Munk and Mixing Story of recipe

Transcription

1 Munk and Mixing Story of recipe Raffaele Ferrari Department of Earth, Atmospheric and Planetary Sciences, MIT Munk Centennial Symposium, Scripps May 15-17

2 munk & mixing Raffaele Ferrari Department of Earth, Atmospheric and Planetary Sciences, MIT Munk Centennial Symposium, Scripps May 15-17

3 The search for a perfect recipe The scientific mind does not so much provide the right answers as ask the right questions. Claude Levi Strauss

4 The classical recipe for the abyssal ocean circulation Lumpkin and Speer, 2007

5 The classical recipe for the abyssal ocean circulation Lumpkin and Speer, 2007

6 The classical recipe for the abyssal ocean circulation Key ingredients for the recipe: 1. The ocean bottom is flat 2. Upwelling and mixing are uniform throughout the ocean Munk, 1966 Stommel and Arons, 1960 wb z ' apple T b zz 0 vertical upwelling apple T ' 10 4 m 2 /s D a Dt ' fw z 0 cyclonic gyre

7 Ingredient 1: flat bottom The sense of the circulation changes if the boundaries are sloping ZZ D a Dt da ' fw za = f(wa) z fwa z apple 0 anticyclonic gyre McDougall 1989, Rhines 1993

8 Ingredient 1I: constant mixing The vertical profile of mixing is not uniform wb z z (apple T b z )=@ z ( ) apple 0 vertical downwelling downwelling upwelling St Laurent et al. 2012

9 Ingredient 1I: constant mixing The vertical profile of mixing is not uniform wb z z (apple T b z )=(@ z apple T )b + apple T (@ z b z ) apple 0 vertical downwelling downwelling upwelling St Laurent et al. 2012

10 Toward an improved recipe Continuously stratified planetary geostrophic equations fẑ u = rp + bẑ ru r u =0 b t + u rb = r (apple T rb) 1.The Rayleigh friction as a momentum closure simplifies boundary layers (cf. Stommel vs. Munk gyre) 2.Turbulent diffusivity increases toward the ocean bottom 3.The bottom topography is not flat

11 Spindown circulation Bathymetry Initially uniform stratification b = N 2 z Boundary conditions b = 0 at z =0 ˆn rb = 0 at z = h(x, y) ˆn u = 0 at z =0, h(x, y) Turbulent diffusivity profile apple T = apple 0 e (z h)/d

12 Spindown circulation upwelling downwelling downwelling upwelling

13 Boundary layer solution Boundary layers satisfy a local balance between downward diffusion and across-slope advection Buoyancy budget b t + u 0 N 2 sin = apple T N 2 cos + b z 0 Momentum budget f0 2 + r 2 cos 2 u 0 = r sin b z 0 Density surfaces cf. Phillips (1970), Wunsch (1970), Garrett et al. (1993)

14 Boundary layer solution Boundary layers satisfy a local balance between downward diffusion and across-slope advection Across-slope flow Density surfaces cf. Phillips (1970), Wunsch (1970), Garrett et al. (1993)

15 Boundary layer solution Boundary layers satisfy a local balance between downward diffusion and across-slope advection Along-slope flow Density surfaces cf. Phillips (1970), Wunsch (1970), Garrett et al. (1993)

16 Boundary layer solution Boundary layers reach steady sate on slopes, but not over flat bathymetry On slopes, diffusive fluxes can be balanced by across-slope advection (local balance). But on flat bathymetry, no dense water can be upwelled. Basin-scale lateral advection must enter the budget there.

17 Equilibrated circulation In the Southern Ocean, winds and mesoscale eddies set the mean isopycnal slope. Together with surface buoyancy fluxes, this sets the stratification at the northern edge of the Southern Ocean. Pacific Ocean WOCE, P16 Mimic Southern Ocean processes by restoring to prescribed stratification b t + u rb = r (apple T rb) (y) b N 2 z

18 Equilibrated circulation The basin stratification is set in the south Outside the boundary layers on slopes and a weakly stratified benthic layer, the stratification in the basin matches that prescribed in the south.

19 Equilibrated circulation A basin-scale circulation exchanges fluid with the boundary layers

20 Equilibrated circulation Large compensation between the up- and down-slope transports

21 Equilibrated circulation A basin-scale circulation exchanges fluid with the boundary layers

22 Equilibrated circulation Frictional western boundary currents cross the equator Dense water is supplied by a bottom-trapped boundary current, lighter waters are exported by a return current at mid-depth.

23 Equilibrated circulation Integrating the up-/downslope transport along the perimeter of the basin yields a prediction for the net transformation and thus the overturning.

24 Testing the theory Field campaign in the bathtub-like bowl of the Rockall Trough Co-PIs: R. F., Matthew Alford, Alberto Naveira Garabato, Kurt Polzin

25 Conclusions Bottom-intensified mixing drives a pattern of up- and downwelling on slopes A basin-scale circulation supplies dense water to the boundary layer upwelling and exports transformed water Boundary layers constrain the global solution; they yield a prediction for the net overturning The configuration of the real ocean is more complicated, but elements of our bathtub case are expected to carry over Ali Mashayek Joern Callies Henri Drake Greg Wagner

26 Happy 100th!