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Patrick Haertel
and
Alexey Fedorov

Abstract

Adiabatic theories of ocean circulation and density structure have a long tradition, from the concept of the ventilated thermocline to the notion that deep ocean ventilation is controlled by westerly winds over the Southern Ocean. This study explores these ideas using a recently developed Lagrangian ocean model (LOM), which simulates ocean motions by computing trajectories of water parcels. A unique feature of the LOM is its capacity to model ocean circulations in the adiabatic limit, in which water parcels exactly conserve their densities when they are not in contact with the ocean surface. The authors take advantage of this property of the LOM and consider the circulation and stratification that develop in an ocean with a fully adiabatic interior (with both isopycnal and diapycnal diffusivities set to zero). The ocean basin in the study mimics that of the Atlantic Ocean and includes a circumpolar channel. The model is forced by zonal wind stress and a density restoring at the surface.

Despite the idealized geometry, the relatively coarse model resolution, and the lack of atmospheric coupling, the nondiffusive ocean maintains a density structure and meridional overturning that are broadly in line with those observed in the Atlantic Ocean. These are generated by just a handful of key water pathways, including shallow tropical cells described by ventilated thermocline theory; a deep overturning cell in which sinking North Atlantic Deep Water eventually upwells in the Southern Ocean before returning northward as Antarctic Intermediate Water; a Deacon cell that results from a topographically steered and corkscrewing circumpolar current; and weakly overturning Antarctic Bottom Water, which is effectively ventilated only in the Southern Hemisphere.

The main conclusion of this study is that the adiabatic limit for the ocean interior provides the leading-order solution for ocean overturning and density structure, with tracer diffusion contributing first-order perturbations. Comparing nondiffusive and diffusive experiments helps to quantify the changes in stratification and circulation that result from adding a moderate amount of tracer diffusion in the ocean model, and these include an increase in the amplitude of the deep meridional overturning cell of several Sverdrups, a 10%–20% increase in Northern Hemispheric northward heat transport, a stronger stratification just below the main thermocline, and a more realistic bottom overturning cell.

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Alexey V. Fedorov
and
W. Kendall Melville

Abstract

A model of surface waves generated on deep water by strong winds is proposed. A two-layer approximation is adopted, in which a shallow turbulent layer overlies the lower, infinitely deep layer. The dynamics of the upper layer, which is directly exposed to the wind, are nonlinear and coupled to the linear dynamics in the deep fluid. The authors demonstrate that in such a system there exist steady wave solutions characterized by confined regions of wave breaking alternating with relatively long intervals where the wave profiles change monotonically. In the former regions the flow is decelerated; in the latter it is accelerated. The regions of breaking are akin to hydraulic jumps of finite width necessary to join the smooth “interior” flows and have periodic waves. In contrast to classical hydraulic jumps, the strongly forced waves lose both energy and momentum across the jumps. The flow in the upper layer is driven by the balance between the wind stress at the surface, the turbulent drag applied at the layer interface, and the wave drag induced at the layer interface by quasi-steady breaking waves. Propagating in the downwind direction, the strongly forced waves significantly modify the flow in both layers, lead to enhanced turbulence, and reduce the speed of the near-surface flow. According to this model, a large fraction of the work done by the surface wind stress on the ocean in high winds may go directly into wave breaking and surface turbulence.

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Alexey V. Fedorov
and
W. Kendall Melville

Abstract

Properties of internal wave fronts or Kelvin fronts travelling eastward in the equatorial waveguide are studied, motivated by recent studies on coastal Kelvin waves and jumps and new data on equatorial Kelvin waves. It has been recognized for some time that nonlinear equatorial Kelvin waves can steepen and break, forming a broken wave of depression, or front, propagating eastward. The three-dimensional structure of the wave field associated with such a front is considered. As for linear Kelvin waves, the front is symmetrical with respect to the equator. Sufficiently far away from the front, the wave profile is Gaussian in the meridional direction, with the equatorial Rossby radius of deformation being its decay scale. Due to nonlinearity, the phase speed of the front is greater than that of linear Kelvin waves, resulting in a supercritical flow. This leads to the resonant generation of equatorially trapped gravity–inertial (or Poincaré) waves, analogous in principle to the resonant mechanism for nonlinear coastal Kelvin waves. First-mode symmetrical Poincaré waves are generated, with their wavelength determined by the amplitude of the front. Finally, the propagation of a Kelvin front gives rise to a nonzero poleward mass transport above the thermocline, in consequence of which there is a poleward heat flux.

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Alexey V. Fedorov
and
W. Kendall Melville

Abstract

The evolution of nonlinear Kelvin waves is studied using analytical and numerical methods. In the absence of dispersive (nonhydrostatic) effects, such waves may evolve to braking. The authors find that one of the effects of rotation is to delay the onset of breaking in time by up to 60%, with respect to a comparable wave in de absence of rotation. This delay is consistent with qualitative conclusions based on transverse averaging of the evolution equations. Further, the onset of breaking occurs almost simultaneously over a zone of uniform phase that is normal to the boundary and extends over a distance comparable to the Rossby radius of deformation. In other words, the process of breaking embraces the most energetic area of the wave. In contrast to the linear Kelvin wave, the nonlinear wave develops a dipole structure in the cross-shelf velocity, with a zero net offshore flow. With increasing nonlinearity the flow develops a stronger offshore jet ahead of the wave crest. The Kelvin wave amplitude at the coast delays slightly with time. This and other major features of the wave are accounted for by an analytical model based on slowly varying averaged variables. As part of the analysis it is demonstrated that the evolution of the wave phase may be described by an inhomogeneous Klein-Gordon equation.

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Giulio Boccaletti
,
Ronald C. Pacanowski
,
S. George
,
H. Philander
, and
Alexey V. Fedorov

Abstract

The salient feature of the oceanic thermal structure is a remarkably shallow thermocline, especially in the Tropics and subtropics. What factors determine its depth? Theories for the deep thermohaline circulation provide an answer that depends on oceanic diffusivity, but they deny the surface winds an explicit role. Theories for the shallow ventilated thermocline take into account the influence of the wind explicitly, but only if the thermal structure in the absence of any winds, the thermal structure along the eastern boundary, is given. To complete and marry the existing theories for the oceanic thermal structure, this paper invokes the constraint of a balanced heat budget for the ocean. The oceanic heat gain occurs primarily in the upwelling zones of the Tropics and subtropics and depends strongly on oceanic conditions, specifically the depth of the thermocline. The heat gain is large when the thermocline is shallow but is small when the thermocline is deep. The constraint of a balanced heat budget therefore implies that an increase in heat loss in high latitudes can result in a shoaling of the tropical thermocline; a decrease in heat loss can cause a deepening of the thermocline. Calculations with an idealized general circulation model of the ocean confirm these inferences. Arguments based on a balanced heat budget yield an expression for the depth of the thermocline in terms of parameters such as the imposed surface winds, the surface temperature gradient, and the oceanic diffusivity. These arguments in effect bridge the theories for the ventilated thermocline and the thermohaline circulation so that previous scaling arguments are recovered as special cases of a general result.

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Alexey Fedorov
,
Marcelo Barreiro
,
Giulio Boccaletti
,
Ronald Pacanowski
, and
S. George Philander

Abstract

The impacts of a freshening of surface waters in high latitudes on the deep, slow, thermohaline circulation have received enormous attention, especially the possibility of a shutdown in the meridional overturning that involves sinking of surface waters in the northern Atlantic Ocean. A recent study by Fedorov et al. has drawn attention to the effects of a freshening on the other main component of the oceanic circulation—the swift, shallow, wind-driven circulation that varies on decadal time scales and is closely associated with the ventilated thermocline. That circulation too involves meridional overturning, but its variations and critical transitions affect mainly the Tropics. A surface freshening in mid- to high latitudes can deepen the equatorial thermocline to such a degree that temperatures along the equator become as warm in the eastern part of the basin as they are in the west, the tropical zonal sea surface temperature gradient virtually disappears, and permanently warm conditions prevail in the Tropics. In a model that has both the wind-driven and thermohaline components of the circulation, which factors determine the relative effects of a freshening on the two components and its impact on climate? Studies with an idealized ocean general circulation model find that vertical diffusivity is one of the critical parameters that affect the relative strength of the two circulation components and hence their response to a freshening. The spatial structure of the freshening and imposed meridional temperature gradients are other important factors.

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