Lawrence J. Pratt

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 In both the laboratory and numerical studies, the recirculation predicted by linear theory is joined and then superseded by an inertial recirculation springing from boundary layer separation as the Reynolds number increases past a critical value.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.

Quantifying transport in numerically generated velocity fields

Abstract Geometric methods from dynamical systems are used to study Lagrangian transport in numerically generated, time-dependent, two-dimensional (2D) vector fields. The flows analyzed here are numerical solutions to the barotropic, β-plane, potential vorticity equation with viscosity, where the partial differential equation (PDE) parameters have been chosen so that the solution evolves to a meandering jet. Numerical methods for approximating invariant manifolds of hyperbolic fixed points for maps are successfully applied to the aperiodic vector field where regions of strong hyperbolicity persist for long times relative to the dominant time period in the flow. Cross sections of these 2D “stable” and “unstable” manifolds show the characteristic transverse intersections identified with chaotic transport in 2D maps, with the lobe geometry approximately recurring on a time scale equal to the dominant time period in the vector field. The resulting lobe structures provide time-dependent estimates for the transport between different flow regimes. Additional numerical experiments show that the computation of such lobe geometries are very robust relative to variations in interpolation, integration and differentiation schemes.

Hydraulic Control of Sill Flow with Bottom Friction

Abstract The hydraulics of strait and sill flow with friction is examined using a reduced gravity model. It is shown that friction moves the critical (or control) point from the sill to a location downstream. If the strait has constant width, the control point lies where the bottom slope is the negative of the drag coefficient Cd. If -Cd exceeds the bottom slope everywhere, the flow cannot be controlled (in the classical sense that energy and flow force are minimized). Friction also decreases the minimum obstacle height required to establish hydraulically controlled flow in the classical laboratory towing experiment. Also, friction greatly encourages the establishment of stationary hydraulic jumps in the lee of the sill and, under certain conditions, gives rise to stationary jumps on the upstream face of the obstacle. Some consequences of these results for deep-ocean overflows are given using the Iceland-Faroe overflow as an example.

Lagrangian Motion and Fluid Exchange in a Barotropic Meandering Jet

Kinematic models predict that a coherent structure, such as a jet or an eddy, in an unsteady flow can exchange fluid with its surroundings. The authors consider the significance of this effect for a fully nonlinear, dynamically consistent, barotropic model of a meandering jet. The calculated volume transport associated with this fluid exchange is comparable to that of fluid crossing the Gulf Stream through the detachment of rings. Although the model is barotropic and idealized in other ways, the transport calculations suggest that this exchange mechanism may be important in lateral transport or potential vorticity budget analyses for the Gulf Stream and other oceanic jets. The numerically simulated meandering jet is obtained by allowing a small-amplitude unstable meander to grow until a saturated state occurs. The resulting flow is characterized by finite-amplitude meanders propagating with nearly constant speed, and the results clearly illustrate the stretching and stirring of fluid particles along the edges of the recirculation regions south of the meander crests and north of the troughs. The fluid exchange and resulting transport across boundaries separating regions of predominantly prograde, retrograde, and recirculating motion is quantified using a dynamical systems analysis. The geometrical structures that result from the analysis are shown to be closely correlated with regions of the flow that are susceptible to high potential vorticity dissipation. Moreover, in a related study this analysis has been used to effectively predict the entrainment and detrainment of particles to and from the jet.

Dynamics of Potential Vorticity Fronts and Eddy Detachment

Abstract The formation and detachment of quasi-geostrophic eddies in a 1½ layer jet is studied using a piecewise uniform potential vorticity model. A vorticity front separates the two pieces, and thus the jet has cusplike character. The evolution of large amplitude initial disturbance (whose origin may be attributed to barotropic-baroclinic instability mechanisms not explicit in our model) is computed by the method of contour dynamics. Certain numerical results such as the steepening of the front prior to eddy detachment can be physically explained in terms of differential mean field advection and vortex induction. Computations are made for a variety of initial conditions and we indicate the amplitude/scale conditions necessary for the detachment of an eddy. The discussion is directed to the problem of the formation of warm/cold rings in the Gulf Stream. The effect of a coast on large perturbations of a jet is also briefly discussed.

Continuous dynamical modes in straits having arbitrary cross sections, with applications to the Bab al Mandab

The continuous dynamical modes of the exchange flow in the Bab al Mandab are computed in an attempt to assess the hydraulic character of the flow at the sill. First, an extended version of the Taylor‐Goldstein equation for long waves that accounts for cross-channel topographic variations, is developed. A series of calculations using idealized background velocity U(z) and buoyancy frequency N(z) are presented to illustrate the effects of simple topographic cross sections on the internal modes and their speeds. Next, hydrographic and direct velocity measurements from April to November 1996 using moored CTDs and a bottom-mounted ADCP are utilized to construct monthly mean vertical profiles of N 2(z) and at the U(z) sill. An analytical approximation of the true topography across the strait is also constructed. The observed monthly mean profiles are then used to solve for the phase speeds of the first and second internal modes. Additional calculations are carried out using a selection of ‘‘instantaneous’’ (2-h average) profiles measured during extremes of the semidiurnal tide. The results are compared with a three-layer analysis of data from the previous year. Many of the authors’ conclusions follow from an intriguing observation concerning the long-wave phase speeds. Specifically, it was nearly always observed that the calculated speeds c21 and c1 of the two waves belonging to the first internal mode obey c21 , Umin , Umax , c1, where Umin and Umax are the minimum and maximum of the velocity profile. An immediate consequence is that neither wave has a critical level. For monthly mean profiles, each of which have Umin , 0 , Umax, the flow is therefore subcritical (the phase speeds of the two waves have opposite signs). For instantaneous profiles this relationship continues to hold, although the velocity profile can be unidirectional. Thus the flow can be critical ( c21 5 0 and/or c1 5 0) or even supercritical (c21 and c1 have the same sign) with respect to the first mode. Similar findings follow for the second baroclinic mode phase speeds (c22 and c 2). The authors conclude that hydraulically critical flow is an intermittent feature, influenced to a great extent by the tides. It is noted that the phase speed pairs for each mode lie very close to Umin and Umax. As suggested by the analysis of idealized profiles, this behavior is characteristic of flows that are marginally stable, perhaps as a result of prior mixing. This suggestion is supported by Richardson number (Ri) profiles calculated from the monthly mean and instantaneous data. Middepth values of Ri were frequently found to be O(1) and sometimes ,1/4, a result consistent with the presence of mixing over portions of the water column.

Dynamics of vorticity fronts

Vorticity fronts can form in a shear flow as the result of fast patches of fluid catching up with slower ones. This process and its consequences are studied in an inviscid two-dimensional model consisting of piecewise uniform-vorticity layers. Calculations using the method of contour dynamics for ‘intrusive’ initial states indicate that the leading edge of the front evolves into a robust structure whose propagation speed can be accounted for by a simple shock-joining theory. Behind the leading edge several different effects can occur depending upon the relative amplitude of the intrusion. These effects include lee-wave generation with possible wave breaking and folding of the front. A critical value of the frontal slope, above which wave breaking occurs, is suggested.

Seasonal overturning circulation in the Red Sea: 1. Model validation and summer circulation

The overturning circulation in the Red Sea exhibits a distinct seasonally reversing pattern and is studied using high-resolution MIT general circulation model simulations. In the first part of this study, the vertical and horizontal structure of the summer overturning circulation and its dynamical mechanisms are presented from the model results. The seasonal water exchange in the Strait of Bab el Mandeb is successfully simulated, and the structures of the intruding subsurface Gulf of Aden intermediate water are in good agreement with summer observations in 2011. The model results suggest that the summer overturning circulation is driven by the combined effect of the shoaling of the thermocline in the Gulf of Aden resulting from remote winds in the Arabian Sea and an upward surface slope from the Red Sea to the Gulf of Aden set up by local surface winds in the Red Sea. In addition, during late summer two processes associated, respectively, with latitudinally differential heating and increased salinity in the southern Red Sea act together to cause the reversal of the contrast of the vertical density structure and the cessation of the summer overturning circulation. Dynamically, the subsurface northward pressure gradient force is mainly balanced by vertical viscosity resulting from the vertical shear and boundary friction in the Strait of Bab el Mandeb. Unlike some previous studies, the three-layer summer exchange flows in the Strait of Bab el Mandeb do not appear to be hydraulically controlled.

Seasonal overturning circulation in the Red Sea : 2. Winter circulation

Author Posting. ©0American Geophysical Union, 2014. This article is posted here by permission of [American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research: Oceans 119 (2014): 2263–2289, doi:10.1002/2013JC009331.

Eddy-Induced Particle Dispersion in the Near-Surface North Atlantic

AbstractThis 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 contr...