Open ocean deep cool, suck Convection ‘takes away’ stratification cold subduction PV 0 eddies Eddies flux PV in from the ‘outside’ warm, pump Building a

Warming and pumping eddies ‘creates’ stratification thermocline PV  0 warm subduction Eddies flux PV ‘away’ warm, suck warm, pump cool, suck Convection in a global context

Role of convection in the general circulation

GFD experiments in climate Pole Eq Pole I. Open Ocean Deep Convection John Marshall, MIT

1 Why is convection important? Laboratory analogue

2 Why is convection interesting? • Modified by rotation • Interplay between convection and baroclinic instability

3 Parameterization Not just of deep convection but lateral processes in mixed layers in general Melting of an ice disk floating on a rotating homogeneous fluid 1 Why is ocean convection important?

1 km Wintertime depth (m)

Lecture III

• Associated (in an as yet unclear way) with the sinking branch of

• Primary agency of water- mass transformation

Salinity in Atlantic Phases of open-ocean deep convection preconditioning cool, suck It’s a swallowing process - not a ‘chimney’

mixing Think of a snake swallowing an egg

spreading 2 Why is Ocean convection interesting?

Involves the interplay of two dynamical processes

• upright convection modified by rotation, ‘plumes’ - mix stratification away to create a ‘mixed patch’

• baroclinic instability, ‘eddies’ - control lateral exchange between the mixed patch and ambient fluid

Studied in laboratory, numerical and field experiments Ultimate, ultra-non-hard…. 2 3 buoyancy flux Scaling ideas v.v.very high Ra Bom s  23 Initially, for small times Ra  10

Scales can be expressed in terms of ‘l ’ Deardorff, 1985 1 Bo  w  u  Bol 3

(i) Scale constrained by depth of ocean (ii) Scale constrained by earth’s rotation

1 Fernando et al, 1991 Non-dimensional  l rot 1 B 2 R Jones and Marshall, 1993 number o  H  H f3 Maxworthy and Narimousa, 1994 Dynamical ideas

• Extract buoyancy from surface of homogeneous, rotating ocean Jones and Marshall, 1993

Helfrich 1994 H Numbers f  104s1

Ocean - rotation important B  107m2s3 H  1km Natural Rossby number R 0. 1 1 1 lrot  1km o   R l rot 1 B 2 o  H  H f3 Atmosphere - rotation not important Radius of deformation on convective scale l B  102m2s3 H  10km   R H o  lrot  100km Ro  10  50 Role of lateral inhomogeneities

Spatially homogeneous

Draws buoyancy 2Bt vertically h  N

Lateral homogeneities are a Spatially inhomogeneous ubiquitous feature of mixed layers B

Deep convection is just an extreme example

Draws buoyancy laterally Slantwise convection PV fbz  uzby

No zonal pressure gradients 1 B Slantwise convection in 2 2 d model Du Dt  fv  0 D Dy Dt u  fy  0 v  Dt z

y thermal wind m surface b surface

angular momentum buoyancy m  u  fy b

Convection sets PV  0 not N2 Haine and Marshall, 1997 Interplay between convection and baroclinic instability

cool Vertical velocity w Relax the angular momentum constraint

Upright convection

Jack Whitehead

Convection Baroclinic instability reminiscent of metrological flows

Baroclinic instability Eddies flux buoyancy vertically to offset loss from the surface Mixed patches

Melting ice disc floating on rotating fluid

Helen Jones

Marshall and Schott, 1999

R  102 o Baroclinic instability is a prime agency Reminds one of meteorology of vertical buoyancy transport Restratification and spreading Helen Jones

John Lazier

March

October

Hydrographic section Depth across Visbeck, Marshall and Jones, JPO, 1996 Scaling for patches Jones and Marshall, JPO, 1997 Fox-Kemperer, Ferrari, JPO, 2007

  v b  Kb y H   where K  v l L H  ;  v  u  f b y l  L L wb b y H  s  L H vb b z  s s  time to hence restratify   H2 always v b  c f b z b y down-gradient and for c=0.027 2 2   H always upward w b  c f b y Prediction from scaling 3 Parameterization (impossible)

• typically plumes are represented as a mixing process setting large- scale PV field to zero. - adjustment - enhanced vertical mixing - entrainment at base

• challenge lies in representation of geostrophic scales

Eddies are a (the?) primary agency of vertical as well as lateral heat transport

Take a residual-mean perspective Review: Eulerian/Residual mean cool, suck

Eulerian-mean buoyancy budget

vb

z v b w b  vb  wb B y  z  y  z  z y

Decompose eddy flux (Held and Schneider, 1999)

            v b ,w b  =+w b /s,w b  v b  w b /s,0 isopycnal horizontal

b y Must recognize that this where s   is the isopycnal slope can be represented as b z an advective flux.

Gent and McWilliams, 1990 Residual-mean buoyancy budget

isopycnal

       w b /s,w b   v b y  w b z 0

  where    w b b y leftover 1

           w b 1 v b w b /s ,0 1 v b where   s        y    v b  v b B R    z

R R where v , and R   z y

 R   Bs v

 David Marshall, JMR,1997 vres  v  v Examples Mixed layer restratification in an idealized numerical experiment MITgcm

Fox-Kemper, Ferrari et al, 2007 3-d model Parameterized, 2d model

     w b b y

2 2   H w b  c f b y •1.5 days, 5-6 Aug 2006 •Mixed layer restratifies under weakening wind AESOP Observations of Rapid forcing Restratification near Monterey Bay •Characterized mixed layer evolution in Lagrangian (float- following) frame.

After one day

30 kt wind 10 kt wind Courtesy E. D’Asaro Ubiquitous feature of mixed-layer evolution

Baylor Fox-Kemperer, MIT Summary

• Ocean is stiffened by rotation on the convective scale

• Plumes are mixing agents set PV to zero • Geostrophic eddies are a primary agency of vertical as well as lateral heat transport profound implications for parameterization

Some aspects are of general interest

• Importance of natural Rossby number • Little scale separation between convective and geostrophic eddy scales

• Spatial inhomogeneity

Upright convection  baroclinic instability Reviews

OPEN-OCEAN CONVECTION: OBSERVATIONS,THEORY AND MODELS Marshall, J and F. Schott Reviews of Geophysics, 37, 1, 1999

General comments A  O

Atmosphere

• dynamics of mixed patches Baroclinic instability as an agency of vertical buoyancy transport

• modern eddy parameterizations GM TEM

Ocean

• lateral inhomogeneities completely change the Rayleigh problem

1 2 • importance of R l rot 1 B o  H  H f3

Does the l ro t scale appear in the atmosphere?