Barotropic versus Baroclinic Eddy 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 wind stress? How does the ACC respond to the increasing winds 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 Ocean? 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 momentum 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 sea 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 deformation: 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 energy 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]