Showing papers on "Pressure gradient published in 1999"

Rossby Wave Instability of Keplerian Accretion Disks

Abstract: We find a linear instability of nonaxisymmetric Rossby waves in a thin nonmagnetized Keplerian disk when there is a local maximum in the radial profile of a key function (r)≡(r)S2/Γ(r), where −1=(∇×v)/Σ is the potential vorticity, S=P/ΣΓ is the entropy, Σ is the surface mass density, P is the vertically integrated pressure, and Γ is the adiabatic index. We consider in detail the special case where there is a local maximum in the disk entropy profile S(r). This maximum acts to trap the waves in its vicinity if its height-to-width ratio max(S)/Δr is larger than a threshold value. The pressure gradient derived from this entropy variation provides the restoring force for the wave growth. We show that the trapped waves act to transport angular momentum outward. A plausible way to produce an entropy variation is when an accretion disk is starting from negligible mass and temperature, therefore, negligible entropy. As mass accumulates by either tidal torquing, magnetic torquing, or Roche-lobe overflow, confinement of heat will lead to an entropy maximum at the outer boundary of the disk. Possible nonlinear developments from this instability include the formation of Rossby vortices and the formation of spiral shocks. What remains to be determined from hydrodynamic simulations is whether or not Rossby wave packets (or vortices) "hold together" as they propagate radially inward.

A front-tracking algorithm for accurate representation of surface tension

Abstract: We present a front tracking algorithm for the solution of the 2D incompressible Navier-Stokes equations with interfaces and surface forces. More particularly, we focus our attention on the accurate description of the surface tension terms and the associated pressure jump. We consider the stationary Laplace solution for a bubble with surface tension. A careful treatment of the pressure gradient terms at the interface allows us to reduce the spurious currents to the machine precision. Good results are obtained for the oscillation of a capil- lary wave compared with the linear viscous theory. A classical test of Rayleigh-Taylor instability is presented.

Initial results from radio occultation measurements with Mars Global Surveyor

Abstract: A series of radio occultation experiments conducted with Mars Global Surveyor in early 1998 has yielded 88 vertical profiles of the neutral atmosphere. The measurements cover latitudes of 29°N to 64°S and local times from 0600 through midnight to 1800 during early summer in the southern hemisphere (Ls = 264°–308°). Retrieved profiles of pressure and temperature versus radius and geopotential extend from the surface to the 10-Pa pressure level. Near-surface uncertainties in temperature and pressure are about 1 K and 2 Pa, respectively, far smaller than in previous radio occultation measurements at Mars. The profiles resolve the radiative-convective boundary layer adjacent to the surface and also reveal gravity waves, particularly at northern and equatorial latitudes, which appear to be breaking in some cases. Distinctive meridional gradients of pressure and temperature indicate the presence of a low-altitude westerly jet at latitudes of 15°–30°S at southern summer solstice. This jet appears in predictions of general circulation models in connection with the strong, seasonal, cross-equatorial Hadley circulation. The pressure gradient at ∼2 km altitude implies a wind speed of 33 m s−1, stronger than predicted, which may help explain the occurrence of numerous local dust storms within this latitude band in late southern spring. These measurements also characterize the response of the atmosphere to stationary thermal forcing at midsouthern latitudes, where high terrain south of Tharsis and low terrain in Hellas Planitia produce large, zonal temperature variations in the lowest scale height above the surface. Pressure measured at constant geopotential decreases at an average rate of 0.13% per degree Ls, due primarily to condensation of CO2 at the North Pole.

Evolution of a wave packet into vortex loops in a laminar separation bubble

Abstract: A laminar boundary layer develops in a favourable pressure gradient where the velocity profiles asymptote to the Falkner & Skan similarity solution. Flying-hot-wire measurements show that the layer separates just downstream of a subsequent region of adverse pressure gradient, leading to the formation of a thin separation bubble. In an effort to gain insight into the nature of the instability mechanisms, a small-magnitude impulsive disturbance is introduced through a hole in the test surface at the pressure minimum. The facility and all operating procedures are totally automated and phase-averaged data are acquired on unprecedently large and spatially dense measurement grids. The evolution of the disturbance is tracked all the way into the reattachment region and beyond into the fully turbulent boundary layer. The spatial resolution of the data provides a level of detail that is usually associated with computations.Initially, a wave packet develops which maintains the same bounded shape and form, while the amplitude decays exponentially with streamwise distance. Following separation, the rate of decay diminishes and a point of minimum amplitude is reached, where the wave packet begins to exhibit dispersive characteristics. The amplitude then grows exponentially and there is an increase in the number of waves within the packet. The region leading up to and including the reattachment has been measured with a cross-wire probe and contours of spanwise vorticity in the centreline plane clearly show that the wave packet is associated with the cat's eye pattern that is a characteristic of Kelvin–Helmholtz instability. Further streamwise development leads to the formation of roll-ups and contour surfaces of vorticity magnitude show that they are three-dimensional. Beyond this point, the behaviour is nonlinear and the roll-ups evolve into a group of large-scale vortex loops in the vicinity of the reattachment. Closely spaced cross-wire measurements are continued in the downstream turbulent boundary layer and Taylor's hypothesis is applied to data on spanwise planes to generate three-dimensional velocity fields. The derived vorticity magnitude distribution demonstrates that the second vortex loop, which emerges in the reattachment region, retains its identity in the turbulent boundary layer and it persists until the end of the test section.

Flow braking and the substorm current wedge

Abstract: Recent models of magnetotail activity have associated the braking of earthward flow with dipolarization and the reduction and diversion of cross-tail current, that is, the signatures of the substorm current wedge. Estimates of the magnitude of the diverted current by Haerendel [1992] and Shiokawa et al. [1997, 1998] tend to be lower than results from computer simulations of magnetotail reconnection and tail collapse [Birn and Hesse, 1996], despite similar underlying models. An analysis of the differences between these estimates on the basis of the simulations gives a more refined picture of the diversion of perpendicular into parallel currents. The inertial currents considered by Haerendel [1992] and Shiokawa et al. [1997] contribute to the initial current reduction and diversion, but the dominant and more permanent contribution stems from the pressure gradient terms, which change in connection with the field collapse and distortion. The major effect results from pressure gradients in the z direction, rather than from the azimuthal gradients [Shiokawa et al., 1998], combined with changes in B y and B x . The reduction of the current density near the equatorial plane is associated with a reduction of the curvature drift which overcompensates changes of the magnetization current and of the gradient B drift current. In contrast to the inertial current effects, the pressure gradient effects persist even after the burst of earthward flow ends.

Momentum balances on the North Carolina inner shelf

Abstract: Four months of moored current, pressure, temperature, conductivity, wave, and wind observations on the North Carolina shelf indicate three dynamically distinct regions: the surf zone, the inner shelf between the surf zone and the 13-m isobath, and the midshelf. In the surf zone the along-shelf momentum balance is between the cross-shelf gradient of the wave radiation stress and the bottom stress. The linear drag coefficient in the surf zone is about 10 times larger than seaward of the surf zone. On the inner shelf the along-shelf momentum balance is also frictional; the along-shelf wind stress and pressure gradient are balanced by bottom stress. In the cross-shelf momentum balance the pressure gradient is the superposition of roughly equal contributions from the Coriolis force (geostrophy) and wave setdown from shoaling, unbroken surface gravity waves. At midshelf the along-shelf momentum balance is less frictional and hence flow accelerations are important. The cross-shelf momentum balance is predominantly geostrophic because the greater depth and smaller bottom slope at midshelf reduce the importance of wave setdown. The cross-shelf density gradient is in thermal wind balance with the vertical shear in the along-shelf flow in depths as shallow as 10 m. The dominant along-shelf momentum balances provide a simple estimate of the depth-averaged, along-shelf current in terms of the measured forcing (i.e., wind stress, wave radiation stress divergence, and along-shelf pressure gradient) that reproduces accurately the observed cross-shelf variation of the depth-averaged, along-shelf current between the surf zone and midshelf.

Similarity scaling of acceleration and pressure statistics in numerical simulations of isotropic turbulence

Abstract: The scaling properties of one- and two-point statistics of the acceleration, pressure, and pressure gradient are studied in incompressible isotropic turbulence by direct numerical simulation Ensemble-averaged Taylor-scale Reynolds numbers (Rλ) are up to about 230 on grids from 323 to 5123 From about Rλ 40 onwards the acceleration variance normalized by Kolmogorov variables is found to increase as Rλ1/2 This nonuniversal behavior is traced to the dominant irrotational pressure gradient contributions to the acceleration (whereas the much weaker solenoidal viscous part is universal) Longitudinal and transverse two-point correlations of the pressure gradient differ according to kinematic constraints, but both (especially the latter) extend over distances of intermediate scale size large compared to the Kolmogorov scale These extended-range properties essentially provide the Eulerian mechanism whereby (as found in recent work) the accelerations of a pair of fluid particles can remain significantly correla

Suboptimal feedback control of vortex shedding at low Reynolds numbers

Abstract: The objective of this study is to develop a method of controlling vortex shedding behind a bluff body using control theory. A suboptimal feedback control procedure for local sensing and local actuation is developed and applied to the flow behind a circular cylinder. The location of sensors for feedback is limited to the cylinder surface and the control input from actuators is the blowing and suction on the cylinder surface. Three different cost functionals to be minimized (J1 and J2) or maximized (J3) are investigated: J1 is proportional to the pressure drag of the cylinder, J2 is the square of the difference between the target pressure (inviscid flow pressure) and real flow pressure on the cylinder surface, and J3 is the square of the pressure gradient on the cylinder surface, respectively. Given the cost functionals, the flow variable to be measured by the sensors and the control input from the actuators are determined from the suboptimal feedback control procedure. Several cases for each cost functional have been numerically simulated at Re = 100 and 160 to investigate the performance of the control algorithm. For all actuations, vortex shedding becomes weak or disappears, and the mean drag and drag/lift fluctuations significantly decrease. For a given magnitude of the blowing/suction, reducing J2 provides the largest drag reduction among the three cost functionals.

Non-isothermal gas flow through rectangular microchannels

Abstract: The mass flow rate of a rarefied gas through a long rectangular channel caused by both pressure and temperature differences was calculated applying the S-model kinetic equation. The calculations have been carried out over wide ranges of the four parameters that determine the solution of the problem: the gas rarefaction, the height-to-width ratio of the channel, the pressure ratio on the channel ends and the analogous temperature ratio. First, the Poiseuille flow and the thermal creep were calculated, separately, as functions of the local rarefaction parameter, assuming the pressure and the temperature gradients to be small. The lateral-wall influence on the flow rates was analyzed. The total mass flow rate for the temperature ratio equal to 3.8 and for two values of the pressure ratio (1 and 100) was calculated. The corresponding numerical program is available at the site: fisica.ufpr.br/sharipov.

Near-Bottom Turbulence Measurements in a Partially Mixed Estuary: Turbulent Energy Balance, Velocity Structure, and Along-Channel Momentum Balance

Abstract: A set of moored, bottom-mounted and shipboard measurements, obtained in a straight section of the lower Hudson estuary during late summer and early fall of 1995, determine velocity, density, and along-channel pressure gradient throughout the 15-m water column, as well as providing direct eddy-correlation estimates of Reynolds stress and indirect inertial-range estimates of dissipation within 3 m of the bottom. The analysis focuses on testing 1) a simplified turbulent kinetic energy equation, in which production balances dissipation; 2) the Prandtl–Karman law of the wall, which is a relationship between bottom stress and near-bottom velocity gradient; and 3) a simplified depth-integrated along-channel momentum balance involving local acceleration, pressure gradient, and bottom stress. Estimates of production and dissipation agree well throughout the entire record. The relationship between bottom stress and velocity gradient is consistent with the law of the wall within approximately 1 m of the sea...

Vertical secondary flows in submersed plant‐like arrays

Abstract: Obstructions that protruded from a laboratory test bed into the benthic boundary layer were exposed to gradients in longitudinal velocity (δu/δz) that produced vertical pressure gradients along the surface of the obstruction. These pressure gradients generated vertical secondary flows that may have ecological significance for benthic fauna and aquatic macrophytes. Laboratory experiments demonstrated that secondary flows of up to 15% of the local longitudinal velocity were produced behind individual obstructions within a submersed plant-like or animal tube array and for conditions like those found in aquatic canopies or colonies. Our observations support theoretical predictions based on a reduced form of the Navier-Stokes equations, confirming that the ascending flow is controlled by a local balance of vertical pressure gradient, proportional to δu2/δz, and viscous stress. The secondary flows were shown to transport dye from the bottom to a height dictated by the in-canopy current speed and turbulence intensity. By extension, the ascending flows can potentially contribute to the advection of nutrients from sediments, where they have been regenerated by microbial processes, to areas higher in the canopy, where they can be used by epiphytes and macrophyte leaves. Pressure gradients generated near the stem base also produce pore-water exfiltration. The coupled pressure-driven exfiltration and vertical advection have the potential to control nutrient availability in the bed.

Numerical and experimental investigations of oblique boundary layer transition

Abstract: A transition scenario initiated by two oblique waves is studied in an incompressible boundary layer. Hot-wire measurements and flow visualizations of this scenario are reported for the first time. The experimental results are compared with spatial direct numerical simulations and a good qualitative agreement is found. Also quantitative agreement is found when the experimental device for disturbance generation is closely modeled and pressure gradient effects taken into account. The oblique waves are found to interact nonlinearly to produce streamwise streaks growing downstream, related to non-modal linear growth mechanisms. The same has previously been observed in channel flows and calculations of both compressible and incompressible boundary layers. The flow structures of oblique transition have many similarities to K- and H-type transition, for which two-dimensional Tollmien-Schlichting waves are the starting point. However, two-dimensional Tollmien-Schlichting waves are usually not initiated or observed in oblique transition and consequently the similarities are due to the oblique waves and streamwise streaks appearing in all three scenarios

Intermittency and scaling of pressure at small scales in forced isotropic turbulence

Abstract: The intermittency of pressure and pressure gradient in stationary isotropic turbulence at low to moderate Reynolds numbers is studied by direct numerical simulation (DNS) and theoretically. The energy spectra scale in Kolmogorov units as required by the universal-equilibrium hypothesis, but the pressure spectra do not. It is found that the variances of the pressure and pressure gradient are larger than those computed using the Gaussian approximation for the fourth-order moments of velocity, and that the variance of the pressure gradient, normalized by Kolmogorov units, increases roughly as [Rscr ]1/2λ, where [Rscr ]λ is the Taylor microscale Reynolds number. A theoretical explanation of the Reynolds number dependence is presented which assumes that the small-scale pressure field is driven by coherent small-scale vorticity–strain domains. The variance of the pressure gradient given by the model is the product of the variance of ui,juj,i, the source term of the Poisson equation for pressure, and the square of an effective length of the small-scale coherent vorticity–strain structures. This length can be expressed in terms of the Taylor and Kolmogorov microscales, and the ratio between them gives the observed Reynolds number dependence. Formal asymptotic matching of the spectral scaling observed at small scales in the DNS with the classical scaling at large scales suggests that at high Reynolds numbers the pressure spectrum in these forced flows consists of three scaling ranges which are joined by two inertial ranges, the classical k−7/3 range and a k−5/3 range at smaller scale. It is not possible, within the classical Kolmogorov theory, to determine the length scale at which the inertial range transition occurs because information beyond the energy dissipation rate is required.

The influence of cross-equatorial pressure gradients on the location of near-equatorial convection

Abstract: Tomas and Webster note that in regions where there is a substantial cross-equator surface pressure gradient, there is locally anticyclonic absolute vorticity on the low pressure side of the equator and thus, the flow in this region meets the parcel criterion for inertial instability. They hypothesize that the atmospheric response to this absolute-vorticity distribution is a convergence-divergence doublet in the boundary layer. The convergence centre results in strong convection and thus is very important in determining the strength and location of convection (i.e. the intertropical convergence zones) whereas the divergence centre results in suppressed convection. In this work, a zonally symmetric model of the boundary layer is developed to investigate this hypothesis further. An analysis of a linearized version of the model indicates that although the observed flow in these regions meets the parcel criterion for instability, it does not satisfy the linear stability criteria, because of the stabilizing influence of dissipation and the finite vertical scale. Much greater shear than that observed is required for linear instability. It is noted, however, that when the parcel criterion is met, one of the nonlinear terms which was neglected in the linear analysis may have an important influence on the flow. Several experiments are performed integrating the full nonlinear model, relaxing back to a pressure distribution having a cross-equatorial gradient, to test whether the observed vorticity, wind and convergence distributions can be well simulated. It is found that the simulations reach a steady state in which there is a region of locally anticyclonic absolute vorticity on the low pressure side of the equator. This absolute-vorticity distribution results in an anomalous acceleration of the meridional wind and a convergence-divergence doublet, similar to that observed by Tomas and Webster. This response is explained as resulting from accelerations that act to bring the zonal flow out of geostrophic balance as it passes through the region of locally anticyclonic absolute vorticity. The response of the meridional wind to the strength of the pressure gradient is quasi-linear for small and somewhat larger values of forcing but, between these values, there is a range where the response is highly nonlinear, i.e. large increases in the strength of the meridional wind result from small changes in the pressure gradient. It is suggested that this nonlinear response may play a role in the observed sudden onset of the monsoon circulations. The nonlinear model is also forced using pressure distributions taken from observations The resulting steady-state simulated vorticity, wind and convergence distributions closely match the observations for the cases of pressure distributions taken from the east Pacific and east Atlantic during July. When forced using the pressure distribution from the Indian Ocean region during July, the model produces an unrealistically strong meridional wind response. Some improvement is obtained by including the latitudinally dependent zonal pressure gradient force, which is moderately strong in this region. Finally, the model is forced using a pressure distribution taken from observations in the central Pacific Ocean during July. In this case the cross-equator pressure gradient is near zero.

Progress in Favre-Reynolds Stress Closures for Compressible Flows

Abstract: A closure for the compressible portion of the pressure-strain covariance is developed. It is shown that, within the context of a pressure-strain closure assumption linear in the Reynolds stresses, an expression for the pressure-dilatation can be used to construct a representation for the pressure-strain. Additional closures for the unclosed terms in the Favre–Reynolds stress equations involving the mean acceleration are also constructed. The closures accommodate compressibility corrections depending on the magnitude of the turbulent Mach number, the mean density gradient, the mean pressure gradient, the mean dilatation, and, of course, the mean velocity gradients. The effects of the compressibility corrections on the Favre–Reynolds stresses are consistent with current DNS results. Using the compressible pressure-strain and mean acceleration closures in the Favre–Reynolds stress equations an algebraic closure for the Favre–Reynolds stresses is constructed. Noteworthy is the fact that, in the absence of mean velocity gradients, the mean density gradient produces Favre–Reynolds stresses in accelerating mean flows. Computations of the mixing layer using the compressible closures developed are described. Favre–Reynolds stress closure and two-equation algebraic models are compared to laboratory data for the mixing layer. Experimental data from diverse laboratories for the Favre–Reynolds stresses appears inconsistent and, as a consequence, comparison of the Reynolds stress predictions to the data is not conclusive. Reductions of the kinetic energy and the spread rate are consistent with the sizable decreases seen in these classes of flows.

Socket/stump interface dynamic pressure distributions recorded during the prosthetic stance phase of gait of a trans-tibial amputee wearing a hydrocast socket:

Abstract: Force sensing resistors (FSR) have been used to measure dynamic stump/socket interface pressures during the gait of a trans-tibial amputee. A total of 350 pressure sensors were attached to the inner wall of a hydrocast socket. Data were sampled at 150Hz during approximately 0.8 seconds of prosthetic stance of gait. The dynamic pressure distributions within a hand cast socket reported by Convery and Buis (1998) are compared with those monitored within a hydrocast socket for the same amputee. The pressure gradients within the hydrocast socket are less than that of the hand cast Patellar-Tendon-Bearing (PTB) socket. The proximal “ring” of high pressure in the hand cast PTB socket is replaced with a more distal pressure in the hydrocast socket.

Flow development of Herschel–Bulkley fluids in a sudden three-dimensional square expansion

Abstract: The flow development of Herschel–Bulkley fluids in a sudden three-dimensional square expansion is studied numerically. The flow is modeled using the mixed-Galerkin finite element formulation to solve the conservation of mass and momentum equations. The Herschel–Bulkley material behavior is described using a regularized model based on the Papanastasiou model. Solutions are obtained for a downstream-to-upstream expansion ratio of 2:1 and for a wide range of pressure gradient values and rheological parameters. The results show that, during the evolution of the flow, two core regions and dead zones at the corners are formed. The extent of the core regions decreases with the pressure gradient and the Reynolds number, and increases with the power-law index. It is also found that the volume flow rate at steady flow increases with the pressure gradient, power-law index, and Reynolds number.

Large-scale gyrokinetic turbulence simulations: Effects of profile variation*

Abstract: Two common computational domains used in gyrokinetic turbulence simulations are a local flux-tube and a global whole plasma volume. The effect of a radially varying pressure gradient is found to explain some of the qualitative differences between these two models. It is shown that a coherent purely radial mode is the result of profile variation. In addition, as profile variation is increased, there is a fairly sudden transition to much lower levels of heat flux. This may explain lower values found in past global simulations. The self-generated purely radial electrostatic potential is found to be 180° out of phase with the flux-surface-averaged ion temperature. A theoretical relation between these two quantities is derived by relating the E×B nonlinearities for ion density and temperature for purely radial modes. This relation is used to explain the various radial mode shapes. Extending these results, a possible scheme is explored to reduce the heat flux by adding a ripple to the ion temperature profile. I...

Method of measuring intracranial pressure

Abstract: A method and apparatus (10) are provided for measuring intracranial pressure. The method includes the steps of measuring arterial inflow, venous outflow, cranial spinal fluid flow (102), calculating an intracranial volume change (104) from the measured arterial inflow, venous outflow, and cranial spinal fluid flow. The method also includes the steps of calculating a pressure gradient (106) of spinal fluid flow from the measured cranial spinal fluid flow, calculating a pressure change per unit volume change based upon the calculated intracranial volume change, and cranial pressure gradient (108).

Self-lubricated transport of bitumen froth

Abstract: Bitumen froth is produced from the oil sands of Athabasca using the Clark's Hot Water Extraction process. When transported in a pipeline, water present in the froth is released in regions of high shear, namely at the pipe wall. This results in a lubricating layer of water that allows bitumen froth pumping at greatly reduced pressures and hence the potential for savings in pumping energy consumption. Experiments establishing the features of the self-lubrication phenomenon were carried out in a 25 mm diameter pipeloop at the University of Minnesota, and in a 0.6 m diameter pilot pipeline at Syncrude, Canada. The pressure gradient of lubricated flows in 25 mm, 50 mm and 0.6 m diameter pipes closely follow the empirical law of Blasius for turbulent pipe flow; the pressure gradient is proportional to the ratio of the 7/4th power of the velocity to the 5/4th power of the pipe diameter, but the constant of proportionality is about 10 to 20 times larger than that for water alone. We used Reichardt's model for turbulent Couette flow with a friction velocity based on the shear stress acting on the pipe wall due to the imposed pressure gradient to predict the effective thickness of the lubricating layer of water. The agreement with direct measurements is satisfactory. Mechanisms for self-lubrication are also considered.

Substorm-associated pressure variations in the magnetotail plasma sheet and lobe

Abstract: Simultaneous pressure measurements by Interball-Tail in the high-latitude lobe and by Geotail in the equatorial plasma sheet were analyzed for 30 substorms which exhibited significant pressure changes. At the onset of a few substorms we observed equatorial pressure peaks with magnitudes up to 50% higher than those in the lobe. These pileups are probably rather localized, and their properties are consistent with plasma sheet thickening between two active regions in the tail. During expansion and recovery phases of more than half of substorms, we observed equatorial pressure depletions relative to the high-latitude lobe pressure. These depletions can last more than 2 hours and are likely formed during the substorm expansion phase near the equatorial plane behind (tailward of) the strongly dipolar near-Earth magnetotail region. The observed pressure gradient is probably a nonstationary feature and can be compensated partially by magnetic tension on the curved field lines. Magnitude and history of the solar wind dynamic pressure appear to significantly influence substorm scenarios in the magnetotail. Possible existence of the pressure difference should be taken into account in single-spacecraft substorm studies.