Barotropic versus Baroclinic Saturation Navid C. Constantinou Andy McC. Hogg Research School of Earth Sciences, Australian National University

Barotropic Eddy Saturation What does the flow looks like? What balances the ? How does the ACC respond to the increasing over the South- Recently, it was shown that barotropic (depth-independent) flow above Vorticity in the top-fluid layer for wind stress peak 0.5 N m−2: ern ? 1-layer configuration 2-layer configuration bathymetry can also show eddy saturation. 1.0 1.0 [Constantinou & Young 2017, Constantinou 2018] 0.8 0.8 form stress form stress wind stress wind stress R R Motivation R 0.6 R bottom drag 0.6 bottom drag

This challenges the current paradigm... and form stress and form stress 0.4 The Antarctic Circumpolar Current (ACC) is an important driver of the 0.4

. global climate. 0 2 0.2 wind stress wind stress bottom drag bottom drag R R Objectives R 0.0 R 0.0 10−3 10−2 10−1 100 101 10−3 10−2 10−1 100 101 wind stress peak [Nm−2] wind stress peak [Nm−2] Demystify the physics behind eddy saturation:

• Most of the is balanced by bottom form stress. • Establish whether barotropic flows show eddy saturation in a primitive-equation model. • The flow shows a transition to a regime with high transport and in • Assess the relative importance of barotropic and baroclinic which the momentum balance changes. processes in the observed eddy-saturated states. (Consistent with Constantinou & Young 2017, Constantinou 2018)

Model

[ACCESS-OM2-010 surface speed, COSIMA Consortium] Westerlies over the Southern Ocean that drive the ACC are getting stronger: [zonal flow structure for 1-layer setup]

[an example configuration with a two-layer fluid]

• Idealized re-entrant channel with ‘bumpy’ bottom [Farneti et al. 2015] • Lx = 3200 km, Ly = 1600 km, and H = 4 km How will the ACC respond to increasing winds? [top-layer zonal flow structure for 2-layer setup] • Beta-plane with Southern Ocean parameters • Modest stratification (few fluid layers of constant ρ) “Eddy saturation” Conclusions • 1st Rossby radius of : 15.7 km (for ≥2 layers) Many models (idealized & realistic) find that: • Modular Ocean Model v6 (MOM6) in isopycnal mode The 1-layer fluid configuration shows eddies. These eddies do not result • There exists a barotropic contribution to eddy saturation (e.g., for as the wind strength increases, from baroclinic instability. 1600 0.05 < wind stress < 1.00). the ACC remains (almost) insensitive. 1600 1200 • 1200 How transport varies with wind stress? The barotropic eddy saturation relies on eddy production due to All excess momentum from the wind goes into eddies: 800 bathymetric features. 800 −→ “eddy saturation” 104 400 • This highlights the role of topographically-induced eddies.

400 meridional coordinate [km] 1 layer

Traditionally, a flow is “eddy saturated” if the volume zonal transport 0 0.05 0.00 0.05 0.10 0.15 0.20 0.25 2 layers • meridional coordinate [km] 0 − 2 slope 2/3 At high wind stress values there is a structural bifurcation to a strong wind stress [N m− ] shows (substantially) less than linear increase with wind stress strength. 0 800 1600 2400 3200 ] zonal coordinate [km] 3 103 3 layers zonal flow that does not “see” the topography. − 4 layers The “textbook” explanation is that: 3600 3680 3760 3840 3920 4000 m s bathymetry depth [m]

6 References 2 increasing −→ isopycnals −→ more available −→ 10 slope 1/2 Constantinou & Young (2017) Beta-plane turbulence above monoscale winds slope more potential slope 1 topography. J. Fluid Mech., 827, 415-447. more eddies produced the mean flow (ACC) −→ −→ 101 Constantinou (2018) A barotropic model for eddy saturation. by baroclinic instability stays the same J. Phys. Oceanogr., 48 (2), 397-411. transport [10 100 Contact Information

10−3 10−2 10−1 100 101 −2 wind stress peak [Nm ] www.navidconstantinou.com [bathymetry, wind stress, 1- and 2-layer stratification discretizations] [email protected] • Baroclinic cases (# layers ≥ 2) show an eddy saturation regime.

• The single-layer case (barotropic) shows insensitivity to wind stress (transport grows only about 10-fold over 100-fold wind stress increase)

[Meredith et al. 2012]