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Ping-Tung Shaw

Abstract

The evolution and propagation of Gulf Stream warm core rings in a flat-bottom, β-plane ocean are studied using a three-dimensional primitive equation model. Rings are produced by a heat source that is turned on and off slowly in the upper 750 m of the water column. Besides an anticyclone in the upper ocean, a deep cyclone is generated below the surface eddy. In the first 30 days, the surface anticyclone moves slowly southwestward because of β dispersion and vorticity advection. In waters 4000 m deep, both the anticyclone and the cyclone intensify, and a barotropic vortex pair is formed. The vortex pair moves rapidly southeastward. Its propagation becomes steady and eastward after the cyclone sheds an eddy. The cyclone in the vortex pair moves away from the ring at the end of 6 months, and both vortices begin to propagate westward separately. Fluid to a depth of 3000 m, much deeper than that of forcing, is transported by the ring.

The formation of a strong vortex pair is associated with the generation of relative vorticity in both vortices by unstable waves of the second azimuthal mode. In strong rings, the increase in vorticity could produce rapid propagation. Eastward propagation is a result of change in planetary vorticity and loss of relative vorticity during cyclone splitting. In waters shallower than 4000 m, the vortex pair is less stable and more vorticity is lost by cyclone splitting. There is still a rapid movement toward the south but the eastward propagation is weak. Rings in waters shallower than 4000 m are likely to remain on the continental slope off the U.S. East Coast and induce large amounts of momentum and mass transfer over the continental margin.

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Ping-Tung Shaw and S. Divakar

Abstract

Numerical experiments were carried out to simulate the generation of topographic waves by a Gulf Stream ring over the continental margin in a stratified ocean on an f-plane. The study was aimed at understanding the combined effect of density advection and bottom topography on the flow field. The momentum equation is linear, and nonlinearity is introduced in the density equation. The mechanism of wave generation was investigated by turning on and off the nonlinear density advection and by changing the strength of the ring and bottom topography.

The results show that topographic waves are generated by advection of density in a ring over a sloping bottom. The vorticity associated with the swirl velocity of a ring is less important during wave generation. The strength of a ring affects the wave amplitude; in the case of a strong ring, self-advection of density may be induced at the surface. However, the generation and propagation of topographic waves are independent of the strength of the ring. Waves of the observed amplitude can be generated by this process over the continental slope and upper rise of the Mid-Atlantic Bight.

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Ping-Tung Shaw and Chern-Yuan Peng

Abstract

The propagation of linear barotropic Rossby waves is investiaged numerically over a one-dimensional topography similar to the continental rise and slope. A point source is used to generate waves with periods from 4 to 36 days. The resulting distribution of streamfunction and kinetic energy density is examined.

The result show that the propagating of tropographic Rossby waves depends on the wave period. Over the continental rise, waves are generated mainly by low-frequency disturbances at periods of about a month. In addition, the continental slope is a good insulator to these waves. Therefore, deep ocean circulation will not influence motions on the continental shelf. At 36 and 15 days, the steep continental slope is a wave guide, and regions of high energy density generated by local sources may be found. Energy of 36-day waves over the continental shelf cannot penetrate the steep slope. Although waves of periods shorter than a week may reach the lower slope, these waves are trapped by the coast, similar to shelf waves, Consequently, the deep ocean circulation is hardly influenced by motions on the shelf and slope.

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Ping-Tung Shaw and H. Thomas Rossby

Abstract

Downstream velocity relative to the axis of the Gulf Stream is examined through the use of data from SOFAR floats. The speed calculated from the position of the floats along constant pressure surfaces is expressed in terms of a transformed cross-stream coordinate given by temperature, which is telemetered from the floats. The result is a distribution of downstream velocity unaffected by meanders from Cape Hatteras to 46°W. The speed at 700 m is about 75 cm s−1 west of 57°W and decreases sharply to 40 cm s−1 to the east. In the deep water from 1300 to 2200 m, the core speed is 35 cm s−1 between 65° and 50°W, if it is present. The flow in the Gulf Stream may be disturbed by local processes, which are frequently observed in satellite imagery. Examples am shingles, ring formation and meanders.

Although SOFAR floats are quasi-Lagrangian (isobaric) devices, the float data can give a Lagrangian description of the Gulf Stream. Above the main thermocline, a current coinciding with the tilting isotherms from Cape Hatteras to 46°W implies that water is efficiently transported downstream. In the deep ocean, water is accelerated by the surface Stream off Cape Hatteras and is at times transported downstream by the deep flow thus formed. The New England Seamounts can block this deep flow. There is little evidence of a deep current and thus, water transport east of the Seamounts.

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Shenn-Yu Chao and Ping-Tung Shaw

Abstract

Steady drift of an ice cover produces a vertically sheared current in the upper ocean of the Arctic. Under the ice cover, mesoscale shallow brine and freshening sources generate submerged anticyclones and cyclones, respectively. A submerged eddy extending deep into the water column experiences differential advections by the vertically sheared current. Interaction between subsurface eddies and the sheared current is examined using a three-dimensional numerical model in a coordinate system moving with the ice. The initial salinity field is in geostrophic balance with the sheared current, and a pulse of brine or freshening forcing produces an anticyclone or a cyclone. In a coordinate system moving with the ice, eddies are in a vertically sheared backward ambient current. To an observer looking into the direction of the backward ambient current, eddies move with the current and deflect to the right (left) for counterclockwise (clockwise) rotating eddies in both hemispheres. The lower half of the eddy always moves faster. The lateral movement can be explained by the Kutta–Zhukhovski lift theorem. Differential advection produces eddy tilting and entails the development of a narrow jet following the moving eddy. The jet reduces eddy straining and tilting, and eddies disperse in cases of sizeable tilts. Driven by a vertically sheared current, cyclones are short-lived compared with anticyclones because the lateral movement of a cyclone exposes the lower part of the eddy into waters of weaker stratification. The results help explain the predominance of anticyclonic eddies under the Arctic ice.

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Shenn-Yu Chao and Ping-Tung Shaw

Abstract

Ocean responses to a single brine source under ice and over a sloping bottom are investigated in numerical experiments. Brine sources considered herein are often much stronger than that anticipated from a single seawater freezing event in a time span of about 10 days. The authors have no evidence that such strong sources exist in the ocean, but the consequent heton-like eddies manifest interesting features over a bottom slope. The numerical model contains a stratified ocean capped by an ice layer. The convection initially generates a top cyclone and a submerged anticyclone vertically stacked together. Under sea ice, the top cyclone dissipates in time and often breaks up into several distinct cyclonic vortices. Through heton-type couplings, the breakaway shallow cyclones are often able to tear the underlying anticyclone apart to form distinct anticyclones. Top cyclones are eventually annihilated by ice-exerted friction, leaving submerged anticyclones in stable existence. Fission from a pair of vertically stacked baroclinic vortices is a fundamental process associated with a strong brine source under sea ice. A bottom slope generally enhances fission, often increasing the number of subsurface anticyclones or causing the resulting anticyclones to break farther away from the source. The slope enhancement is consistent with the potential vorticity conservation requirement and a changing Rossby radius with water depths. The foregoing conclusions remain the same in cases with a stationary brine source moving rigidly with a uniform current. Under the less likely scenario of a stationary source embedded in a mean flow, brine waters spread downstream and become less effective in producing distinct vortices. Granting the occurrence of strong baroclinic vortices under sea ice, the preferable increase of anticyclones at depths may help explain the overwhelming predominance of submerged anticyclones in the ice-covered Arctic Ocean.

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Shenn-Yu Chao and Ping-Tung Shaw

Abstract

The lateral injection of dense outflow into an Arctic baroclinic current though a submarine canyon is examined using a three-dimensional nonhydrostatic numerical model. The oceanographic setting in this model retains essential features of the active outflow region from the Chukchi shelf to the Beaufort Sea. The coastal ocean mainly consists of a continental shelf and slope region indented by a submarine canyon. The ocean surface is partially frictional to account for the ice-exerted friction. A boundary current is bounded to the left by the continental slope and, in the most interesting cases, is bounded below by a reverse undercurrent. Dense water is released from the upper canyon and produces a sinking plume that follows the canyon axis seaward. As it approaches the maximum sinking depth, the subsurface plume moves out of the canyon and turns to the right to become a right-bounded undercurrent over the continental slope. The right turn generates anticyclonic vorticity. The sinking motion also induces a surface cyclone trapped over the canyon. If the centers of the top cyclone and subsurface anticyclone are sufficiently separated horizontally, the pair can form a self-propagating heton moving seaward from the canyon. Thus the heton shedding is an efficient way to produce halocline anticyclones that are known to populate the Beaufort Sea. Shedding is most active for fast release of dense water and if the maximum sinking depth is in the lower halocline. Heton shedding can occur in the absence of a boundary current. A unidirectional boundary current enhances heton shedding. An undercurrent provides background negative vorticity to the subsurface anticyclone and moves the anticyclone in the direction favorable for the seaward heton propagation. In consequence, the addition of an undercurrent facilitates much more efficient heton shedding.

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Ping-Tung Shaw and G. T. Csanady

Abstract

Current meter data taken during a one-year period over the continental slope and upper rise in three cross-isobath sections have been examined for energy distribution, coherence, and phase propagation of topographic waves. A peak at 15 days is present in the energy preserving spectrum of the near-bottom currents on the rise and slope. Phase propagation is offshore, and little energy is found in reflected waves. These results are consistent with earlier findings on the lower rise at Site D. Onshore energy flux associated with topographic waves is deflected by the continental slope, and wave energy propagates along isobaths on the lower slope and upper rise. The along-isobath coherence scale is about 200 km. The waves are probably generated by meanders in the Gulf Stream.

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Ping-Tung Shaw and G. T. Csanady

Abstract

Bottom water movement on the continental shelf is modeled by the nonlinear interaction between long-shore bottom geostrophic flow and the density field. Bottom geostrophic velocity, subject to linear steady momentum equations with linear bottom friction, can be generated by along-isobath density variations over a sloping bottom. At the same time, the density field is slowly adveced by the velocity field. Away from boundary layers, the interplay is governed by Burgers' equation, which shows the formation and self-propulsion of strong density gradients along an isobath. The direction of propagation of a dense water blob is to have shallow water on the right- (left-) hand side facing downstream in the Northern (Southern) Hemisphere. The propagation of a light water blob is opposite to that of a dense water blob.

The problem is further investigated by solving the governing equations numerically. Under forcing by localized surface cooling, the flow in the mid-shelf region shows the characteristics of the solution a Burgers' equation. A coastal buoyancy source generates a shore-hugging plume, slowly moving along the coast in the direction of Kelvin wave propagation. The flow associated with coastal dense water discharge has different characteristics: the dense water moves away from the coast initially. The accumulation of dense water on the mid-shelf then invokes the same self-advection process as found for surface cooling.

The theory sheds light on bottom water movements in the Adriatic Sea over the Antarctic continental shelf, and in the Middle Atlantic Bight. It also describes the dispersion of river water and dense water outflow an the shelf. The model results agree qualitatively with the observed distribution of bottom water and give correct order-of-magnitude estimates for the propagation speed of density perturbations.

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Shenn-Yu Chao and Ping-Tung Shaw

Abstract

Initialization and development of cyclonic and anticyclonic eddies under the influence of a frictional surface, as with Arctic eddies under ice cover, are examined both analytically and numerically using a three-dimensional numerical model. Solutions of the linear Rossby adjustment problem show that energy released from an initial density anomaly in the barotropic mode and the first few baroclinic modes destabilizes the numerical computation for small Arctic eddies. This result suggests the necessity of slow spinup to reduce energy release in these modes and sufficient vertical resolution to resolve higher baroclinic modes. The numerical computation shows that in an initially stratified and motionless ocean, a surface cyclone (an anticyclone) is produced by a localized salinity source (sink). In open waters, the stable flow field consists of a vertically aligned pair of counterrotating eddies. When dampened by surface friction, an eddy pair produced by deep forcing has features dissimilar to the submerged eddies under Arctic ice. In the case, of shallow forcing with depth scales about 100 m or so, surface friction can quickly eliminate the top eddy while leaving the lower eddy intact. This leads to the counterintuitive results that warming or freshening generates a submerged cyclone, while cooling or brine ejection produces a submerged anticyclone. The resulting eddies have many attributes of observed Arctic eddies under sea ice.

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