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Peter D. Killworth
,
Jeffrey R. Blundell
, and
William K. Dewar

Abstract

The linear stability of two-layer primitive equation ocean rings is considered in the case when the rings are wide compared with a deformation radius, as is usually observed. Asymptotic theory is developed to show the existence of solutions for arbitrarily wide rings, and these solutions can be followed as the rings are made successively narrower. An exponential cubic radial dependence is used for the mean flow, rather than the more usual Gaussian structure. There are two reasons: a Gaussian shape was fully discussed in a previous paper, and a Gaussian has exceptional properties, unlike other power laws. The specific cases of warm and cold Gulf Stream rings are considered in detail. The theory provides an accurate prediction of phase velocity and growth rate for cold rings and a reasonable prediction for warm rings. Solutions in the asymptotic regime have a larger growth rate than other (nonasymptotic) solutions for cold rings, but not for warm rings. Attention is given to the role of the mean barotropic circulation, which had been found in earlier work to have a strong effect on ring stability. There is still evidence for stabilization when the mean flow in the lower layer vanishes, but other features are also involved. In particular, the linear stability of a ring appears to be as sensitive to subtle shape details as it is to the sense of the deep flow. The authors generally find warm co-rotating rings with a cubic exponential form to be unstable, although somewhat less so than counterrotating rings.

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Jossy P. Jacob
,
Eric P. Chassignet
, and
William K. Dewar

Abstract

An analytical and numerical study of isolated coherent vortices and topography is presented. The motivation for this work comes from many observations of vortices influenced in trajectory, propagation, and decay by encounters with midocean ridges, seamounts, and bottom slopes. In particular, analytical predictions relevant to vortex propagation and evolution are compared with numerical results for lenses on bottom slopes and mixed barotropic–baroclinic eddies over a variety of topographies. The latter case includes examination of short-term and long-term behavior. Analytical theories are found to work well for the bottom lenses, and short-term behavior is captured well by a simple theory that emphasizes barotropic dynamics for mixed vortices. The exception for the latter case occurs for counterrotating eddies (i.e., eddies with opposing upper- and lower-layer swirl), for which the evolution is dominated by vortex instability. Long-term evolution has no comparable theory, and the various possibilities for vortex behavior are delineated by means of exploratory numerical work. A specific application to the case of North Brazil current rings, which are observed to move at anomalous rates, is presented.

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William K. Dewar
,
Ya Hsueh
,
Trevor J. McDougall
, and
Dongliang Yuan

Abstract

Many state-of-the-art numerical ocean models calculate pressure using the hydrostatic balance, or an equation derived from it. The proper form of this deceptively simple-looking equation, ∂p/∂z = −(S, T, p) (where notation is standard), is nonlinear in the pressure p. In contrast, most numerical models solve the linear equation ∂p/∂z = −(S, T, z). This modification essentially replaces the total pressure, which includes a time-dependent signal, with an approximate time-independent pressure associated with the depth of a model grid point. In this paper, the authors argue that the inclusion of the total pressure when solving the hydrostatic equation can generate a depth-dependent baroclinic pressure gradient equivalent to a geostrophic velocity of several centimeters per second. Further, this effective velocity can increase with depth and is largest in dynamically important areas like western boundary currents. These points suggest that the full feedback of pressure on density should be included in numerical models. Examples of the effect using oceanic data and output from a typical primitive equation model run are discussed. Finally, algorithms for both rigid-lid and free surface models that explicitly include full pressure are derived, and some related numerical issues are discussed.

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M. Jeroen Molemaker
,
James C. McWilliams
, and
William K. Dewar

Abstract

The California Undercurrent (CUC) flows poleward mostly along the continental slope. It develops a narrow strip of large negative vertical vorticity through the turbulent boundary layer and bottom stress. In several downstream locations, the current separates, aided by topographic curvature and flow inertia, in particular near Point Sur Ridge, south of Monterey Bay. When this happens the high-vorticity strip undergoes rapid instability that appears to be mesoscale in “eddy-resolving” simulations but is substantially submesoscale with a finer computational grid. The negative relative vorticity in the CUC is larger than the background rotation f, and Ertel potential vorticity is negative. This instigates ageostrophic centrifugal instability. The submesoscale turbulence is partly unbalanced, has elevated local dissipation and mixing, and leads to dilution of the extreme vorticity values. Farther downstream, the submesoscale activity abates, and the remaining eddy motions exhibit an upscale organization into the mesoscale, resulting in long-lived coherent anticyclones in the depth range of 100–500 m (previously called Cuddies) that move into the gyre interior in a generally southwestward direction. In addition to the energy and mixing effects of the postseparation instability, there is are significant local topographic form stress and bottom torque that retard the CUC and steer the mean current pathway.

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William K. Dewar
,
Peter D. Killworth
, and
Jeffrey R. Blundell

Abstract

The study of barotropic structure and its effects on oceanic ring stability has yielded seemingly conflicting results. Some studies suggest that the stability of a given ring profile is as sensitive to the sense of the barotropic mode as it is to the vertical shear, while others suggest the vertical shear is the sole dominant effect. Here numerical evidence that supports both views is presented. Warm rings with a favorable barotropic structure can retain their monopole nature while cold rings do not. These results are of interest given the observed long lifetimes of oceanic rings.

As evidence a series of initial value integrations is presented. The initial ring profile consists of an exponential profile decaying as the cube of the radial distance, rather than as the squared decay law of the commonly used Gaussian. The reasons for this choice are that previous studies have examined the Gaussian initial condition extensively and recent analysis suggests the Gaussian profile has special stability properties.

The authors find that the barotropic mode affects the coherence of warm rings, yielding essentially stable, monopolar structures for the case that the initial deep flow is in the same sense as the surface flow (i.e., in the“co-rotating” case), even if the initial underlying ring is linearly unstable. Thus, warm rings remain dominantly monopolar, although an underlying, weak tripole is often seen in the final state. Cold rings in the oceanic parameter regime, on the other hand, experience no such stabilizing effects from deep structure. Quasigeostrophic dynamics fails to capture the stabilization tendencies of warm rings with corotating deep flow, suggesting the effect is related to the finite-amplitude thickness changes of a warm ring. The transition from an unstable, warm monopolar initial state to an effectively stable, warm initial monopolar state is a sensitive function of the barotropic mode. Finally, beta-plane experiments demonstrate the robustness of the primitive equation result.

Thus, it is suggested that the barotropic component of a warm ring can enhance ring stability as a monopole by providing for the existence of a nearby tripolar state to which the ring evolves and thereafter remains. The observed stability of cold rings, however, remains a mystery.

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Dongliang Yuan
,
Zhichun Zhang
,
Peter C. Chu
, and
William K. Dewar

Abstract

Absolute geostrophic currents in the North Pacific Ocean are calculated from the newly gridded Argo profiling float data using the P-vector method for the period of 2004–11. The zonal geostrophic currents based on the Argo profile data are found to be stronger than those based on the traditional World Ocean Atlas 2009 (WOA09) data. A westward mean geostrophic flow underneath the North Equatorial Countercurrent is identified using the Argo data, which is evidenced by sporadic direct current measurements and geostrophic calculations in history. This current originates east of the date line and transports more than 4 × 106 m3 s−1 of water westward in the subsurface northwestern tropical Pacific Ocean. The authors name this current the North Equatorial Subsurface Current. The transport in the geostrophic currents is compared with the Sverdrup theory and found to differ significantly in several locations. Analyses have shown that errors of wind stress estimation cannot account for all of the differences. The largest differences are found in the area immediately north and south of the bifurcation latitude of the North Equatorial Current west of the date line and in the recirculation area of the Kuroshio and its extension, where nonlinear activities are vigorous. It is, therefore, suggested that the linear dynamics of the Sverdrup theory is deficient in explaining the geostrophic transport of the tropical northwestern Pacific Ocean.

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Joseph Schoonover
,
William K. Dewar
,
Nicolas Wienders
, and
Bruno Deremble

Abstract

Robust and accurate Gulf Stream separation remains an unsolved problem in general circulation modeling whose resolution will positively impact the ocean and climate modeling communities. Oceanographic literature does not face a shortage of plausible hypotheses that attempt to explain the dynamics of the Gulf Stream separation, yet a single theory that the community agrees on is missing. In this paper, the authors investigate the impact of the deep western boundary current (DWBC), coastline curvature, and continental shelf steepening on the Gulf Stream separation within regional configurations of the Massachusetts Institute of Technology General Circulation Model. Artificial modifications to the regional bathymetry are introduced to investigate the sensitivity of the separation to each of these factors. Metrics for subsurface separation detection confirm the direct link between flow separation and the surface expression of the Gulf Stream in the Mid-Atlantic Bight. It is shown that the Gulf Stream separation and mean surface position are most sensitive to the continental slope steepening, consistent with a theory proposed by Melvin Stern in 1998. In contrast, the Gulf Stream separation exhibits minimal sensitivity to the presence of the DWBC and coastline curvature. The implications of these results to the development of a “separation recipe” for ocean modeling are discussed. This study concludes adequate topographic resolution is a necessary, but not sufficient, condition for proper Gulf Stream separation.

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Youfang Yan
,
Eric P. Chassignet
,
Yiquan Qi
, and
William K. Dewar

Abstract

Subsurface salinity anomalies propagating between mid- and low latitudes along isopycnal surfaces have been shown to play an important role in modulating ocean and climate variability. In this study, a sustained freshening and southwestward propagation of subsurface salinity anomalies in the northwest Pacific subtropical gyre and its dynamical mechanism are investigated using observations, numerical outputs, and a predictive model. Analyses of the observations show a pronounced subsurface freshening with salinity decreasing about 0.25 PSU near the 24.5-σ θ surface in the northwest Pacific subtropical gyre during 2003–11. This freshening is found to be related to the surface forcing of salinity anomalies in the outcrop zone (25°–35°N, 130°–160°E). A predictive model based on the assumption of salinity conservation along the outcrop isopycnals is derived and used to examine this surface-forcing mechanism. The resemblance between the spatial structures of the subsurface salinity derived from the predictive model and from observations and numerical outputs suggests that subsurface salinity anomalies are ventilated over the outcrop zone. A salinity anomaly with an amplitude of about 0.25 PSU generated by the surface forcing is subducted in the outcrop zone and then propagates southwestward, accompanied by potential vorticity anomalies, to the east of Luzon Strait (~15°N) in roughly one year. When the anomalies reach 15°N, they turn and move gradually eastward toward the central Pacific, associated with an eastward countercurrent on the southern subtropical gyre.

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Andrew Mc C. Hogg
,
William K. Dewar
,
Pavel Berloff
,
Sergey Kravtsov
, and
David K. Hutchinson

Abstract

Small-scale variation in wind stress due to ocean–atmosphere interaction within the atmospheric boundary layer alters the temporal and spatial scale of Ekman pumping driving the double-gyre circulation of the ocean. A high-resolution quasigeostrophic (QG) ocean model, coupled to a dynamic atmospheric mixed layer, is used to demonstrate that, despite the small spatial scale of the Ekman-pumping anomalies, this phenomenon significantly modifies the large-scale ocean circulation. The primary effect is to decrease the strength of the nonlinear component of the gyre circulation by approximately 30%–40%. This result is due to the highest transient Ekman-pumping anomalies destabilizing the flow in a dynamically sensitive region close to the western boundary current separation. The instability of the jet produces a flux of potential vorticity between the two gyres that acts to weaken both gyres.

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Andrew Mc C. Hogg
,
William K. Dewar
,
Peter D. Killworth
, and
Jeffrey R. Blundell

Abstract

The design and implementation of a midlatitude basin-scale coupled climate model are described. The development of the model is motivated by the clear indications of important low-frequency midlatitude ocean variability in ocean-only models and the lack of the same in coupled climate models. Currently, the best comprehensive coupled climate models run at resolutions far coarser than those needed to model intrinsic ocean variability. The model presented here is an attempt to explicitly include ocean eddies within the framework of an idealized climate setting. It is proposed that the model will help resolve how intrinsic ocean variability is altered by coupling and the extent to which such variability may force the climate. The objective of this paper is to describe the theory behind the model formulation and its implementation.

The basic model consists of a quasigeostrophic channel atmosphere coupled to a simple, rectangular quasigeostrophic ocean. Heat and momentum exchanges between the ocean and the atmosphere are mediated via mixed-layer models, and the system is driven by steady, latitudinally dependent incident solar radiation. Model spinup is described, some basic descriptors of the solution are discussed, and it is argued that the model exhibits skill in capturing essential features of the midlatitude climate system.

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