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Lawrence J. Pratt

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Lawrence J. Pratt

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Whereas long-wave theories have proved successful in describing, the nonlinear effects of single obstructions on narrow flows, the theories can fail when several obstructions are present. This failure is demonstrated using a simple laboratory flow which is predicted by long-wave theory to be unstable, but which is stability in practice by short-wave effects. A nonlinear dispersive theory leads to an interpretation of the short waves as a combination of cnoidal and solitary waves, and upstream control is found for the second (downstream) obstacle only.

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Lawrence J. Pratt

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The slow, horizontal circulation in a deep, hydraulically drained basin is discussed within the context of reduced-gravity dynamics. The basin may have large topographic variations and is fed from above or from the sides by mass sources. Dissipation is provided by bottom friction. To the order of the appromixations made (weak forcing and dissipation), the nonlinear hydraulic control is found to influence only the mean level of the interface separating upper and lower layers, and not the horizontal circulation. For the case of forcing from above the interior basin flow is anticyclonic about closed geostrophic contours and feeds into diffusive boundary layers leading to the draining strait and sill. With sidewall forcing, the interior is motionless and flow is channeled directly to the strait in boundary layers. The latter may circle the basin cyclonically or anticyclonically depending on the source distribution, and a circulation integral is shown to predict the sense of the overall swirl velocity and the presence of eastern and western boundary currents. Modifications caused by the presence of open geostrophic contours or horizontal friction are commented upon. The model is used to predict pathways for deep flow entering the Norwegian Sea from the Greenland Sea and escaping through the Faroe–Shetland Channel. Comparison with the few existing observations are made.

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Jiayan Yang and Lawrence J. Pratt

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The East Greenland Current (EGC) had long been considered the main pathway for the Denmark Strait overflow (DSO). Recent observations, however, indicate that the north Icelandic jet (NIJ), which flows westward along the north coast of Iceland, is a major separate pathway for the DSO. In this study a two-layer numerical model and complementary integral constraints are used to examine various pathways that lead to the DSO and to explore plausible mechanisms for the NIJ’s existence. In these simulations, a westward and NIJ-like current emerges as a robust feature and a main pathway for the Denmark Strait overflow. Its existence can be explained through circulation integrals around advantageous contours. One such constraint spells out the consequences of overflow water as a source of low potential vorticity. A stronger constraint can be added when the outflow occurs through two outlets: it takes the form of a circulation integral around the Iceland–Faroe Ridge. In either case, the direction of overall circulation about the contour can be deduced from the required frictional torques. Some effects of wind stress forcing are also examined. The overall positive curl of the wind forces cyclonic gyres in both layers, enhancing the East Greenland Current. The wind stress forcing weakens but does not eliminate the NIJ. It also modifies the sign of the deep circulation in various subbasins and alters the path by which overflow water is brought to the Faroe Bank Channel, all in ways that bring the idealized model more in line with observations. The sequence of numerical experiments separates the effects of wind and buoyancy forcing and shows how each is important.

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Jiayan Yang and Lawrence J. Pratt

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The overflow of the dense water mass across the Greenland–Scotland Ridge (GSR) from the Nordic Seas drives the Atlantic meridional overturning circulation (AMOC). The Nordic Seas is a large basin with an enormous reservoir capacity. The volume of the dense water above the GSR sill depth in the Nordic Seas, according to previous estimates, is sufficient to supply decades of overflow transport. This large capacity buffers overflow’s responses to atmospheric variations and prevents an abrupt shutdown of the AMOC. In this study, the authors use a numerical and an analytical model to show that the effective reservoir capacity of the Nordic Seas is actually much smaller than what was estimated previously. Basin-scale oceanic circulation is nearly geostrophic and its streamlines are basically the same as the isobaths. The vast majority of the dense water is stored inside closed geostrophic contours in the deep basin and thus is not freely available to the overflow. The positive wind stress curl in the Nordic Seas forces a convergence of the dense water toward the deep basin and makes the interior water even more removed from the overflow-feeding boundary current. Eddies generated by the baroclinic instability help transport the interior water mass to the boundary current. But in absence of a robust renewal of deep water, the boundary current weakens rapidly and the eddy-generating mechanism becomes less effective. This study indicates that the Nordic Seas has a relatively small capacity as a dense water reservoir and thus the overflow transport is sensitive to climate changes.

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Lawrence J. Pratt and Laurence Armi

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The hydraulics of flow contained in a channel and having nonuniform potential vorticity is considered from a general standpoint. The channel cross section is rectangular and the potential vorticity is assumed to be prescribed in terms of the streamfunction. We show that the general computational problem can be expressed in two traditional forms, the first of which consists of an algebraic relation between the channel geometry and a single dependent flow variable and the second of which consists of a pair of quasi-linear differential equations relating the geometry to two dependent flow variables. From these forms we derive a general “branch condition” indicating a merger of different solutions having the same flow rate and energy and show that this condition implies that the flow is critical with respect to a certain long wave. It is shown that critical flow can occur only at the sill in a channel of constant width (with one exception) at a point of width extremum in a flat bottom channel. We also discuss the situation in which the fluid becomes detached from one of sidewalls.

An example is given in which the potential vorticity is a linear function of the streamfunction and the rotation rate is zero, a case which can be solved analytically. When the potential vorticity gradient points downstream, allowing propagation of potential vorticity waves against the flow, multiple pairs of steady states are possible, each having a unique modal structure. Critical control of the higher-mode solutions is primarily over vorticity, rather than depth. Flow reversals arise in some situations, possible invalidating the prescription of potential vorticity.

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Karl R. Helfrich and Lawrence J. Pratt

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The flow in a source-fed f-plane basin drained through a strait is explored using a single-layer (reduced gravity) shallow-water numerical model that resolves the hydraulic flow within the strait. The steady upstream basin circulation is found to be sensitive to the nature of the mass source (uniform downwelling, localized downwelling, or boundary inflow). In contrast, the hydraulically controlled flow in the strait is nearly independent of the basin circulation and agrees very well with the Gill-theory solution obtained using the strait geometry and the numerically determined average potential vorticity in the strait entrance region. This Gill solution, however, gives a unique value of the upstream boundary layer flux splitting that does not agree with any of the full numerical solutions. The coupled basin–strait system is shown to select an average overflow potential vorticity corresponding to the Gill solution with maximum fluid depth on the strait boundaries. This state also corresponds to one of maximal upstream basin potential energy. This result is robust to changes in the basin geometry, strait characteristics, the dissipation parameter (linear drag), and the net mass flux. The nonunique relation between basin conditions and overflow transport is significant with regard to deep overflow transport monitoring. It is shown that the potential vorticity selection leads to overflow, or “weir,” transport relations that are well approximated by the zero potential vorticity theory. However, accurate estimates of the transport can only be obtained if conditions within the strait entrance region, and not the basin, are used.

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Lawrence J. Pratt and Stefan G. Llewellyn Smith

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An asymptotic method for coupling circulations in basins to hydraulically controlled overflows is introduced. The method is applicable when the forcing, dissipation, and coupling with the overflow are weak, in which case the lowest order solution for the homogeneous or 1½-layer model consists of the natural basin modes including gravity, inertia–gravity, potential vorticity, Helmholtz, and steady geostrophic modes. At the next order of approximation, the mode amplitudes are found to vary slowly with time as the result of forcing, dissipation, interior nonlinear mode interactions, and, most importantly, coupling with the overflow. Even when the latter are absent, the overflow dynamics generally introduce nonlinearity.

Although the basin dynamics are assumed linear to lowest order, the overflow is intrinsically nonlinear. To couple the two systems, the overflow model must be adapted to serve as a nonlinear boundary condition on the basin flow. To do so, a rotating-channel model introduced by Whitehead et al. valid for relatively shallow sills is employed. Although not the central focus, corresponding formulations are derived for straits acting as geostrophic controls or which are dominated by bottom drag.

The principle aim of Part I is to derive the evolution equations governing the coupling between basin and sill. Parts II and III of this work contain a number of examples intended to illustrate the general method and provide insight into physical phenomena associated with hydraulically drained, time-dependent flow in deep basins such as those that occur in the Nordic seas.

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Karl R. Helfrich and Lawrence J. Pratt

Abstract

The flow in a source-fed f-plane basin drained through a strait is explored using a single-layer (reduced gravity) shallow-water numerical model that resolves the hydraulic flow within the strait. The steady upstream basin circulation is found to be sensitive to the nature of the mass source (uniform downwelling, localized downwelling, or boundary inflow). In contrast, the hydraulically controlled flow in the strait is nearly independent of the basin circulation and agrees very well with the Gill-theory solution obtained using the strait geometry and the numerically determined average potential vorticity in the strait entrance region. This Gill solution, however, gives a unique value of the upstream boundary layer flux splitting that does not agree with any of the full numerical solutions. The coupled basin–strait system is shown to select an average overflow potential vorticity corresponding to the Gill solution with maximum fluid depth on the strait boundaries. This state also corresponds to one of maximal upstream basin potential energy. This result is robust to changes in the basin geometry, strait characteristics, the dissipation parameter (linear drag), and the net mass flux. The nonunique relation between basin conditions and overflow transport is significant with regard to deep overflow transport monitoring. It is shown that the potential vorticity selection leads to overflow, or “weir,” transport relations that are well approximated by the zero potential vorticity theory. However, accurate estimates of the transport can only be obtained if conditions within the strait entrance region, and not the basin, are used.

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Irina I. Rypina, Igor Kamenkovich, Pavel Berloff, and Lawrence J. Pratt

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This study investigates the anisotropic properties of the eddy-induced material transport in the near-surface North Atlantic from two independent datasets, one simulated from the sea surface height altimetry and one derived from real-ocean surface drifters, and systematically examines the interactions between the mean- and eddy-induced material transport in the region. The Lagrangian particle dispersion, which is widely used to characterize the eddy-induced tracer fluxes, is quantified by constructing the “spreading ellipses.” The analysis consistently demonstrates that this dispersion is spatially inhomogeneous and strongly anisotropic. The spreading is larger and more anisotropic in the subtropical than in the subpolar gyre, and the largest ellipses occur in the Gulf Stream vicinity. Even at times longer than half a year, the spreading exhibits significant nondiffusive behavior in some parts of the domain. The eddies in this study are defined as deviations from the long-term time-mean. The contributions from the climatological annual cycle, interannual, and subannual (shorter than one year) variability are investigated, and the latter is shown to have the strongest effect on the anisotropy of particle spreading. The influence of the mean advection on the eddy-induced particle spreading is investigated using the “eddy-following-full-trajectories” technique and is found to be significant. The role of the Ekman advection is, however, secondary. The pronounced anisotropy of particle dispersion is expected to have important implications for distributing oceanic tracers, and for parameterizing eddy-induced tracer transfer in non-eddy-resolving models.

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