKinnon, Talley, Waterhouse 2015

36 Diapycnal (vertical) Mixing Mechanisms Quantifying turbulence: Turbulent dissipation rate: ϵ [W/kg] Associated eddy diffusivity: K ρ =0.2 ϵ N 2 [m 2 /s] Buoyancy Flux: J b =0.2ϵ

37 Turbulent mixing makes the ocean go round 2 PW heat deep convection ~ 1 TW Low Latitudes downward heat diffustion (κ) heat convergence upwelling vortex strecthing Stommel and Aarons High Latitudes Low Latitudes downward heat diffustion (K) breaking internal waves internal tide ~ 1 TW High Latitudes Determines large scale vertical transport of heat, C02, nutrients, etc. Drives meridional overturning circulation by creating potential energy.

38 Measuring turbulent mixing Direct method: dye dispersal (Ledwell et al., 2004) Assume K ρ ~ Kdye Indirect method 1: measure turbulence, assume mixing follows K 0.2 N 2 turbulent dissipation rate (Osborn, 1980)

39 Measuring mixing: microstructure Measure inertial subrange of turbulence, either with velocity probes or fast thermistors. Fit turbulence model to estimate turbulent dissipation rate ( ) ϵ (Wesson and Gregg 94)

40 Measuring mixing: inference Next largest scale - cant see full turbulent cascasde, but maybe the outer scales of turbulence. The Thorpe scale (Lt) estimates the size of an overturn. z / m L t = 3.7 m Eddy energy overturning time σ θ This type of measurement can often be made with CTD data = mixing for the masses

41 Patchy mixing matters Palmer et al. (2007): bottom-enhanced diffusivity => deep overturning Constant κ = Bottom-enhanced diffusivity Simmons et al. (2003): enhanced mixing over rough topography => change in global MOC bottom-enhanced, spatially-variable mixing uniform mixing also: Hasumi & Suginohara (1999), Huang (1999), Katsman (2006), Saenko (2006), Jochum (2009)

42 circulation. Climate models that do not rep- of enhanced turbulence over rough topogra- Antarctic Peninsula. They propose that turburesent this mixing appropriately will be unable phy (Fig. 1). Recent analysis5 of climate models lent mixing associated with breaking internal to reproduce present or future climate accu- has shown that modelled ocean circulation and lee waves, when globally integrated, contribrately1. Many previous studies have focused heat content are sensitive not only to the aver- utes one-third of the mixing required to transon the breaking internal waves that are driven age level of turbulent mixing in the deep ocean, form the deepest dense water into less-dense by tides and winds as the dominant source but also to its detailed geography. water. Using formulations for mixing induced of that turbulence. In a paper published in In their study, Nikurashin and Ferrari dis- by lee waves and by internal tides, they calcugeophysical Research Letters, Nikurashin cuss a related but relatively new player on the late the total rate of water-mass transformation and Ferrari2 describe a previously under- scene internal lee waves. These are inter- to be sverdrups (1 sverdrup is 106 m3 s 1), appreciated dynamic mechanism internal nal waves that are produced by comparatively which is of the same order as that calculated by lee waves that may significantly contribute steady flow over sea-floor topography. As other measures of the deepest component of to mixing in the deep ocean. Away from the direct influence of surface forcing, most turbulent mixing in the ocean interior is driven by breaking internal gravity waves3. These propagate along and across density interfaces within the ocean, similar to the Solar heat interfacial waves you might see between oil and vinegar in a glass or even between coffee and milk in a well-made cappuccino. Compared with the more familiar surface waves, internal Wind-generated waves are much slower, with periods of hours internal waves Sun- and Mooninstead of seconds. Their breaking is in many generated tides Downward ways analogous to that of surface waves on the turbulent Turbulent beach, albeit in a slow-motion, larger-than-life heat diffusion mixing way the wave height may reach tens or even Warmer, hundreds of metres3. But unlike waves at the lighter water Internal beach (which lose all of their energy to heat lee waves or sound with each thunderous crash), some of the energy lost by breaking internal waves Internal increases the potential energy of the ocean by tides Deep cold water mixing stratified water and raising its centre of mass. It is this potential energy that is eventually converted into the kinetic energy of the meridional overturning circulation. (MacKinnon 13 Over the past decade, most of the focus of ) Figure 1 Ocean mixing. Turbulent mixing (curly arrows) is driven by breaking internal waves in oceanographers has been on the geography the ocean interior. It transports solar heat downwards from the surface to the abyss and transforms and life cycle of internal waves created by Parameterizations of internal wave driven will less-dense be waters. Internal waves are generated by three main the deepest, coldest mixing waters into warmer, winds and tides4. In the deep ocean, inter- mechanisms: Moon- and Sun-generated tidal flow over steep or rough topography (lower right); BAMS article, December available fortidal general community use ( nal waves with frequencies have been fluctuating wind stress on the ocean surface (upper left); and quasi-steady flow over rough topography assumed to be a dominant mechanism for (lower left). This last mechanism, which produces the internal lee waves investigated by Nikurashin and Climate Process Team, Our task: use what we collectively know about internal wave physics to develop a dynamic parameterization of diapycnal mixing that captures global patterns properly so that they can evolve in a changing climate. 17

43 x Convolving patterns =??

44 Lateral mixing FIG. 6. Instantaneous surface speed in 1 and 1 6 models after 40 yr. Note that the large-scale structure of the 1 model is quite similar to the 1 6 model (the currents have similar locations and have similar horizontal extents). The main difference is in the presence of intense jets and eddies in the 1 6 model.

45 Lateral dispersion eddy diffusivity characteristic length scale K ~ u L characteristic velocity

46 Lateral dispersion depends on strength/energy of eddies... Eddy velocity scale u EKE Eddy diffusivity derived from drifter separations Zhurbas and Oh 2004

47 Climate change uncertainties