The Temporal-Residual-Mean Velocity. Part II: Isopycnal Interpretation and the Tracer and Momentum Equations

McDougall, Trevor J.; McIntosh, Peter C.

doi:10.1175/1520-0485(2001)031<1222:ttrmvp>2.0.co;2

Cited by 139 publications

(200 citation statements)

References 29 publications

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“…In contrast, mapping the deviation in density coordinates (A ≡ A − A, compared at constant density) onto the mean depth of each isopycnal yields ∇ 3 · U = 0 and U · n = 0. This concern is the reason why McDougall and McIntosh (2001) suggested to replace the set of the isopycnal mean velocity and the bolus velocity (each of which is threedimensionally divergent and does not satisfy a no-normal-flow boundary condition) in Gent et al (1995) with the set of the Eulerian mean velocity and the quasi-Stokes velocity, each of which is three-dimensionally nondivergent and satisfies a no-normal-flow boundary condition (Appendix B). The exact definition of the quasiStokes stream function is…”

Section: Maintenance Of the Eddy Field Energymentioning

confidence: 99%

Energetics of the Global Ocean: The Role of Mesoscale Eddies

Aiki

Zhai

Greatbatch

2015

World Scientific Series on Asia-Pacific Weather and Climate

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This article reviews the energy cycle of the global ocean circulation, focusing on the role of baroclinic mesoscale eddies. Two of the important effects of mesoscale eddies are: (i) the flattening of the slope of large-scale isopycnal surfaces by the eddy-induced overturning circulation, the basis for the Gent-McWilliams parametrization; and (ii) the vertical redistribution of the momentum of basic geostrophic currents by the eddy-induced form stress (the residual effect of pressure perturbations), the basis for the Greatbatch-Lamb parametrization. While only point (i) can be explained using the classical Lorenz energy diagram, both (i) and (ii) can be explained using the modified energy diagram of Bleck as in the following energy cycle. Wind forcing provides an input to the mean KE, which is then transferred to the available potential energy (APE) of the large-scale field by the wind-induced Ekman flow. Subsequently, the APE is extracted by the eddy-induced overturning circulation to feed the mean KE, indicating the enhancement of the vertical shear of the basic current. Meanwhile, the vertical shear of the basic current is relaxed by the eddy-induced form stress, taking the mean KE to endow the eddy field with an energy cascade. The above energy cycle is useful for understanding the dynamics of the Antarctic Circumpolar Current. On the other hand, while the source of the eddy field energy has become clearer, identifying the sink and flux of the eddy field energy in both physical and spectral space remains major challenges of present-day oceanography. A recent study using a combination of models, satellite altimetry, and climatological hydrographic data shows that the western boundary acts as a "graveyard" for the westward-propagating eddies.

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Section: Maintenance Of the Eddy Field Energymentioning

confidence: 99%

Energetics of the Global Ocean: The Role of Mesoscale Eddies

Aiki

Zhai

Greatbatch

2015

World Scientific Series on Asia-Pacific Weather and Climate

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“…As McDougall and McIntosh (2001) showed, at the ocean's surface the stream function satisfies the boundary condition W(0) = 0. We concentrate on the horizontal component of this condition:…”

Section: Inapplicability Of the Standard Rmt To The MLmentioning

confidence: 99%

Comparison of four mixed layer mesoscale parameterizations and the equation for an arbitrary tracer

Canuto¹,

Dubovikov²

2011

Ocean Modelling

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a b s t r a c tIn this paper we discuss two issues, the inter-comparison of four mixed layer mesoscale parameterizations and the search for the eddy induced velocity for an arbitrary tracer. It must be stressed that our analysis is limited to mixed layer mesoscales since we do not treat sub-mesoscales and small turbulent mixing.As for the first item, since three of the four parameterizations are expressed in terms of a stream function and a residual flux of the RMT formalism (residual mean theory), while the fourth is expressed in terms of vertical and horizontal fluxes, we needed a formalism to connect the two formulations. The standard RMT representation developed for the deep ocean cannot be extended to the mixed layer since its stream function does not vanish at the ocean's surface.We develop a new RMT representation that satisfies the surface boundary condition. As for the general form of the eddy induced velocity for an arbitrary tracer, thus far, it has been assumed that there is only the one that originates from the curl of the stream function. This is because it was assumed that the tracer residual flux is purely diffusive.On the other hand, we show that in the case of an arbitrary tracer, the residual flux has also a skew component that gives rise to an additional bolus velocity. Therefore, instead of only one bolus velocity, there are now two, one coming from the curl of the stream function and other from the skew part of the residual flux. In the buoyancy case, only one bolus velocity contributes to the mean buoyancy equation since the residual flux is indeed only diffusive.Published by Elsevier Ltd.

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“…Section 2.1 summarizes the thickness-weighted temporalmean momentum and density equations that have been investigated by de Szoeke and Bennett (1993), McDougall and McIntosh (2001), and Jacobson and Aiki (2006). Readers not familiar with expressions in Sect.…”

Section: Adiabatic Mean Formulationmentioning

confidence: 99%

“…However, the energy diagram and associated energy cycle may vary with the definitions of the mean and perturbation fields. An energy diagram for the transformed Eulerian mean (TEM) theory (Andrews and McIntyre, 1976) is given by Plumb (1983) andt z Fig. 1.…”

Section: Introductionmentioning

confidence: 99%

Energetics of the layer-thickness form drag based on an integral identity

Aiki

Yamagata

2006

Ocean Sci.

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Abstract. The vertical redistribution of the geostrophic momentum by the residual effects of pressure perturbations (called the layer-thickness form drag) is investigated using thickness-weighted temporal-averaged mean primitive equations for a continuously stratified fluid in an adiabatic formulation. A four-box energy diagram, in which the mean and eddy kinetic energies are defined by the thickness-weighted mean velocity and the deviation from it, respectively, shows that the layer-thickness form drag reduces the mean kinetic energy and endows the eddy field with an energy cascade. The energy equations are derived using an identity (called the "pile-up rule") between cumulative sums of the Eulerian mean quantity and the thickness-weighted mean quantity in each vertical column. The pile-up rule shows that the thickness-weighted mean velocity satisfies a no-normal-flow boundary condition at the top and bottom of the ocean, which enables the volume budget of pressure flux divergence in the energy diagram to be determined. With the pile-up rule, the total kinetic energy based on the Eulerian mean can be rewritten in a thickness-weighted form. The four-box energy diagram in the present study should be consistent with energy diagrams of layer models, the temporal-residual-mean theory, and Iwasaki's atmospheric theory. Under certain assumptions, the work of the layer-thickness form drag in the global ocean circulation is suggested to be comparable to the work done by the wind forcing.

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The Temporal-Residual-Mean Velocity. Part II: Isopycnal Interpretation and the Tracer and Momentum Equations

Cited by 139 publications

References 29 publications

Energetics of the Global Ocean: The Role of Mesoscale Eddies

Energetics of the Global Ocean: The Role of Mesoscale Eddies

Comparison of four mixed layer mesoscale parameterizations and the equation for an arbitrary tracer

Energetics of the layer-thickness form drag based on an integral identity

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