Showing papers on "Pressure gradient published in 1994"

Stability, accuracy and efficiency of a semi-implicit method for three-dimensional shallow water flow☆

Abstract: The stability analysis, the accuracy and the efficiency of a semi-implicit finite difference scheme for the numerical solution of a three-dimensional shallow water model are presented and discussed. The governing equations are the three-dimensional Reynolds equations in which pressure is assumed to be hydrostatic. The pressure gradient in the momentum equations and the velocities in the vertically integrated continuity equation are discretized with the θ-method, with θ being an implicitness parameter. It is shown that the method is stable for 1 2 ≤ θ ≤ 1, unstable for θ 1 2 and highest accuracy and efficiency is achieved when θ = 1 2 . The resulting algorithm is mass conservative and naturally allows for the simulation of flooding and drying of tidal flats.

The Pressure Gradient Conundrum of Sigma Coordinate Ocean Models

Abstract: Much has been written of the error in computing the horizontal pressure gradient associated with sigma coordinates in ocean or atmospheric numerical models. There also exists the concept of “hydrostatic inconsistency” whereby, for a given horizontal resolution, increasing the vertical resolution may not be numerically convergent. In this paper, it is shown that the differencing scheme cited here, though conventional, is not hydrostatically inconsistent; the sigma coordinate, pressure gradient error decreases with the square of the vertical and horizontal grid size. Furthermore, it is shown that the pressure gradient error is advectively eliminated after a long time integration. At the other extreme, it is shown that diagnostic calculations of the North Atlantic Ocean using rather coarse resolution, and where the temperature and salinity and the pressure gradient error are held constant, do not exhibit significant differences when compared to a calculation where horizontal pressure gradients are c...

A turbulent equilibrium boundary layer near separation

Abstract: The experimental results for an equilibrium boundary layer in a strong adverse pressure gradient flow are reported. The measurements show that similarity in the mean flow and the turbulent stresses has been achieved over a substantial streamwise distance where the skin friction coefficient is kept at a low, constant level. Although the Reynolds stress distribution across the layer is entirely different from the flow at zero pressure gradient, the ratios between the different turbulent stress components were found to be similar, showing that the mechanism for distributing the turbulent energy between the different components remains unaffected by the mean flow pressure gradient. Close to the surface the gradient of the mixing length was found to increase from Kl ≈ 0.41 to Kl ≈ 0.78, almost twice as high as for the zero pressure gradient case. Similarity in the triple correlations was also found to be good. The correlations show that there is a considerable diffusion of turbulent energy from the central part of the boundary layer towards the wall. The diffusion mechanism is caused by a second peak in the turbulence production, located at y/δ ≈ 0.45. This production was for the present case almost as strong as the production found near the wall. The energy budget for the turbulent kinetic energy also shows that strong dissipation is not restricted to the wall region, but is significant for most of the layer.

Averaged equations for inviscid disperse two-phase flow

Abstract: Averaged equations governing the motion of equal rigid spheres suspended in a potential flow are derived from the equation for the probability distribution. A distinctive feature of this work is the derivation of the disperse-phase momentum equation by averaging the particle equation of motion directly, rather than the microscopic equation for the particle material. This approach is more flexible than the usual one and leads to a simpler and more fundamental description of the particle phase. The model is closed in a systematic way (i.e. with no ad hoc assumptions) in the dilute limit and in the linear limit. One of the closure quantities is related to the difference between the gradient of the average pressure and the average pressure gradient, a well-known problem in the widely used two-fluid engineering models. The present result for this quantity leads to the introduction of a modified added mass coefficient (related to Wallis's ‘exertia’) that remains very nearly constant with changes in the volume fraction and densities of the phases. Statistics of this coefficient are provided and exhibit a rather strong variability of up to 20% among different numerical simulations. A detailed comparison of the present results with those of other investigators is given in § 10.As a further illustration of the flexibility of the techniques developed in the paper, in Appendix C they are applied to the calculation of the so-called ‘particle stress’ tensor. This derivation is considerably simpler than others available in the literature.

Structure of turbulent boundary layers on smooth and rough walls

Abstract: The structure of turbulent boundary layers which develop with zero pressure gradient on a smooth wall and a k-type rough wall was examined using arrays of X-wires. Although the data were obtained only on two orthogonal planes, the technique provides some information on the three-dimensionality of the large-scale structures. The major effect of the roughness is to tilt the inclination of the structures towards the wall-normal direction. This is caused by the reduced damping of the wall-normal velocity fluctuations close to the rough surface and the break-up of structures whose scales are comparable to the size of the roughness elements. Both effects cause a reduction in the streamwise lengthscales, as suggested by all the measured two-point correlations. The correlations also show that the roughness tends to reduce the overall anisotropy of the large-scale motion. There is evidence to suggest that the magnitude of the vorticity field is larger over the rough wall.

The unit response of groundwater outflow from a hillslope

Abstract: Subsurface flow from a hillslope can be described by hydraulic groundwater theory, as formulated by the Boussinesq equation. Solution of its linear version brings out some of the essential features of this phenomenon. Arbitrary inputs can be accommodated by simple convolution of the sudden drawdown problem. The relative magnitude of the driving mechanisms, namely the streamwise pressure gradient, resulting in diffusion and gravity (i.e., slope), resulting in advection, can be determined by a simple dimensionless parameter.

Peristaltic flow of a second-order fluid in tubes

Abstract: We have analyzed the mechanics of peristaltic pumping of a non-Newtonian fluid through an axisymmetric conduit. The material was represented by the constitutive equation for a second-order fluid. A perturbation series (to second order) in dimensionless wavenumber of an infinite harmonic traveling wave was used to obtain explicit forms for the velocity field and a relation between the flow rate and the pressure gradient, in terms of the Reynolds number, the dimensionless non-Newtonian parameters, and the occlusion. Results were compared with other studies, in both Newtonian and non-Newtonian cases. Also, we have shown that the flow of a Newtonian fluid through a rigid, axisymmetric tube with an axial, sinusoidal variation of radius is a special case of this analysis.

Couple-stresses in peristaltic transport of fluids

Abstract: Peristaltic pumping by a sinusoidal travelling wave in the walls of a two-dimensional channel filled with a viscous incompressible couple-stress fluid, is investigated theoretically. A perturbation solution is obtained, which satisfies the momentum equation for the case in which the amplitude ratio (wave amplitude:channel half width) is small. The results show that the mean axial velocity decreases with increasing couple-stress parameter eta . The phenomenon of reflux (mean flow reversal) is discussed. A reversal of velocity in the neighbourhood of the centre line occurs when the pressure gradient is greater than that of the critical reflux condition. It is found that the critical reflux pressure increases with the couple-stress parameter. Numerical results are reported for various values of the physical parameters of interest.

Effects of Free-Stream Turbulence and Adverse Pressure Gradients on Boundary Layer Transition

Abstract: Boundary layer measurements are presented through transition for six different free- stream turbulence levels and a complete range of adverse pressure gradients for attached laminar flow. Measured intermittency distributions provide an excellent similarity basis for characterizing the transition process under all conditions tested when the Narasimha procedure for determining transition inception is used. This inception location procedure brings consistency to the data. Velocity profiles and integral parameters are influenced by turbulence level and pressure gradient and do not provide a consistent basis

Control of airway pressure during mechanical ventilation

Abstract: A endotracheal tube for patient ventilation is modified to permit measurement of pressure at the patient trachea by providing a chamber in the end of the ET tube to be located in the patient, airway. This chamber has a highly pliant external wall with a degree of redundancy and is connected to a pressure measuring device exterior of the patient by a lumen in the wall of the ET tube. In addition, apparatus for controlling airway pressure during exhalation comprises valve means connected via a first inlet to an exhalation tube from a patient airway, connected to a source of negative pressure through an outlet and having a second inlet with a variable flow control means for controlling the flow of gas therethrough. Gas pressure is controlled within the valve by varying the pressure gradient between the upstream and downstream sides of the second inlet so that it equals the pressure gradient between the patient airway and the downstream side of the second inlet.

Thermal generation of cosmological seed magnetic fields in ionization fronts

Abstract: Quasar spectra indicate that the intergalactic medium (IGM) was reionized at some redshift z≥ 5, probably due to discrete sources of ionizing photons like QSOs and young galaxies. In such a circumstance, ionization fronts will expand away from these sources until they percolate and encompass a substantial part of the IGM. The pressure gradients in the ionization front acting on electrons can lead to a thermally generated electric field. This field will have a non-vanishing curl and hence imply a growing magnetic field, provided the pressure gradient in the front is not parallel to the density gradient. Such a situation obtains naturally in the cosmological context because the IGM harbours primordial (growing) density fluctuations whose density gradients are not correlated with the pressure gradients produced by an arbitrarily placed ionizing source. In this process, magnetic fields can be thermally generated, over a good fraction of the IGM. In particular, they can have strengths ~3 × 10-20 G on galactic scales, and can serve as seed fields for further amplification by the galactic dynamo.

Continuous non-invasive blood pressure monitoring system

Abstract: A sensor for sensing blood pressure within an underlying artery as the underlying artery is compressed includes a transducer and a compressible sidewall. The transducer senses blood pressure of blood pressure pulses as the pulses travel beneath the sensor. As each blood pressure pulses crosses an edge of the sensor, each pulse exerts a force on the sensor in a direction parallel to the underlying artery. Tissue surrounding the underlying artery also exerts a force. The compressible sidewall is distant from the transducer and engages tissue surrounding the underlying artery. The compressible side wall neutralizes the force exerted by the tissue surrounding the underlying artery and dampens the force parallel to the underlying artery so that a substantially zero pressure gradient exists across the transducer.

Estimating seismic velocities at ultrasonic frequencies in partially saturated rocks

Abstract: Seismic velocities in rocks at ultrasonic frequencies depend not only on the degree of saturation but also on the distribution of the fluid phase at various scales within the pore space. Two scales of saturation heterogeneity are important: (1) saturation differences between thin compliant pores and larger stiffer pores, and (2) differences between saturated patches and undersaturated patches at a scale much larger than any pore. We propose a formalism for predicting the range of velocities in partially saturated rocks that avoids assuming idealized pore shapes by using measured dry rock velocity versus pressure and dry rock porosity versus pressure. The pressure dependence contains all of the necessary information about the distribution of pore compliances for estimating effects of saturation at the finest scales where small amounts of fluid in the thinnest, most compliant parts of the pore space stiffen the rock in both compression and shear (increasing both P- and S-wave velocities) in approximately the same way that confining pressure stiffens the rock by closing the compliant pores. Large-scale saturation patches tend to increase only the high-frequency bulk modulus by amounts roughly proportional to the saturation. The pore-scale effects will be most important at laboratory and logging frequencies when pore-scale pore pressure gradients are unrelaxed. The patchy-saturation effects can persist even at seismic field frequencies if the patch sizes are sufficiently large and the diffusivities are sufficiently low for the larger-scale pressure gradients to be unrelaxed.

A model for characterization of a vortex pair formed by shock passage over a light-gas inhomogeneity

Abstract: This work investigates the two-dimensional flow of a shock wave over a circular light-gas inhomogeneity in a channel with finite width. The pressure gradient from the shock wave interacts with the density gradient at the edge of the inhomogeneity to deposit vorticity around the perimeter, and the structure rolls up into a pair of counter-rotating vortices. The aim of this study is to develop an understanding of the scaling laws for the flow field produced by this interaction at times long after the passage of the shock across the inhomogeneity. Numerical simulations are performed for various initial conditions and the results are used to guide the development of relatively simple algebraic models that characterize the dynamics of the vortex pair, and that allow extrapolation of the numerical results to conditions more nearly of interest in practical situations. The models are not derived directly from the equations of motion but depend on these equations and on intuition guided by the numerical results. Agreement between simulations and models is generally good except for a vortex-spacing model which is less satisfactory. A practical application of this shock-induced vortical flow is rapid and efficient mixing of fuel and oxidizer in a SCRAMJET combustion chamber. One possible injector design uses the interaction of an oblique shock wave with a jet of light fuel to generate vorticity which stirs and mixes the two fluids and lifts the burning jet away from the combustor wall. Marble proposed an analogy between this three-dimensional steady flow and the two-dimensional unsteady problem of the present investigation. Comparison is made between closely corresponding three-dimensional steady and two-dimensional unsteady flows, and a mathematical description of Marble's analogy is proposed.

A comparison of second‐order and fourth‐order pressure gradient algorithms in a σ‐co‐ordinate ocean model

Abstract: In stratified three-dimensional models the use of a boundary-fitted vertical co-ordinate is known to produce errors in the horizontal pressure gradient calculation near steep topography. The error is due to the splitting of the horizontal pressure gradient term in each of the momentum equations into two parts and the subsequent incomplete cancellation of the truncation errors of those parts. In order to minimize these pressure gradient errors, a fourth-order-accurate pressure gradient calculation has been implemented and installed in SPEM, a three-dimensional primitive equation ocean model. The stability and accuracy of the new scheme are compared with those of the original second-order-accurate model in a series of calculations of unforced flow in the vicinity of an isolated seamount. The new scheme is shown to have much smaller pressure gradient errors over a wide range of parameter space as well as a greater parametric domain of numerical stability.

The Subinertial Mixed Layer Approximation

Abstract: The density of the mixed layer is approximately uniform in the vertical but has dynamically important horizontal gradients. These nonuniformities in density result in a vertically sheared horizontal pressure gradient. Subinertial motions balance this pressure gradient with a vertically sheared velocity. Systematic incorporation of shear into a three-dimensional mixed layer model is both the goal of the present study and its majority novelty. The sheared flow is partitioned between a geostrophic response and a frictional, ageostrophic response. The relative weighting of them two components is determined by a nondimensional parameters μ≡1/fτU, where τU is the timescale for vertical mixing of momentum and f−1 is the inertial timescale. If μ is of order unity, then the velocity has vertical shear at leading order. Differential advection by this shear flow will tilt over vertical isosurfaces of heat and salt so as to “unmix” or “restratify” the mixed layer. The unmixing process is balanced by intermit...

Observations of purely elastic instabilities in the Taylor-Dean flow of a Boger fluid

Abstract: An experimental and theoretical investigation of the stability of the viscoelastic flow of a model Boger fluid between rotating cylinders with an applied pressure gradient is presented. In our theoretical study, a linear stability analysis based on the Oldroyd-B fluid model which predicts the critical conditions and the structure of the vortex flow at the onset of instability is developed. Our results reveal that certain non-axisymmetric modes are more unstable than the previously studied axisymmetric mode when the shearing by the cylinder rotation is the dominant flow-driving force. This is consistent with recent results presented by Beris & Avgousti (1992) on the stability of elastic Taylor–Couette flow. On the other hand, the axisymmetric mode is more unstable when the pressure gradient becomes dominant. Furthermore, we investigate the mechanism of purely elastic Taylor–Dean instability with respect to non-axisymmetric disturbances through an examination of the disturbance-energy equation. It is found that the mechanism of the elastic Taylor–Dean instability is associated with the coupling between the disturbance polymeric stresses due to the azimuthal variation of the disturbance flow and the base state velocity gradients. In our experimental study, evidence of non-inertial, cellular instabilities in the Taylor–Dean flow of a well-characterized polyisobutylene/polybutene Boger fluid is presented. A stationary, meridional obstruction is placed between independently rotating, concentric cylinders to generate an azimuthal pressure gradient in opposition to the shearing flow. Flow visualization experiments near the critical conditions show the transition from purely azimuthal flows to secondary vortex flows, and the development of evenly spaced, banded vortex structures. The critical wavenumber obtained from spectral image analysis of the visualizations, and the critical Deborah number are presented for various ratios of the pressure gradient to the shear driving force. Although there is a quantitative discrepancy between data and theory, the qualitative trends in the data are in agreement with our theoretical predictions. In addition, laser-Doppler velocimetry (LDV) measurements show that the instability is a stationary mode when the pressure gradient is the dominant flow-driving force, while it is an oscillatory instability when the shearing is dominant, again as predicted by the theory.

Dynamics of low to high (‘‘L’’ to ‘‘H’’) confinement bifurcation: Poloidal flow and ion pressure gradient evolution

Abstract: A self‐consistent model of the low to high (‘‘L’’ to ‘‘H’’) transition is derived from coupled nonlinear envelope equations for the fluctuation level and radial electric field shear, Er’, as determined by ion pressure gradient, ∇Pi, and poloidal flow. These equations extend the phase transition model of the L to H bifurcation by including ∇Pi effects. In this model, the transition occurs when the turbulence drive is large enough to overcome the damping of the total E×B flow. Near the critical power for transition, poloidal flow shear dominates Er’, but at high power, ∇Pi gives the main contribution. The inclusion of ∇Pi also introduces a quenched fluctuation state that is accessible at high power and may be the experimentally observed H‐mode state for P≫Pcrit. In this state, the radial electric field is determined only by ∇Pi because no fluctuation energy is available to produce a turbulent Reynolds stress.

Pore pressure profiles in fractured and compliant rocks1

Abstract: Fluid permeability in fractured rocks is sensitive to pore-pressure changes. This dependence can have large effects on the flow of fluids through rocks. The authors define the permeability compliance [gamma] = 1/k([partial derivative]k/[partial derivative]p[sub p])[sub pc], which is the sensitivity of the permeability k to the pore pressure p[sub p] at a constant confining pressure p[sub c], and solve the specific problems of constant pressure at the boundary of a half-space, a cylindrical cavity and a spherical cavity. The results show that when the magnitude of permeability compliance is large relative to other compliances, diffusion is masked by a piston-like pressure profile. The authors expect this phenomenon to occur in highly fractured and compliant rock systems where [gamma] may be large. The pressure profile moves rapidly when fluids are pumped into the rock and very slowly when fluids are pumped out. Consequently, fluid pressure, its history and distribution around injection and production wells may be significantly different from pressures predicted by the linear diffusion equation. The propagation speed of the pressure profile, marked by the point where [partial derivative]p[sub p]/[partial derivative]x is a maximum, decreases with time approximately as [radical]t, and the amplitude of the profile also dissipates with timemore » (or distance). The effect of permeability compliance can be important for fluid injection into and withdrawal from reservoirs. For example, excessive drawdown could cause near-wellbore flow suffocation. Also, estimates of the storage capacity of reservoirs may be greatly modified when [gamma] is large. The large near-wellbore pressure gradients caused during withdrawal by large [gamma] can cause sanding and wellbore collapse due to excessive production rates.« less

Turbulence structural changes for a three-dimensional turbulent boundary layer in a 30° bend

Abstract: A three-dimensional turbulent boundary layer (3DTBL) was generated on the floor of a low-speed wind tunnel by the imposition of a cross-stream pressure gradient using a 30° bend in the horizontal plane. The surface streamlines were deflected by as much as 22° relative to the local tunnel centreline. Downstream of the bend, the 3DTBL gradually relaxed towards a 2DTBL; this was an impulse-and-recovery experiment which focused on the outer layer. Mean velocities were measured with a three-hole yawmeter and turbulence quantities, which included the Reynolds-stress tensor and the triple products, were measured with a cross-wire hot-wire anemometer. The experiment isolated the effects of crossflow from those of adverse streamwise pressure gradients, which may have clouded interpretations of previous 3DTBL experiments. In particular, the detailed developments of the cross-stream shear stress and of the stress/energy ratio become clearer. The shear-stress vector lagged behind the velocity-gradient vector as crossflow developed; however, the two vectors became more closely aligned downstream of the bend. Reductions in the stress/energy ratio implied that crossflow made shear-stress production less efficient. Another effect of three-dimensionality was a change of sign in the vertical transport of turbulent kinetic energy by turbulence, in the inner part of the boundary layer.

Viscous and elastic fingering instabilities in foam

Abstract: We investigate pattern formation in the immiscible displacement of foam from a confining geometry. The dominant length scales with the driving pressure gradient as for a Newtonian fluid, but depends surprisingly on the ratio of plate separation to bubble diameter. The pattern morphology exhibits a transition from a jagged, presumably elastic, character to a smooth, viscous character as the shear strain rate rises far above the natural internal relaxation time scale of the foam. These features may result from the two-dimensional nature of the flows and the unusual rheology of foams.

Vortical motion contributions to stress transport in turbulent boundary layers

Abstract: Four‐wire hot‐wire probe measurements are used to examine the relationships between the motions bearing spanwise vorticity, ωz, and the mechanisms responsible for turbulent stress transport. The measurements were carried out in thick zero pressure gradient turbulent boundary layers over the Reynolds number range, 1010

A unified approach to geopressuring, low‐permeability zone formation, and secondary porosity generation in sedimentary basins

Abstract: Geopressuring, secondary porosity, and low-permeability zones occur in many of the world's sedimentary basins and are often associated with major petroleum reservoirs. We present a mechanical model which simultaneously reproduces these phenomena. Assuming pressure solution to be the dominant rock deformation mechanism, a solid-state rock skeleton viscosity is introduced which relates the deformation of the rock skeleton to the effective stress. Numerical solutions for compaction indicate that a soft sedimentary layer preferentially compacts to form a low-permeability zone. There is a large liquid pressure gradient through the low-permeability zone. In the more slowly compacting region beneath the low-permeability zone, the pressure gradient remains hydrostatic but the absolute pressure can exceed the lithostatic pressure in the absence of hydraulic fracturing. This results in the formation of secondary porosity.

Origin and Decay of Longitudinal Vortices in Developing Flow in a Curved Rectangular Duct (Data Bank Contribution)

Abstract: Developing turbulent flow in a 90 deg curved duct of rectangular cross-section, and an aspect ratio of 6, was investigated. Mean-velocity and Reynolds-stress components were measured using a five-hole pressure problem and two-sensor hot-wire probes, respectively, in the boundary layers on the duct walls to document the pressure-driven secondary motion and the formation of a longitudinal vortex near the corner on the convex wall. Special attention was paid to the three-dimensionality of the flow exiting the two-dimensional contraction of the wind tunnel in order to provide proper inlet boundary conditions for future computational work. The mean velocities and wall shear stresses were measured at seven sections and turbulence measurement were made at four section. The data provide insights into the development of three-dimensional turbulent boundary layers under the influence of strong streamwise curvature, both convex or concave, and attendant pressure gradients, and clearly elucidate the mechanism by which strong pressure-driven secondary motion results in a longitudinal vortex.

Peristaltic transport of a particle-fluid suspension in a cylindrical tube

Abstract: Peristaltic pumping induced by a sinusoidal travelling wave of moderate amplitude is analysed in the axisymmetrical case for a viscous incompressible and Newtonian fluid mixed with rigid spherical particles which are of identical size. A perturbation method has been employed to find the solution of the problem, choosing the amplitude ratio (i.e., wave amplitude/tube radius) as a parameter. The analysis has been carried out by duly accounting for the nonlinear convective acceleration terms, and the nonslip condition for the fluid part on the wavy wall. The governing equations are developed up to the second order of the amplitude ratio. The zeroth order terms yield the Poiseuille flow and the first order terms give the Orr-Sommerfeld equation. In the absence of the pressure gradient and the wall motion, the mean flows (for the fluid and the solid particles) and the mean pressure gradient (averaged over time) are all found to be proportional to the square of the amplitude ratio. Numerical results are obtained for this simple case by approximating complicated groups of the products of Bessel functions by polynomials. It is observed that a reversal of flow occurs when the pressure gradient exceeds the critical value; this is favoured by the presence of the solid particles. The reversal of flow may take place near the boundaries also.

MR measurements of pulsatile pressure gradients.

Abstract: A magnetic resonance (MR) imaging method for evaluating pulsatile pressure gradients in laminar blood flow is presented. The technique is based on an evaluation of fluid shear and inertial forces from cardiac-gated phase-contrast velocity measurements. The technique was experimentally validated by comparing MR and manometer pressure gradient measurements performed in a pulsatile flow phantom. Analyses of random noise propagation and sampling error were performed to determine the precision and accuracy of the method. The results indicate that a precision of 0.01-0.03 mmHg/cm and an accuracy of better than 8% can be achieved by using standard clinical pulse sequences in tubes exceeding 6 mm in diameter. The authors conclude that MR measurement of pressure gradients is feasible and that additional hemodynamic information may be derived from conventional phase-contrast imaging studies.

Generation of region 1 current by magnetospheric pressure gradients

Abstract: The Rice Convection Model (RCM) is used to illustrate theoretical possibilities for generating region 1 Birkeland currents by pressure gradients on closed field lines in the Earth's magnetosphere. Inertial effects and viscous forces are neglected. The RCM is applied to idealized cases, to emphasize the basic physical ideas rather than realistic representation of the actual magnetosphere. Ionospheric conductance is taken to be uniform, and the simplest possible representations of the magnetospheric plasma are used. Three basic cases are considered: (1) the case of pure northward Interplanetary Magnetic Field (IMF), with cusp merging assumed to create new closed field lines near the nose of the magnetosphere, following the suggestion by Song and Russell (1992); (2) the case where Dungey-type reconnection occurs at the nose, but magnetosheath plasma somehow enters closed field lines on the dawnside and duskside of the merging region, causing a pressure-driven low-latitude boundary layer; and (3) the case where Dungey-type reconnection occurs at the nose, but region 1 currents flow on sunward drifting plasma sheet field lines. In case 1, currents of region 1 sense are generated by pressure gradients, but those currents do not supply the power for ionospheric convection. Results for case 2 suggest that pressure gradients at the inner edge of the low-latitude boundary layer might generate a large fraction of the region 1 Birkeland currents that drive magnetospheric convection. Results for case 3 indicate that pressure gradients in the plasma sheet could provide part of the region 1 current.