Journal of Fluid Mechanics 729 (2013) 69-102
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.
Modulation of eddy kinetic energy, temperature variance, and eddy heat fluxes by surface buoyancy forcing
Ocean Modelling 62 (2013) 27-38
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.
JOURNAL OF PHYSICAL OCEANOGRAPHY 43 (2013) 95-103
Journal of Physical Oceanography 43 (2013) 1798-1810
International Geophysics 103 (2013) 257-282
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.
Geophysical Research Letters 40 (2013)
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. © 2013. American Geophysical Union. All Rights Reserved.
JOURNAL OF PHYSICAL OCEANOGRAPHY 43 (2013) 2699-2717
JOURNAL OF PHYSICAL OCEANOGRAPHY 42 (2012) 1357-1365
JOURNAL OF PHYSICAL OCEANOGRAPHY 42 (2012) 539-557
Accurate representation of geostrophic and hydrostatic balance in unstructured mesh finite element ocean modelling
Ocean Modelling 39 (2011) 248-261
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.
JOURNAL OF MARINE RESEARCH 69 (2011) 167-189
Journal of Climate 24 (2011) 5619-5632
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)
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.
Geophysical Research Letters 38 (2011)
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.
Journal of Physical Oceanography 41 (2011) 960-978
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.
Ocean Dynamics 60 (2010) 835-850
The problem of flow separation around islands is investigated using a dynamically adaptive finite element model to allow for resolution of the shear layers that form in the advent of separation. The changes in secondary circulation and vertical motion that occur in both attached and separated flows are documented, as is the degree of closure of the wake eddies. In the numerical experiments presented, the strongest motion always takes place at the sides of the idealised island, where flow curvature and shear act together to induce ascent. In contrast, it is the slower motion within the wake eddies that allow streamlines to extend from the bottom to the surface. We find no evidence for closure of the wake eddies. Rather, all of our separated experiments show that streamlines that pass through the eddies originate outside of the shear layers and frictional boundary layers on the upstream side of the idealised island. The numerical experiments demonstrate the potential for dynamically adaptive, unstructured meshes to resolve the separated shear layers that occur downstream of the idealised island, as well as the narrow boundary layers that form on the island itself. © 2010 Springer-Verlag.
Parameterization of ocean eddies: Potential vorticity mixing, energetics and Arnold's first stability theorem
Ocean Modelling 32 (2010) 188-204
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.
Nature Geoscience 3 (2010) 608-612
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.
Geophysical Research Letters 37 (2010)
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.