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Peter B. Rhines

Abstract

The presence of broad, flowing water masses in the deep ocean requires dynamical explanation. Vertical density diffusion andβ-effect are invoked in classical theories; here we show how topographic potential vorticity can control broad baroclinic flows with diffusion playing a secondary role. The theory and numerical experiments involve a zonal flow over topography, such as one finds in the Southern Ocean, although similar effects occur in source-sink flows at middle latitudes.

A 1½ layer model (that is, one active deep layer beneath a thick upper layer) of the deep circulation shows intense interactions with both small-scale O(500 km wide) and Large-scale O(2500 km wide) seafloor slopes. Broad, gentle slopes can block an initially uniform flow, expelling the circulation to an outer rim (defined by hyperbolic characteristics) where it forms into jets. With smaller-scale topography, planetary-scale flow encountering a midocean ridge develops transient distortions of the flow and density fields, which convert large-scale potential energy to kinetic energy. These distortions move up- or downstream from the topography, leaving a bound vortex permanently over the topography. The “free” and “bound” circulations are connected by a long ridge or trough in dynamic height, which is the site of intense jets. These features become permanent with dissipation. Small-amplitude theory resembles classic open-channel hydraulics, yet at topographic heights of only, say, 300 m and mean flow speeds of O(0.01 m s−1) one is already in a large-amplitude, nonlinear regime. Above the topography the characteristics of the wave equation form closed curves, preventing upstream boundary conditions from determining the solution there. Instead, the density interface winds into a tight spiral, with perturbation energy growing as t 2. This resembles a form of shear dispersion, yet the shearing field is the group velocity rather than the fluid velocity; a theoretical calculation of the process is given, and the connection is made between energy increase in the flow and the pressure drag on the topography. The 1½ layer model exaggerates some time-dependent aspects of baroclinic adjustment.

Two kinds of blocking occur, in which permanent flow and distortion of the density field are transmitted far downstream or upstream. First, the nondiffusive problem is governed by hyperbolic characteristics in (x, y, t) which can be “reflected” from a seafloor ridge or trough, either due to shear in the upstream flow or due to the secular change in Rossby wavespeed with latitude. Second, at bounding or stagnation characteristics, dissipative terms can send a block far from the topography. Blocking occurs at infinitesmal ridge height when there is a critical characteristic intersecting the topography. Ridges even of O(300 m) in height can completely block the oncoming flow, for example sending an eastward zonal flow back to the west at a higher latitude. Elongated gyres of circulation way result, reaching far from the topography.

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Peter B. Rhines and Richard Schopp

Abstract

Simulations of the wind-driven Ocean circulation, carded out with an eddy-resolving quasi-geostrophic numerical model, and symmetric, idealized wind forcing have a large-scale structure that is predicted wen by the steady nonlinear theory of Rhines and Young. The sharp jet and inertial recirculation am often confined weft inside the region of closed hyperbolic characteristics, defined by that theory, and hence do not affect the Sverdrup-dynamics part of the gyre. The characteristics make possible simple predictions about the development of the circulation, including time dependence and eddy stirring. By tilting the line of vanishing Ekman pumping away from the east-west orientation (as it is tilted in the North Atlantic, and less so the North Pacific), we explore a family of circulations. As the tilt of the wind held is increased, characteristics originating at the eastern boundary begin to thread through the energetic region occupied by the free jet. Then, extensive new branches of eddy-driven flow occur, reaching poleward into the subpolar gyre.

Lagrangian float trajectories are shown and Lagrangian mean circulation and diffusivity discussed. A Peclet number measuring the relative strengths of advection and eddy mixing of potential vorticity is defined and mapped. Its value, typically 3 to 5, suggests the dominant nature of mesoscale eddy mixing in the ocean. Stirring by mesoscale eddies arises in midocean from baroclinic instability. It leads to a loss of 'memory” of quasi-conserved properties over typically 300 to 1000 km. Eddies are essential to the transport of potential vorticity from subpolar to subtropical regions, across the limiting characteristic, finally determining the structure of the recirculating subtropical gyre.

Permanent tongues of potential vorticity invade the subtropics from the subpolar gyre, entering where the characteristics of the theory form a stagnation point.

The experiments exhibit several features of the observed circulation of the ocean. With increasing tilt of the winds we find: decreasing total energy of the circulation; great decrease in the length of the eastward-flowing free jet; increased concentration of the circulation in the upper ocean where it wore closely resembles the simple Sverdrup transport function, with broad regions of eastward flow., increased production of cutoff rings near the western boundary (rather than just at the eastern end of the jet, as with symmetric winds); shrinkage of the north-south extent of the subtropical gyre at the 300–1000 m level yet increase in its consent extent (so that it reaches 5000 km northeastward, to the eastern boundary); and displacement of the boundary current separation point poleward of the line of vanishing Ekman pumping. The subpolar gyre shrinks in size. The simulations help one to understand the differences between, on the one hand, the North Atlantic Ocean, with its very confined middepth circulation and NE-SW strike of the 1000-m potential vorticity contours, and a relative small region of penetration of the concentrated Gulf Stream jet into the interior, and, on the other hand, the North Pacific, where the subtropical anticyclone penetrates much deeper and the Kuroshio jet penetrates a greater distance eastward.

A review of relevant observations of the North Atlantic is given, particularly to show that the regime of the model is realistic; as one moves toward the “quiet” parts of midocean, the ratio of eddy to mean kinetic energy actually rises, suggesting that eddy mixing cannot be neglected there.

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Thomas Jung and Peter B. Rhines

Abstract

Some effects of Greenland on the Northern Hemisphere wintertime circulation are discussed. Inviscid pressure drag on Greenland’s slopes, calculated from reanalysis data, is related to circulation patterns. Greenland lies north of the core of the tropospheric westerly winds. Yet strong standing waves, which extend well into the stratosphere, produce a trough/ridge system with jet stream lying close to Greenland, mean Icelandic low in its wake, and storm track that interacts strongly with its topography. In the lower troposphere, dynamic height anomalies associated with strongly easterly pressure drag on the atmosphere are quite localized in space and relatively short-lived compared to upper levels, yet they involve a hemispheric-scale dislocation of the stratospheric polar vortex. It is a two-scale problem, however; the high-pass time-filtered part of the height field, responsible for 73% of the pressure drag, is quite different, and expresses propagating cyclonic development in the Atlantic storm track. Eliassen–Palm flux (EP flux) analysis shows that the atmospheric response is (counterintuitively) an acceleration of the westerly winds. The hemispheric influence is consistent with the model results of Junge et al. suggesting that Greenland affects the stationary waves in winter.

This discussion shows that Greenland is not a simple “stirring rod” in the westerly circulation, yet involvement of Greenland’s topography with the shape, form, and intensity of the storm track is strong. Interaction of traveling storms, the jet stream, and the orographic wake frequently leads to increase of the lateral scale such that cyclonic system expands to the size of Greenland itself (∼2500 km). Using the global ECMWF general circulation model, the authors explore the effect of model resolution on these circulations. Statistically, in two case studies, and in higher-resolution global models at TL255 to TL799 resolution, intense tip jet, hydraulic downslope jet, and gravity wave radiation appear in strong flow events, in accord with the work of Doyle and Shapiro. Three-dimensional particle trajectories and vorticity maps show the nature and intensity of the summit-gap flow. Cyclonic systems in the lee of Greenland are strongly affected by the downslope jet. Penetration of the Arctic Basin by cyclonic systems arises from this source region, and the amplitude of the pressure drag is enhanced at high resolution. At the higher resolutions, storm-track analysis verifies the splitting of the storm track by Greenland with a substantial minority of storms moving northward through Baffin Bay. Finally, analysis of 20 winters of 40-yr ECMWF Re-Analysis (ERA-40) reforecasts shows little evidence that negative pressure-drag events are followed by anomalously large forecast errors over Europe, throughout the forecast. Forecast skill for the pressure drag is surprisingly good, with a correlation of 0.65 at 144 h.

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Parker MacCready and Peter B. Rhines

Abstract

The turbulent bottom boundary layer for rotating, stratified flow along a slope is explored through theory and numerical simulation. The model flow begins with a uniform current along constant-depth contours and with flat isopycnals intersecting the slope. The boundary layer is then allowed to evolve in time and in distance from the boundary. Ekman transport up or down the slope advects the initial density gradient, eventually giving rise to substantial buoyancy forces. The rearranged density structure opposes the cross-slope flow, causing the transport to decay exponentially from its initial value (given by Ekman theory) to near zero, over a time scale proportional to f/(Nα)2, where f is the Coriolis frequency, N is the buoyancy frequency, and α is the slope angle. The boundary stress slowing the along-slope flow decreases simultaneously, leading to a very “slippery” bottom boundary compared with that predicted by Ekman theory.

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Parker MacCready and Peter B. Rhines

Abstract

Experiments are performed using a two-layer isopycnic numerical model in a zonal channel with a large meridional topographic ridge in the lower layer. The model is forced only by a steady meridional volume transport in the upper layer, and develops a current structure similar to the Antarctic Circumpolar Current. Meridional volume flux across time-mean geostrophic streamlines is found to be due to a combination of the geostrophic eddy bolus flux and the lateral Reynolds stress. The proportion of each depends on the strength of the forcing. The Reynolds stress increases with the forcing, while the bolus flux is relatively constant. Topography localizes the eddy fluxes at and downstream of the topography, where eddy energies are greatest. The strength of the zonal transport is governed by the onset of baroclinic instability and so is relatively insensitive to the strength of the meridional transport.

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David W. Pierce and Peter B. Rhines

Abstract

The convective building of a pycnocline is examined using a two-dimensional nonhydrostatic numerical model forced by a balanced salinity dipole (source and sink). Although the forcing fields are steady, the model develops oscillations that renew the model’s analog of “deep waters” only intermittently. The oscillation cycle consists of a freshwater layer that advects along the surface, capping off the water column under the dense source and preventing sinking; after a time, continuing densification forms a plume that breaks through the salinity barrier and convects beneath the dense source, ventilating the deep water. Increasing the viscosity reduces but does not eliminate this cycle. When the hydrostatic assumption is added, the model evolves systematically different salinity distributions than the nonhydrostatic model due to the isolation of part of the tank by a persistent convective column. The deep flow is also different in this case because of differences between the entrainment/detrainment profile of a hydrostatic plume and one modeled explicitly. The model evolves a characteristically skewed distribution of densities that is similar to the distribution of temperature in the World Ocean. Rotation increases the range of this distribution due to the inhibition of meridional flow.

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Jonathan M. Lilly and Peter B. Rhines

Abstract

During June–November 1994, a mooring in the central Labrador Sea near the former Ocean Weather Station Bravo recorded a half-dozen anomalous events that prove to be two different types of coherent eddies. Comparisons with simple analytical models are used to classify these events as coherent eddies on the basis of their velocity signatures. The first clear examples of long-lived convectively generated eddies are reported. These four small (radius ∼5–15 km) eddies are exclusively anticyclonic, with cold, fresh middepth potential temperature (θ) and salinity (S) cores surrounded by azimuthal currents of ∼15 cm s−1. Their θ/S properties identify them unambiguously as the products of wintertime deep convection in the interior Labrador Sea. Compared with eddies in other regions, these anticyclones are unusual for their strong surface expressions and composite θ/S cores. Two warm cyclones are also seen; these are larger (radius ∼15 km) than the anticyclones and about as energetic (currents ∼15 cm s−1). Their θ/S and potential vorticity properties suggest that they are created by stretching a column of water from the Irminger Current, which surrounds the Labrador Sea on three sides.

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William R. Holland and Peter B. Rhines

Abstract

Gyre scale and local vorticity balances are examined for a single numerical experiment designed to elucidate the role of eddies in the oceanic general circulation. Due to the complex nature of the flow, a combination of different analyses is needed. In particular the mean potential vorticity fields are calculated and related to local and global vorticity fluxes. The nature of eddy generation and decay is discussed in terms of eddy enstrophy balances in the fluid. Momentum balances in various parts of the gyre are deduced through the application of the circulation theorem. Fields of eddy diffusivity for the mixing of potential vorticity and heat are determined. The applicability of Sverdrup dynamics in various parts of the fluid and the manner in which the deep abyssal gyres are driven are examined.

The net picture is a complex but consistent one. In the upper layer, eddy generation occurs in the separation region of the eastward jet and in the region of westward return flow. Eddy decay occurs principally at the eastern end of the free jet accompanied by upgradient eddy fluxes of heat and potential vorticity. The lower layer is driven from above by inviscid pressure forcing at the interface., this is accompanied by downgradient potential vorticity flux everywhere in the lower layer. The deep dynamics is essentially a “turbulent” Sverdrup balance, Ū3·∇ Q̄3= ∇·κ ∇Q̄3, driven by eddy rather than wind stresses.

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David W. Pierce and Peter B. Rhines

Abstract

The convective building of a pycnocline is examined using a laboratory model forced by surface fluxes of saline water at one end and fresh water at the other. A deep recirculation evolves in the tank, which homogenizes the interior fluid by repeated passes through the dense, descending plume. A thin, fresh surface layer develops and modifies the effective buoyancy flux into the dense plume, causing the interior velocities to fall to an intermediate-time minimum. Adding bottom topography under the dense source greatly reduces the amount of entrainment that the descending plume undergoes. In this case, the tank fills with a deep, heavy layer, which causes the plume to “lift off” the bottom of the tank and detrain at successively higher depths in the water column. A simple numerical “plume” model shows that this cannot be a steady state, as it is not in diffusive balance; the plume must eventually return to the bottom of the tank and ventilate the interior waters. Adding rotation increases the surface mixing, thickens the halocline, and increases the observed variability in the salinity field.

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Xiaobiao Xu, Peter B. Rhines, and Eric P. Chassignet

Abstract

Diapycnal water mass transformation is the essence behind the Atlantic meridional overturning circulation (AMOC) and the associated heat/freshwater transports. Existing studies have mostly focused on the transformation that is forced by surface buoyancy fluxes, and the role of interior mixing is much less known. This study maps the three-dimensional structure of the diapycnal transformation, both surface forced and mixing induced, using results of a high-resolution numerical model that have been shown to represent the large-scale structure of the AMOC and the North Atlantic subpolar/subtropical gyres well. The analyses show that 1) annual mean transformation takes place seamlessly from the subtropical to the subpolar North Atlantic following the surface buoyancy loss along the northward-flowing upper AMOC limb; 2) mixing, including wintertime convection and warm-season restratification by mesoscale eddies in the mixed layer and submixed layer diapycnal mixing, drives transformations of (i) Subtropical Mode Water in the southern part of the subtropical gyre and (ii) Labrador Sea Water in the Labrador Sea and on its southward path in the western Newfoundland Basin; and 3) patterns of diapycnal transformations toward lighter and denser water do not align zonally—the net three-dimensional transformation is significantly stronger than the zonally integrated, two-dimensional AMOC streamfunction (50% in the southern subtropical North Atlantic and 60% in the western subpolar North Atlantic).

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