Michael A. Spall

Specification of Eddy Transfer Coefficients in Coarse-Resolution Ocean Circulation Models*

Parametric representations of oceanic geostrophic eddy transfer of heat and salt are studied ranging from horizontal diffusion to the more physically based approaches of Green and Stone (GS) and Gent and McWilliams (GM). The authors argue for a representation that combines the best aspects of GS and GM: transfer coefficients that vary in space and time in a manner that depends on the large-scale density fields (GS) and adoption of a transformed Eulerian mean formalism (GM). Recommendations are based upon a two-dimensional (zonally or azimuthally averaged) model with parameterized horizontal and vertical fluxes that is compared to three-dimensional numerical calculations in which the eddy transfer is resolved. Three different scenarios are considered: 1) a convective ‘‘chimney’’ where the baroclinic zone is created by differential surface cooling; 2) spindown of a frontal zone due to baroclinic eddies; and 3) a wind-driven, baroclinically unstable channel. Guided by baroclinic instability theory and calibrated against eddy-resolving calculations, the authors recommend a form for the horizontal transfer coefficient given by 2 fM 2 2 k 5 a l 5 a l, N ˇRi where Ri 5 f2N2/M4 is the large-scale Richardson number and f is the Coriolis parameter; M2 and N2 are measures of the horizontal and vertical stratification of the large-scale flow, l measures the width of the baroclinic zone, and a is a constant of proportionality. In the very different scenarios studied here the authors find a to be a ‘‘universal’’ constant equal to 0.015, not dissimilar to that found by Green for geostrophic eddies in the atmosphere. The magnitude of the implied k, however, varies from 300 m2 s21 in the chimney to 2000 m2 s21 in the wind-driven channel.

The Relation between Decadal Variability of Subtropical Mode Water and the North Atlantic Oscillation

The Bermuda station ‘‘S’’ time series has been used to define the variability of subtropical mode water (STMW) from 1954 to 1995. This record, which shows decadal variability at a nominal period of about 12‐14 yr, has been used as a baseline for seeking correlation with large-scale atmospheric forcing and with decadal north‐south excursions of the Gulf Stream position defined by the subsurface temperature at 200-m depth. A common time period of 1954‐89 inclusive, defined by the data sources, shows a high degree of correlation among the STMW potential vorticity (PV), Gulf Stream position, and large-scale atmospheric forcing (buoyancy flux, SST, and sea level pressure). Two pentads with anomalously small and large STMW PV were further studied and composites were made to define a revised North Atlantic Oscillation (NAO) index associated with the decadal forcing. During years of low PV at Bermuda, the NAO index is low, the Gulf Stream is in a southerly position, and the zero wind stress curl latitude is shifted south as are the composite extratropical winter storm tracks, in comparison to the period of high PV at Bermuda. Because the NAO, Gulf Stream separation latitude, and STMW PV variations are in phase with maximum annually averaged correlation at zero year time lag, the authors hypothesize that all must be either coupled with one another or with some other phenomenon that determines the covariability. A mechanism is proposed that could link all of the above together. It relies on the fact that during periods of high STMW PV, associated with a northerly Gulf Stream and a high NAO, one finds enhanced production of mode water in the subpolar gyre and Labrador Sea. Export of the enhanced Labrador Sea Water (LSW) component into the North Atlantic via the Deep Western Boundary Current can influence the separation point of the Gulf Stream in the upper ocean once the signal propagates from the source region to the crossover point with the Gulf Stream. If the SST signal produced by the 100-km shift of the Gulf Stream along a substantial (1000 km) length of its path as it leaves the coast can influence the NAO, a negative feedback oscillation may develop with a timescale proportional to the time delay between the change of phase of the air‐ sea forcing in the Labrador Basin and the LSW transient at the crossover point. Both a simple mechanistic model as well as a three-layer numerical model are used to examine this feedback, which could produce decadal oscillations given a moderately strong coupling.

Deep convection in the Irminger Sea forced by the Greenland tip jet.

Open-ocean deep convection, one of the processes by which deep waters of the worlds oceans are formed, is restricted to a small number of locations (for example, the Mediterranean and Labrador seas). Recently, the southwest Irminger Sea has been suggested as an additional location for open-ocean deep convection. The deep water formed in the Irminger Sea has the characteristic temperature and salinity of the water mass that fills the mid-depth North Atlantic Ocean, which had been believed to be formed entirely in the Labrador basin. Here we show that the most likely cause of the convection in the Irminger Sea is a low-level atmospheric jet known as the Greenland tip jet, which forms periodically in the lee of Cape Farewell, Greenland, and is associated with elevated heat flux and strong wind stress curl. Using a history of tip-jet events derived from meteorological land station data and a regional oceanic numerical model, we demonstrate that deep convection can occur in this region when the North Atlantic Oscillation Index is high, which is consistent with observations. This mechanism of convection in the Irminger Sea differs significantly from those known to operate in the Labrador and Mediterranean seas.

Western Arctic Shelfbreak Eddies: Formation and Transport

Abstract The mean structure and time-dependent behavior of the shelfbreak jet along the southern Beaufort Sea, and its ability to transport properties into the basin interior via eddies are explored using high-resolution mooring data and an idealized numerical model. The analysis focuses on springtime, when weakly stratified winter-transformed Pacific water is being advected out of the Chukchi Sea. When winds are weak, the observed jet is bottom trapped with a low potential vorticity core and has maximum mean velocities of O(25 cm s−1) and an eastward transport of 0.42 Sv (1 Sv ≡ 106 m3 s−1). Despite the absence of winds, the current is highly time dependent, with relative vorticity and twisting vorticity often important components of the Ertel potential vorticity. An idealized primitive equation model forced by dense, weakly stratified waters flowing off a shelf produces a mean middepth boundary current similar in structure to that observed at the mooring site. The model boundary current is also highly v...

Boundary Currents and Watermass Transformation in Marginal Seas

The properties of watermass transformation and the thermohaline circulation in marginal seas with topography and subject to a spatially uniform net surface cooling are discussed. The net heat loss within the marginal sea is ultimately balanced by lateral advection from the open ocean in a narrow boundary current that flows cyclonically around the basin. Heat loss in the interior is offset by lateral eddy fluxes originating in the boundary current. The objectives of this study are to understand better what controls the density of waters formed within the marginal sea, the temperature of the outflowing waters, the amount of downwelling, and the mechanisms of heat transport within the marginal sea. The approach combines heat budgets with linear stability theory for a baroclinic flow over a sloping bottom to provide simple theoretical estimates of each of these quantities in terms of the basic parameters of the system. The theory compares well to a series of eddy-resolving primitive equation model calculations. The downwelling is concentrated within the boundary current in both a diffusive boundary layer near topography and an eddy-driven region on the offshore edge of the boundary current. For most high-latitude regions, the horizontal gyre is expected to transport more heat than does the overturning gyre.

The coherent structures of shallow‐water turbulence: Deformation‐radius effects, cyclone/anticyclone asymmetry and gravity‐wave generation

Over a large range of Rossby and Froude numbers, we investigate the dynamics of initially balanced decaying turbulence in a shallow rotating fluid layer. As in the case of incompressible two-dimensional decaying turbulence, coherent vortex structures spontaneously emerge from the initially random flow. However, owing to the presence of a free surface, a wealth of new phenomena appear in the shallow-water system. The upscale energy cascade, common to strongly rotating flows, is arrested by the presence of a finite Rossby deformation radius. Moreover, in contrast to near-geostrophic dynamics, a strong asymmetry is observed to develop as the Froude number is increased, leading to a clear dominance of anticyclonic vortices over cyclonic ones, even though no beta effect is present in the system. Finally, we observe gravity waves to be generated around the vortex structures, and, in the strongest cases, they appear in the form of shocks. We briefly discuss the relevance of this study to the vortices observed in Jupiters atmosphere.

Mesoscale Variability in Denmark Strait: The PV Outflow Hypothesis*

Abstract The outflow through Denmark Strait shows remarkable mesoscale variability characterized by the continuous formation of intense mesoscale cyclones just south of the sill. These cyclones have a diameter of about 30 km and clear signatures at the sea surface and in currents measured near the bottom. They have a remnant of Arctic Intermediate Water (AIW) in their core. The authors’ hypothesis is that these cyclones are formed by stretching of the high potential vorticity (PV) water column that outflows through Denmark Strait. The light, upper layer of the outflow, the East Greenland Current, remains on the surface in the Irminger Sea, while the dense overflow water descends the east Greenland continental slope. The midlevel waters, mostly AIW, could thus be stretched by more than 100%, which would induce very strong cyclonic relative vorticity. The main test of this new hypothesis is by way of numerical experiments carried out with an isopycnal coordinate ocean model configured to have a marginal sea...

Does Stommel's Mixed Layer “Demon” Work?

Abstract Stommel argued that the seasonal cycle leads to a bias in the coupling between the surface mixed layer and the main thermocline of the ocean. He suggested that a “demon” operated that effectively only allowed fluid at the end of winter to pass from the mixed layer into the main thermocline. In this study, Stommels hypothesis is examined using diagnostics from a time-dependent coupled mixed layer-primitive equation model of the North Atlantic (CME). The influence of the seasonal cycle on the properties of the main thermocline is investigated using two methods. In the first, the rate and timing of subduction into the main thermocline is diagnosed using kinematic methods from the 1° resolution CME fields. In the second, tracer diagnostics of the CME and idealized experiments using a “date” tracer identifying the timing of subduction are performed. Over the subtropical gyre, both approaches generally support Stommels hypothesis that fluid is only transferred from the mixed layer into the main therm...

Circulation around islands and ridges

The circulation in an ocean basin containing an island is studied under nearly geostrophic, beta plane dynamics. The model is a fluid of uniform density driven by wind forcing or sources and sinks of mass at the upper boundary of the flow. The circulation is studied analytically, numerically, as well as in the laboratory through the device of the “sliced cylinder” model for the ocean circulation. Of particular interest is the estimate of the transport between the island and the oceanic basin’s boundary. The model is conceived as relevant to both the wind-driven circulation as well as the circulation of abyssal waters around deep topographic features such as mid-ocean ridge segments. Godfrey’s Island Rule for the transport is rederived in general form and the validity of the original approximation of Godfrey (1989) is examined in a variety of circumstances. In particular, the role of dissipative boundary layers and inertial effects such as vortex shedding are scrutinized to determine their role in determining the net transport around the island. Linear theory in many cases predicts a recirculation on the eastern side of the island, provided the meridional extent of the island is large enough. The existence of the recirculation, containing trapped fluid, is confirmed in both laboratory and numerical experiments and the evolution of the structure of the recirculation is examined as a function of the boundary layer Reynolds number. In both the laboratory and numerical studies, the recirculation predicted by linear theory is joined and then superseded by an inertial recirculation springing from boundary layer separation as the Reynolds number increases past a critical value. Even in the linear limit it is shown that the recirculation region, which is closed in quasigeostrophic theory, is subject to a small leak due to planetary geostrophic effects, which prediction is confirmed in the laboratory. The original island rule of Godfrey yields an estimate of the transport which is surprisingly robust and generally within 75% of the values measured in our numerical experiments. Agreement is moderately good when island western boundary layer transport is used as a basis for comparison. Several cases are discussed, however, in which the assumptions made by Godfrey are violated. One occurs when the frictional boundary layers of the island and the basin boundary overlap. We derive a threshold width for the gap for the case where the island is close to a northern or southern boundary of the basin and show how the transport is increasingly blocked as the gap is reduced. A second case occurs when the island is thin and zonally elongated so that the dissipative effects on the northern and southern boundaries of the island become important. Here the vorticity balance assumed in the simple Island Rule is fundamentally altered, and we extend the Island Rule to account for the new dissipation.

Boundary Current Eddies and Their Role in the Restratification of the Labrador Sea

An idealized model is used to study the restratification of the Labrador Sea after deep convection, with emphasis on the role of boundary current eddies shed near the west coast of Greenland. The boundary current eddies carry warm, buoyant Irminger Current water into the Labrador Sea interior. For a realistic end-of-winter state, it is shown that these Irminger Current eddies are efficient in restratifying the convected water mass in the interior of the Labrador Sea. In addition, it is demonstrated that Irminger Current eddies can balance a significant portion of the atmospheric heat loss and thus play an important role for the watermass transformation in the Labrador Sea.