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P. B. Rhines

Abstract

This paper describes qualitative features of the generation of jetlike concentrated circulations, wakes, and blocks by simple mountainlike orography, both from idealized laboratory experiments and shallow-water numerical simulations on a sphere. The experiments are unstratified with barotropic lee Rossby waves, and jets induced by mountain orography. A persistent pattern of lee jet formation and lee cyclogenesis owes its origins to arrested topographic Rossby waves above the mountain and potential vorticity (PV) advection through them. The wake jet occurs on the equatorward, eastern flank of the topography. A strong upstream blocking of the westerly flow occurs in a Lighthill mode of long Rossby wave propagation, which depends on βa 2/U, the ratio of Rossby wave speed based on the scale of the mountain, to zonal advection speed, U (β is the meridional potential vorticity gradient, f is the Coriolis frequency, and a is the diameter of the mountain). Mountains wider (north–south) than the east–west length scale of stationary Rossby waves will tend to block the oncoming westerly flow. These blocks are essentially β plumes, which are illustrated by their linear Green function. For large βa 2/U, upwind blocking is strong; the mountain wake can be unstable, filling the fluid with transient Rossby waves as in the numerical simulations of Polvani et al. For small values, βa 2/U ≪ 1 classic lee Rossby waves with large wavelength compared to the mountain diameter are the dominant process. The mountain height, δh, relative to the mean fluid depth, H, affects these transitions as well. Simple lee Rossby waves occur only for such small heights, δh/h/f, that the f/h contours are not greatly distorted by the mountain. Nongeostrophic dynamics are seen in inertial waves generated by geostrophic shear, and ducted by it, and also in a texture of finescale, inadvertent convection. Weakly damped circulations induced in a shallow-water numerical model on a sphere by a lone mountain in an initially simple westerly wind are also described. Here, with βa 2/U ∼1, potential vorticity stirring and transient Rossby waves dominate, and drive zonal flow acceleration. Low-latitude critical layers, when present, exert strong control on the high-latitude waves, and with no restorative damping of the mean zonal flow, they migrate poleward toward the source of waves. While these experiments with homogeneous fluid are very simplified, the baroclinic atmosphere and ocean have many tall or equivalent barotropic eddy structures owing to the barotropization process of geostrophic turbulence.

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P. L. Read, P. B. Rhines, and A. A. White

Abstract

A scatter diagram may be constructed by choosing an appropriate closed or open horizontal curve in physical space and plotting the value of any scalr quantity q against the geostrophic streamfunction ψ for each data point on the curve. The area enclosed on the scatter diagram is equal to the net geostrophic advective flux of q across the chosen curve in physical space. When q is the (quasi-geostrophic) potential vorticity Q, and suitable normalizations are adopted, this result may he exploited to derive measures of departure from free-mode form Q)= Q(ψ) along the curve in physical space. For a certain class of open space curves, an appropriate measure is the width-to-length ratio of the circuit in (ψ, Q) space. Most scatter diagrams that have appeared in the literature included the (ψ, Q) points corresponding to all the data or grid points within a given horizontal domain. The significance of the area enclosed on these diagrams is less clear, but the spread about some curve Q) = Q(ψ) is evidently a qualitative measure of the extent to which the flow deviates from free-mode form. For steady or time-averaged flows which are approximately of this form, the gradient dQ/dψ of the scatter diagram may be used to infer some properties of the forcing and dissipative processes acting. When dissipation is principally due to Qtransfer by transient eddy motion (or viscosity), the key diagnostic relation iswhere S is the potential vorticity forcing, K the lateral eddy (or viscous) v the horizontal velocity, and the integrals are taken over and around any region enclosed by a mean streamline. Hence dQ/dψis often negative. corresponding to two common properties of quasi-geostrophic circulations: that the eddy motion (or viscosity) transport Q down its mean gradient (K > 0) and that the circulation integral have the same sign as the potential vorticity forcing. Two sets of examples, both involving (Q,ψ) scatter diagrams constructed from numerically simulated data, are presented. One relates to steady baroclinic wave motion in a rotating annulus system, and the other to the time-averaged circulation in an ocean basin.

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Y. D. Afanasyev, P. B. Rhines, and E. G. Lindahl

Abstract

Results from new experiments on baroclinic instability of a coastal jet demonstrate that this almost balanced flow spontaneously emits inertial waves when the Rossby radius of deformation is relatively small such that the characteristics of baroclinic meanders match the dispersion relation for the inertial waves. The energy of the waves is small compared to the energy of the flow. A single event of wave emission is identified in the experiment with larger radius of deformation and is interpreted in terms of vorticity dynamics. The flows are generated on a laboratory polar β plane where the Coriolis parameter varies quadratically with latitude. A new method for imaging the rotating flows, which the authors call “altimetric imaging velocimetry,” is employed. Optical color coding of slopes of the free-surface elevation field allows the authors to derive the fields of pressure, surface elevation, geostrophic velocity, or the “gradient wind” velocity with very high spatial resolution (typically several million vectors) limited largely by the pixel resolution of the available imaging sensors. The technique is particularly suited for the investigations of small-amplitude waves, which are often difficult to detect by other methods.

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Jerome Cuny, Peter B. Rhines, Pearn P. Niiler, and Sheldon Bacon

Abstract

The general circulation of the Labrador Sea is studied with a dataset of 53 surface drifters drogued at 15 m and several hydrographic sections done in May 1997. Surface drifters indicate three distinct speed regimes: fast boundary currents, a slower crossover from Greenland to Labrador, and a slow, eddy-dominated flow in the basin interior. Mean Eulerian velocity maps show several recirculation cells located offshore of the main currents, in addition to the cyclonic circulation of the Labrador Sea. Above the northern slope of the basin, the surface drifters have two preferential paths: one between the 1000-m and 2000-m isobaths and the other close to the 3000-m isobath. The vertical shear estimated from CTD data supports the presence of two distinct currents around the basin. One current, more baroclinic, flows between the 1000-m and 2000-m isobaths. The other one, more barotropic, flows above the lower continental slope. The Irminger Sea Water carried by the boundary currents is altered as it travels around the basin. Profiling Autonomous Lagrangian Circulation Explorer (PALACE) floats that followed approximately the Irminger Sea Water in the Labrador Sea show signs of isopycnal mixing between the interior and the boundary current in summer–fall and convection across the path of the Irminger Sea Water in winter–spring.

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

Abstract

This study investigates the circulation structure and relative contribution of circulation components to the time-mean meridional heat and freshwater transports in the North Atlantic, using numerical results of a high-resolution ocean model that are shown to be in excellent agreement with the observations. The North Atlantic circulation can be separated into the large-scale Atlantic meridional overturning circulation (AMOC) that is diapycnal and the subtropical and subpolar gyres that largely flow along isopycnal surfaces but also include prominent gyre-scale diapycnal overturning in the Subtropical Mode Water and Labrador Sea Water. Integrals of the meridional volume transport as a function of potential temperature θ and salinity S yield streamfunctions with respect to θ and to S, and heat functions. These argue for a significant contribution to the heat transport by the southward circulation of North Atlantic Deep Water. At 26.5°N, the isopycnic component of the subtropical gyre is colder and fresher in the northward-flowing western boundary currents than the southward return flows, and it carries heat southward and freshwater northward, opposite of that of the diapycnal component. When combined, the subtropical gyre contributes virtually zero to the heat transport and the AMOC is responsible for all the heat transport across this latitude. The subtropical gyre however significantly contributes to the freshwater transport, reducing the 0.5-Sv (1 Sv ≡ 106 m3 s–1) southward AMOC freshwater transport by 0.13 Sv. In the subpolar North Atlantic near 58°N, the diapycnal component of the circulation, or the transformation of warm saline upper Atlantic water into colder fresher deep waters, is responsible for essentially all of the heat and freshwater transports.

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W. R. Young, P. B. Rhines, and C. J. R. Garrett

Abstract

Two models of advection-diffusion in the oscillatory, sheared-velocity field of an internal wave are discussed. Our goal is to develop intuition about the role of such currents in horizontal ocean mixing through the mechanism of shear dispersion. The analysis suggests simple parameterizations of this process, i.e., those in Eqs. (7), (36) and (42). The enhanced horizontal diffusion due to the interaction of the vertical diffusion and vertical shear of the wave field can be described by an “effective horizontal diffusivity” which is equal to the actual horizontal diffusivity plus a term equal to the mean-square vertical shear of horizontal displacement times the vertical diffusivity, provided the vertical length scale of the horizontal velocity field is not too small. In the limit of small vertical length scale the expression reduces to Taylor's (1953) result in which the effective horizontal diffusivity is inversely proportional to the actual vertical diffusivity.

The solutions also incidentally illuminate a variety of other advection-diffusion problems, such as unsteady shear dispersion in a pipe and enhanced diffusion through wavenumber cascade induced by steady shearing and straining velocity fields.

These solutions also serve as models of horizontal stirring by mesoscale eddies. Simple estimates of mesoscale shears and strains, together with estimates of the horizontal diffusivity due to shear dispersion by the internal wave field, suggest that horizontal mesoscale stirring begins to dominate internal-wave-shear dispersion at horizontal scales larger than 100 m.

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N. L. Beaird, P. B. Rhines, and C. C. Eriksen

Abstract

This paper presents new observations of the overflow waters downstream of the Faroe Bank Channel (FBC) and the Iceland–Faroe Ridge (IFR). Between 2006 and 2009, over 17 400 hydrographic profiles were collected during quarterly deployments in the region by autonomous gliders, providing previously unrealized spatial resolution to observations downstream of the FBC. Observations show that the second sill of the FBC coincides with the largest changes in the overflow plume, including significant thinning, widening, and entrainment. Between the second sill and a topographic feature 75 km downstream, the plume bifurcates with the densest portion (65% of the transport), descending below 1000 m. On the IFR, near-bottom velocities are directed alongslope with speeds averaging 21.5 cm s−1. Observations indicate that 80% of baroclinic velocities associated with mesoscale variability of the overflow plume are smaller than the alongslope topographically induced circulation. Evidence of overflow is found at all locations on the Atlantic flank of the IFR. However, the meridionally oriented portion at 13°W has anomalously warm bottom water and divides FBC and eastern IFR overflow from overflow found in the Western Valley. Individual Seaglider sections identify IFR overflow in a narrow current (8–14 km wide) along the Iceland shelf with a mean transport of 0.43 Sv (1 Sv ≡ 106 m3 s−1) with significant variability from days to weeks. A lower-bound estimate of 0.8 Sv of total IFR overflow is presented. These results provide constraints on regional models that inform the representation of this crucial, yet underresolved, region in large-scale ocean and climate models.

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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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Xiaobiao Xu, Peter B. Rhines, Eric P. Chassignet, and William J. Schmitz Jr.

Abstract

The oceanic deep circulation is shared between concentrated deep western boundary currents (DWBCs) and broader interior pathways, a process that is sensitive to seafloor topography. This study investigates the spreading and deepening of Denmark Strait overflow water (DSOW) in the western subpolar North Atlantic using two ° eddy-resolving Atlantic simulations, including a passive tracer injected into the DSOW. The deepest layers of DSOW transit from a narrow DWBC in the southern Irminger Sea into widespread westward flow across the central Labrador Sea, which remerges along the Labrador coast. This abyssal circulation, in contrast to the upper levels of overflow water that remain as a boundary current, blankets the deep Labrador Sea with DSOW. Farther downstream after being steered around the abrupt topography of Orphan Knoll, DSOW again leaves the boundary, forming cyclonic recirculation cells in the deep Newfoundland basin. The deep recirculation, mostly driven by the meandering pathway of the upper North Atlantic Current, leads to accumulation of tracer offshore of Orphan Knoll, precisely where a local maximum of chlorofluorocarbon (CFC) inventory is observed. At Flemish Cap, eddy fluxes carry ~20% of the tracer transport from the boundary current into the interior. Potential vorticity is conserved as the flow of DSOW broadens at the transition from steep to less steep continental rise into the Labrador Sea, while around the abrupt topography of Orphan Knoll, potential vorticity is not conserved and the DSOW deepens significantly.

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