A Barotropic Model of Eddy Saturation

Geophysical Research Letters

Hogg

2019

Self Cite

“Eddy saturation” is the regime in which the total time‐mean volume transport of an oceanic current is relatively insensitive to the wind stress forcing and is often invoked as a dynamical description of Southern Ocean circulation. We revisit the problem of eddy saturation using a primitive equations model in an idealized channel setup with bathymetry. We apply only mechanical wind stress forcing; there is no diapycnal mixing or surface buoyancy forcing. Our main aim is to assess the relative importance of two mechanisms for producing eddy‐saturated states: (i) the commonly invoked baroclinic mechanism that involves the competition of sloping isopycnals and restratification by production of baroclinic eddies and (ii) the barotropic mechanism that involves production of eddies through lateral shear instabilities or through the interaction of the barotropic current with bathymetric features. Our results suggest that the barotropic flow component plays a crucial role in determining the total volume transport.

Section: Resultssupporting

confidence: 81%

Section: Transport Per Fluid Layer and Momentum Balancesupporting

confidence: 87%

Eddy Saturation of the Southern Ocean: A Baroclinic Versus Barotropic Perspective

Geophysical Research Letters

Hogg

2019

Self Cite

“…After the flow equilibrates, we average (for at least 30 years) to obtain the time-mean fields. The results from the barotropic runs (single-layer configuration) are qualitatively similar to those of Constantinou and Young (2017) and Constantinou (2018). For very weak wind stress forcing (τ ≤ 0.02 N m −2 ) the transport increases linearly with wind stress.…”

Section: Setupsupporting

confidence: 63%

Eddy saturation of the Southern Ocean: a baroclinic versus barotropic perspective

Hogg

2020

Preprint

Key Points:• An isopycnal layered model, with a varying number of fluid layers, is used to assess relative importance of barotropic and baroclinic processes in the Southern Ocean.• Both baroclinic and barotropic flows exhibit regimes in which mean zonal transport is insensitive to wind stress.• Eddies actively shape the time-mean flow, irrespective of the instabilities from which they originate.Abstract "Eddy saturation" is the regime in which the total time-mean volume transport of an oceanic current is relatively insensitive to the wind stress forcing and is often invoked as a dynamical description of Southern Ocean circulation. We revisit the problem of eddy saturation using a primitive-equations model in an idealized channel setup with bathymetry. We apply only mechanical wind stress forcing; there is no diapycnal mixing or surface buoyancy forcing. Our main aim is to assess the relative importance of two mechanisms for producing eddy saturated states: (i) the commonly invoked baroclinic mechanism that involves the competition of sloping isopycnals and restratification by production of baroclinic eddies, and (ii) the barotropic mechanism, that involves production of eddies through lateral shear instabilities or through the interaction of the barotropic current with bathymetric features. Our results suggest that the barotropic flow-component plays a crucial role in determining the total volume transport. Plain language summaryWind stress at the surface of the ocean is an important driver of ocean currents. However, what sets up the strength of the currents remains puzzling. The strongest ocean current flows around Antarctica: the Antarctic Circumpolar Current (ACC). It is believed that the ACC is close to a so-called "eddy saturated" state, a regime in which changes in the strength of the wind stress forcing do not alter the strength of the mean current. Instead, the swirling oceanic eddy motions that accompany the current are enhanced. Here, we investigate the physics and assess the relative importance of the two mechanisms proposed in the literature to explain this phenomenon: the most commonly invoked baroclinic mechanism and the recently proposed barotropic mechanism that crucially involves the interaction of the oceanic flow with bathymetric features. Our results suggest that the oftentimes ignored depth-averaged (barotropic) component of the ocean flow and its interaction with bathymetry play a dominant role in setting up the strength of the current in certain regimes.

“…Moreover, the main controlling factor for eddy saturation in this barotropic model is whether the geostrophic contours are open or closed -the numerical value of β * is important only in so far as β * determines whether the geostrophic contours are open or closed. For example, the "unidirectional" topography in (8.10) always has open geostrophic contours; using this sinusoidal topography Constantinou (2017) shows that there is barotropic eddy saturation with β * as low as 0.1. Thus it is the structure of the geostophic contours, rather than the numerical value of β * , that is decisive as far as barotropic eddy saturation is concerned.…”

Section: Discussionmentioning

confidence: 99%

“…Both (i) and (ii) are defining symptoms of the eddy-saturation phenomenon documented in eddy resolving Southern-Ocean models. Constantinou (2017) identifies a third symptom common to barotropic and baroclinic eddy saturation: increasing the Ekman drag coefficient µ increases the large-scale mean flow . This somewhat counterintuitive dependence on µ can be rationalized by arguing that the main effect of increasing Ekman drag is to damp the transient eddies responsible for producing κ eff in (8.3).…”

Section: Discussionmentioning

confidence: 99%

Beta-plane turbulence above monoscale topography

Young

2017

J. Fluid Mech.

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Using a one-layer quasi-geostrophic model, we study the effect of random monoscale topography on forced beta-plane turbulence. The forcing is a uniform steady wind stress that produces both a uniform large-scale zonal flow U (t) and smaller-scale macroturbulence characterized by both standing and transient eddies. The large-scale flow U is retarded by a combination of Ekman drag and the domain-averaged topographic form stress produced by the eddies. The topographic form stress typically balances most of the applied wind stress, while the Ekman drag provides all of the energy dissipation required to balance the wind work. A collection of statistically equilibrated numerical solutions delineates the main flow regimes and the dependence of the time-average of U on parameters such as the planetary vorticity gradient β and the statistical properties of the topography. We obtain asymptotic scaling laws for the strength of the large-scale flow U in the limiting cases of weak and strong forcing.If β is significantly smaller than the topographic PV gradient then the flow consists of stagnant pools attached to pockets of closed geostrophic contours. The stagnant dead zones are bordered by jets and the flow through the domain is concentrated into a narrow channel of open geostrophic contours. In most of the domain the flow is weak and thus the large-scale flow U is an unoccupied mean.If β is comparable to, or larger than, the topographic PV gradient then all geostrophic contours are open and the flow is uniformly distributed throughout the domain. In this open-contour case there is an "eddy saturation" regime in which U is insensitive to large changes in the wind stress. We show that eddy saturation requires strong transient eddies that act effectively as PV diffusion. This PV diffusion does not alter the kinetic energy of the standing eddies, but it does increase the topographic form stress by enhancing the correlation between topographic slope and the standing-eddy pressure field. Using bounds based on the energy and enstrophy power integrals we show that as the strength of the wind stress increases the flow transitions from a regime in which most of the form stress balances the wind stress to a regime in which the form stress is very small and large transport ensues.