The Eliassen-Palm flux tensor

Journal of Fluid Mechanics 729 (2013) 69-102

JR Maddison, DP Marshall

The aim of this paper it to derive general coordinate-invariant forms of the Eliassen-Palm flux tensor and thereby characterize the true geometric nature of the eddy-mean-flow interaction in hydrostatic Boussinesq rotating fluids. In the quasi-geostrophic limit previous forms of the Eliassen-Palm flux tensor are shown to be related to each other via a gauge transformation; a general form is stated and its geometric properties are discussed. Similar methodology is applied to the hydrostatic Boussinesq Navier-Stokes equations to re-derive the residual-mean equations in a coordinate-invariant form. Thickness-weighted averaging in buoyancy coordinates is carefully described, via the definition of a volume-form-weighted average, constructed so as to commute with the covariant divergence of a vector. The procedures leading to the thickness-weight averaged equation are discussed, and forms of the Eliassen-Palm flux tensor which arise are identified. © 2013 Cambridge University Press.

Shear at the Base of the Oceanic Mixed Layer Generated by Wind Shear Alignment

Journal of Physical Oceanography 43 (2013) 1798-1810

L Brannigan, Y-D Lenn, TP Rippeth, E McDonagh, TK Chereskin, J Sprintall

Vertical Eddy Energy Fluxes in the North Atlantic Subtropical and Subpolar Gyres


X Zhai, DP Marshall

Modulation of eddy kinetic energy, temperature variance, and eddy heat fluxes by surface buoyancy forcing

Ocean Modelling 62 (2013) 27-38

DR Munday, X Zhai

Although mesoscale eddies are a ubiquitous feature of the world's oceans, mechanisms determining their strength and variability remain poorly understood. Here we investigate the effects of surface buoyancy forcing on eddy kinetic energy (EKE), temperature variance, and lateral eddy heat fluxes. In keeping with previous investigations, sustained heat loss ultimately leads to an increase in the magnitude of EKE, whereas sustained heat gain only alters the spatial pattern of EKE, albeit enhancing the temperature variance. These changes to the eddy field and stratification are shown to result in changes in meridional eddy heat flux and residual meridional overturning circulation, which acts to bring the system to equilibrium with the applied surface buoyancy forcing. © 2012 Elsevier Ltd.

Rossby rip currents

Geophysical Research Letters 40 (2013) 4333-4337

DP Marshall, B Vogel, X Zhai

Oceanic Rossby waves and eddies flux energy and fluid westward, the latter through the Stokes drift or bolus transport. While the wave energy is largely dissipated at the western boundary, mass conservation requires that the fluid be returned offshore through Rossby rip currents. The form and magnitude of these rip currents are investigated through linear Rossby wave theory, a nonlinear numerical model, and analysis of sea surface height satellite observations. The net eastward volume transport by Rossby rip currents over the global ocean is estimated to be of order 10 Sv (1 Sv ≡10 m s ). In an eddying ocean, both the westward Stokes drift and eastward rip currents can assume the form of banded quasi-zonal jets. Key Points Oceanic Rossby waves and eddies carry a westward Stokes drift The westward Stokes drift may be compensated by eastward Rossby rip currents Both the Stokes drift and rip currents can assume the form of banded zonal jets. © 2013. American Geophysical Union. All Rights Reserved.

Conceptual models of the wind-driven and thermohaline circulation

International Geophysics 103 (2013) 257-282

SS Drijfhout, DP Marshall, HA Dijkstra

Conceptual models are a vital tool for understanding the processes that maintain the global ocean circulation, both in nature and in complex numerical ocean models. In this chapter we provide a broad overview of our conceptual understanding of the wind-driven circulation, the thermohaline circulation, and their transient behavior. While our conceptual understanding of the time-mean wind-driven circulation is now fairly mature, basic questions remain regarding the thermohaline circulation, for example, surrounding its overall strength and stability. Similarly, basic questions remain regarding the transient adjustment and internal variability of the ocean circulation. © 2013 Elsevier Ltd.

Propagation of Meridional Circulation Anomalies along Western and Eastern Boundaries


DP Marshall, HL Johnson

A Framework for Parameterizing Eddy Potential Vorticity Fluxes


DP Marshall, JR Maddison, PS Berloff

On the Wind Power Input to the Ocean General Circulation


X Zhai, HL Johnson, DP Marshall, C Wunsch

Remote forcing of the Antarctic Circumpolar Current by diapycnal mixing

Geophysical Research Letters 38 (2011)

DR Munday, DP Marshall, LC Allison, HL Johnson

We show that diapycnal mixing can drive a significant Antarctic Circumpolar Current (ACC) volume transport, even when the mixing is located remotely in northern-hemisphere ocean basins. In the case of remote forcing, the globally-averaged diapycnal mixing coefficient is the important parameter. This result is anticipated from theoretical arguments and demonstrated in a global ocean circulation model. The impact of enhanced diapycnal mixing on the ACC during glacial periods is discussed. Copyright 2011 by the American Geophysical Union.

Momentum balance of the wind-driven and meridional overturning circulation

Journal of Physical Oceanography 41 (2011) 960-978

DP Marshall, HR Pillar

When a force is applied to the ocean, fluid parcels are accelerated both locally, by the applied force, and nonlocally, by the pressure gradient forces established to maintain continuity and satisfy the kinematic boundary condition. The net acceleration can be represented through a "rotational force" in the rotational component of the momentum equation. This approach elucidates the correspondence between momentum and vorticity descriptions of the large-scale ocean circulation: if two terms balance pointwise in the rotational momentum equation, then the equivalent two terms balance pointwise in the vorticity equation. The utility of the approach is illustrated for three classical problems: barotropic Rossby waves, wind-driven circulation in a homogeneous basin, and the meridional overturning circulation in an interhemispheric basin. In the hydrostatic limit, it is shown that the rotational forces further decompose into depth-integrated forces that drive the wind-driven gyres and overturning forces that are confined to the basin boundaries and drive the overturning circulation. Potential applications of the approach to diagnosing the output of ocean circulation models, alternative and more accurate formulations of numerical ocean models, the dynamics of boundary layer separation, and eddy forcing of the large-scale ocean circulation are discussed. © 2011 American Meteorological Society.

Spin-up and adjustment of the Antarctic Circumpolar Current and global pycnocline


LC Allison, HL Johnson, DP Marshall

Accurate representation of geostrophic and hydrostatic balance in unstructured mesh finite element ocean modelling

Ocean Modelling 39 (2011) 248-261

JR Maddison, DP Marshall, CC Pain, MD Piggott

Accurate representation of geostrophic and hydrostatic balance is an essential requirement for numerical modelling of geophysical flows. Potentially, unstructured mesh numerical methods offer significant benefits over conventional structured meshes, including the ability to conform to arbitrary bounding topography in a natural manner and the ability to apply dynamic mesh adaptivity. However, there is a need to develop robust schemes with accurate representation of physical balance on arbitrary unstructured meshes. We discuss the origin of physical balance errors in a finite element discretisation of the Navier-Stokes equations using the fractional timestep pressure projection method. By considering the Helmholtz decomposition of forcing terms in the momentum equation, it is shown that the components of the buoyancy and Coriolis accelerations that project onto the non-divergent velocity tendency are the small residuals between two terms of comparable magnitude. Hence there is a potential for significant injection of imbalance by a numerical method that does not compute these residuals accurately. This observation is used to motivate a balanced pressure decomposition method whereby an additional "balanced pressure" field, associated with buoyancy and Coriolis accelerations, is solved for at increased accuracy and used to precondition the solution for the dynamical pressure. The utility of this approach is quantified in a fully non-linear system in exact geostrophic balance. The approach is further tested via quantitative comparison of unstructured mesh simulations of the thermally driven rotating annulus against laboratory data. Using a piecewise linear discretisation for velocity and pressure (a stabilised P P discretisation), it is demonstrated that the balanced pressure decomposition method is required for a physically realistic representation of the system. © 2011 Elsevier Ltd.

A model of Atlantic heat content and sea level change in response to thermohaline forcing

Journal of Climate 24 (2011) 5619-5632

X Zhai, DP Marshall, HL Johnson

The response of ocean heat content in the Atlantic to variability in the meridional overturning circulation (MOC) at high latitudes is investigated using a reduced-gravity model and the Massachusetts Institute of Technology (MIT) general circulationmodel (MITgcm). Consistent with theoretical predictions, the zonal-mean heat content anomalies are confined to lowlatitudeswhen the high-latitude MOC changes rapidly, but extends to mid- and high latitudes when the high-latitude MOC varies on decadal or multidecadal time scales. This low-passfiltering effect of the mid- and high latitudes on zonal-mean heat content anomalies, termed here the "Rossby buffer," is shown to be associated with the ratio of Rossby wave basin-crossing time to the forcing period at high northern latitudes. Experiments using the MITgcm also reveal the importance of advective spreading of cold water in the deep ocean, which is absent in the reduced-gravity model. Implications for monitoring ocean heat content and sea level changes are discussed in the context of both models. It is found that observing global sea level variability and sea level rise using tide gauges can substantially overestimate the global-mean values. © 2011 American Meteorological Society.

Sustained monitoring of the Southern Ocean at Drake Passage: Past achievements and future priorities

Reviews of Geophysics 49 (2011)

MP Meredith, J-B Sallée, PL Woodworth, CW Hughes, MAM Maqueda, TK Chereskin, J Sprintall, DP Marshall, DR Munday, LC Allison, GR Bigg, K Donohue, KJ Heywood, A Hibbert, H Leach, AM Hogg, HL Johnson, L Jullion, BA King, ACN Garabato, Y-D Lenn, C Provost

Drake Passage is the narrowest constriction of the Antarctic Circumpolar Current (ACC) in the Southern Ocean, with implications for global ocean circulation and climate. We review the long-term sustained monitoring programs that have been conducted at Drake Passage, dating back to the early part of the twentieth century. Attention is drawn to numerous breakthroughs that have been made from these programs, including (1) the first determinations of the complex ACC structure and early quantifications of its transport; (2) realization that the ACC transport is remarkably steady over interannual and longer periods, and a growing understanding of the processes responsible for this; (3) recognition of the role of coupled climate modes in dictating the horizontal transport and the role of anthropogenic processes in this; and (4) understanding of mechanisms driving changes in both the upper and lower limbs of the Southern Ocean overturning circulation and their impacts. It is argued that monitoring of this passage remains a high priority for oceanographic and climate research but that strategic improvements could be made concerning how this is conducted. In particular, long-term programs should concentrate on delivering quantifications of key variables of direct relevance to large-scale environmental issues: In this context, the time-varying overturning circulation is, if anything, even more compelling a target than the ACC flow. Further, there is a need for better international resource sharing and improved spatiotemporal coordination of the measurements. If achieved, the improvements in understanding of important climatic issues deriving from Drake Passage monitoring can be sustained into the future. © 2011 by the American Geophysical Union.

Rossby wormholes


DP Marshall

Where do winds drive the antarctic circumpolar current?

Geophysical Research Letters 37 (2010)

LC Allison, HL Johnson, DP Marshall, DR Munday

The strength of the Antarctic Circumpolar Current (ACC) is believed to depend on the westerly wind stress blowing over the Southern Ocean, although the exact relationship between winds and circumpolar transport is yet to be determined. Here we show, based on theoretical arguments and a hierarchy of numerical modeling experiments, that the global pycnocline depth and the baroclinic ACC transport are set by an integral measure of the wind stress over the path of the ACC, taking into account its northward deflection. Our results assume that the mesoscale eddy diffusivity is independent of the mean flow; while the relationship between wind stress and ACC transport will be more complicated in an eddy-saturated regime, our conclusion that the ACC is driven by winds over the circumpolar streamlines is likely to be robust. Copyright 2010 by the American Geophysical Union.

Parameterization of ocean eddies: Potential vorticity mixing, energetics and Arnold's first stability theorem

Ocean Modelling 32 (2010) 188-204

DP Marshall, AJ Adcroft

A family of eddy closures is studied that flux potential vorticity down-gradient and solve an explicit budget for the eddy energy, following the approach developed by Eden and Greatbatch (2008, Ocean Modelling). The aim of this manuscript is to demonstrate that when energy conservation is satisfied in this manner, the growth or decay of the parameterized eddy energy relates naturally to the instability or stability of the flow as described by Arnold's first stability theorem. The resultant family of eddy closures therefore possesses some of the ingredients necessary to parameterize the gross effects of eddies in both forced-dissipative and freely-decaying turbulence. These ideas are illustrated through their application to idealized, barotropic wind-driven gyres in which the maximum eddy energy occurs within the viscous boundary layers and separated western boundary currents, and to freely-decaying turbulence in a closed barotropic basin in which inertial Fofonoff gyres emerge as the long-time solution. The result that these eddy closures preserve the relation between the growth or decay of eddy energy and the instability or stability of the flow provides further support for their use in ocean general circulation models. © 2010 Elsevier Ltd.

Significant sink of ocean-eddy energy near western boundaries

Nature Geoscience 3 (2010) 608-612

X Zhai, DP Marshall, HL Johnson

Ocean eddies generated through instability of the mean flow are a vital component of the energy budget of the global ocean. In equilibrium, the sources and sinks of eddy energy have to be balanced. However, where and how eddy energy is removed remains uncertain. Ocean eddies are observed to propagate westwards at speeds similar to the phase speeds of classical Rossby waves, but what happens to the eddies when they encounter the western boundary is unclear. Here we use a simple reduced-gravity model along with satellite altimetry data to show that the western boundary acts as a "graveyardg" for the westward-propagating ocean eddies. We estimate a convergence of eddy energy near the western boundary of approximately 0.1-0.3 TW, poleward of 10°in latitude. This energy is most probably scattered into high-wavenumber vertical modes, resulting in energy dissipation and diapycnal mixing. If confirmed, this eddy-energy sink will have important implications for the ocean circulation. © 2010 Macmillan Publishers Limited. All rights reserved.

Oscillatory sensitivity of Atlantic overturning to high-latitude forcing

Geophysical Research Letters 37 (2010)

L Czeschel, HL Johnson, DP Marshall

The Atlantic Meridional Overturning Circulation (AMOC) carries warm upper waters into northern highlatitudes and returns cold deep waters southward. Under anthropogenic greenhouse gas forcing the AMOC is expected to weaken due to high-latitude warming and freshening. Here, we show that the sensitivity of the AMOC to an impulsive forcing at high latitudes is an oscillatory function of forcing lead time. This leads to the counter-intuitive result that a stronger AMOC can emerge as a result of, although some years after, anomalous warming at high latitudes. In our model study, there is no simple one-to-one correspondence between buoyancy forcing anomalies and AMOC variations, which retain memory of surface buoyancy fluxes in the subpolar gyre for 15-20 years. These results make it challenging to detect secular change from short observational time series. Copyright © 2010 by the American Geophysical Union.