Showing papers on "Pressure gradient published in 1995"

A consistent hydrodynamic boundary condition for the lattice Boltzmann method

Abstract: A hydrodynamic boundary condition is developed to replace the heuristic bounce‐back boundary condition used in the majority of lattice Boltzmann simulations. This boundary condition is applied to the two‐dimensional, steady flow of an incompressible fluid between two parallel plates. Poiseuille flow with stationary plates, and a constant pressure gradient is simulated to machine accuracy over the full range of relaxation times and pressure gradients. A second problem involves a moving upper plate and the injection of fluid normal to the plates. The bounce‐back boundary condition is shown to be an inferior approach for simulating stationary walls, because it actually mimics boundaries that move with a speed that depends on the relaxation time. When using accurate hydrodynamic boundary conditions, the lattice Boltzmann method is shown to exhibit second‐order accuracy.

The motion of long bubbles in polygonal capillaries. Part 2. Drag, fluid pressure and fluid flow

Abstract: This work determines the pressure–velocity relation of bubble flow in polygonal capillaries. The liquid pressure drop needed to drive a long bubble at a given velocity U is solved by an integral method. In this method, the pressure drop is shown to balance the drag of the bubble, which is determined by the films at the two ends of the bubble. Using the liquid-film results of Part 1 (Wong, Radke & Morris 1995), we find that the drag scales as Ca2/3 in the limit Ca → 0 (Ca μU/σ, where μ is the liquid viscosity and σ the surface tension). Thus, the pressure drop also scales as Ca2/3. The proportionality constant for six different polygonal capillaries is roughly the same and is about a third that for the circular capillary.The liquid in a polygonal capillary flows by pushing the bubble (plug flow) and by bypassing the bubble through corner channels (corner flow). The resistance to the plug flow comes mainly from the drag of the bubble. Thus, the plug flow obeys the nonlinear pressure–velocity relation of the bubble. Corner flow, however, is chiefly unidirectional because the bubble is long. The ratio of plug to corner flow varies with liquid flow rate Q (made dimensionless by σa2/μ, where a is the radius of the largest inscribed sphere). The two flows are equal at a critical flow rate Qc, whose value depends strongly on capillary geometry and bubble length. For the six polygonal capillaries studied, Qc [Lt ] 10−6. For Qc [Lt ] Q [Lt ] 1, the plug flow dominates, and the gradient in liquid pressure varies with Q2/3. For Q [Lt ] Qc, the corner flow dominates, and the pressure gradient varies linearly with Q. A transition at such low flow rates is unexpected and partly explains the complex rheology of foam flow in porous media.

On the existence of uniform momentum zones in a turbulent boundary layer

Abstract: Instantaneous velocity fields in the x‐y plane of a zero pressure gradient turbulent boundary layer are measured using particle image velocimetry. It is found that there exist random, time‐varying zones in the u‐ν fields in which the streamwise momentum is remarkably uniform. The largest dimension of a typical zone is proportional to the boundary layer thickness. The zone closest to the wall contains viscous‐inertial inclined structures similar to those found in low Reynolds number wall turbulence. A second zone is located above the wall zone in a region that coincides roughly with the logarithmic layer. The wake region of the boundary layer contains a complicated, time‐varying pattern of several nearly‐constant‐momentum zones. The zones are separated from each other and from the free stream by thin viscous shear layers that contain concentrations of spanwise vorticity.

The influence of cerebrospinal fluid pressure on the lamina cribrosa tissue pressure gradient.

Abstract: PURPOSE To measure the tissue pressure gradient through the optic disk and to determine the relationship between intraocular, cerebrospinal fluid, and retrolaminar tissue pressures. The relationship of optic nerve subarachnoid space pressure to intracranial cerebrospinal fluid pressure also was explored. METHODS Micropipettes coupled to a pressure transducer were passed through pars plana and vitreous to enter the optic disk in the anesthetized dog. Using a micromanipulator, pipettes penetrated the optic disk in steps while pressure measurements were taken. In some animals, pipettes also were passed into the optic nerve subarachnoid space. Lateral ventricle cerebrospinal fluid pressure, intraocular pressure, and arterial blood pressure were measured concurrently, and the effect of raising CSF pressure was explored. RESULTS Retrolaminar tissue pressure was largely dependent on the surrounding cerebrospinal fluid pressure, which was on average 8.6 +/- 3.5 mm Hg (SD, n = 8) higher, and was independent of intraocular pressure. Most (85% +/- 15% [SD, n = 8]) of the pressure drop between intraocular pressure and retrolaminar pressure occurred across the anterior 400 microns of disk tissue. When the intraocular pressure was 21 mm Hg and the cerebrospinal fluid pressure was zero, retrolaminar tissue pressure averaged 7 mm Hg and the translaminar pressure gradient was 3.08 +/- 0.29 mm Hg/100 microns tissue (SD, n = 3). Optic nerve subarachnoid space pressure was equivalent to lateral ventricular pressure. CONCLUSIONS These results show that cerebrospinal fluid pressure largely determines retrolaminar tissue pressure; hence, along with intraocular pressure, it is of major importance in setting the translaminar tissue pressure gradient. Results also demonstrate hydrostatic continuity between the optic nerve subarachnoid space and the lateral ventricle. That the translaminar pressure gradient can vary independently of intraocular pressure may be of importance in understanding the pathophysiology of glaucoma.

Effects of vorticity on rocket combustion stability

Abstract: Combustion stability computations are currently based on an irrotational model that allows slip flow at the burning surface. However, the no-slip boundary condition must be satisfied when gas motions are parallel to the combustion zone. Then waves of vorticity are created that distort the acoustic wave structure and modify the fluctuating normal velocity component upon which system stability is so strongly dependent. This flow problem is solved here in analytical form to bring the physical details into focus. Crocco's theorem shows that the creation of vorticity is due primarily to the axial unsteady pressure gradient across mean flow streamlines at the surface. Hence, there is a transfer of energy from the pressure oscillations (acoustic field) to the rotational waves (vorticity field). It is in this interaction that the incoming flow acquires the axial motion of the acoustic wave. Stability calculations based on this model yield the three-dimensional form of Culick's one-dimensional flow-turning correction and clarify its origin. However, continuity at the burning surface requires a correction to the radial velocity fluctuations. Incorporation of this new driving effect leads to a motor system that is significantly less stable than in the classical prediction (Standard Stability Prediction Program) for some configurations.

Experimental investigation of a salt water turbulent boundary layer modified by an applied streamwise magnetohydrodynamic body force

Abstract: Single‐component velocity field measurements, mean and fluctuating wall shear stress measurements, and photographic flow visualizations have been made of a magnetohydrodynamic (MHD) body‐force modified turbulent boundary layer. The turbulent boundary layer flowed over a flat plate in salt water at zero pressure gradient; the MHD force was created by the interaction of a permanent magnetic field and an applied electric field from a magnet/electrode array integral to the surface of the plate. A MHD force, when applied to an electroconducting fluid and acting in a streamwise direction, can generate a near‐wall jet, decreasing the boundary layer thickness and suppressing the intensity of the turbulent fluctuations across the boundary layer. At very high interactions, the force causes an increase in mean wall shear and in turbulence; in the zero free‐stream velocity limit, the force acts as a pump. An increase in local skin friction, however, is offset by a grain in thrust due to the force. At moderate interac...

MEMS for pressure distribution studies of gaseous flows in microchannels

Abstract: The first ever experimental data on the pressure distribution of gaseous flows in micron-sized channels (microchannels) is successfully obtained This is achieved by using our newly developed microflow MEMS systems that consist of both microchannels and distributed pressure sensors Two type of microchannels are developed One is a straight channel with a uniform cross section, and the other has a variable cross section with Venturi-meter-like transitions It is discovered that gaseous pressure distributions in microchannels are not linear Moreover, it is also discovered that transitions in microchannels can result in either pressure drops or rises depending on their geometry The Navier-Stokes equation with slip boundary conditions has been solved to model the gas flow in microchannels with uniform cross-sectional area It is found that the model (first used by Arkilic et al, 1994) can fit the experimental data One interesting phenomenon found in both microflow systems is that the pressure gradients near the inlet and outlet are very small Such a phenomenon, however, can not be explained by this slip flow model

Permeability for cross flow through columnar-dendritic alloys

Abstract: Experiments for measuring permeability in columnar-dendritic microstructures have provided data only up to a volume fraction of liquid of 0.66. Hence, the permeability for flow perpendicular to the primary dendrite arms in columnar-dendritic microstructures was calculated, extending our data base for permeability to volume fractions of liquid as high as 0.98. Analyses of the dendritic microstructures were undertaken first by detecting the solid-liquid interfaces with a special computer program and then by generating a mesh for a finite-element fluid flow simulation. Using a Navier-Stokes solver, the velocity and pressure at the nodes were calculated at the microstructural level. In turn, the average pressure gradient was used to calculate the Darcy permeability. Permeabilities calculated by this versatile technique provided data at high volume fractions of liquid that merged with the empirical data at the lower volume fractions.

Influence of a strong adverse pressure gradient on the turbulent structure in a boundary layer

Abstract: A comparison between the turbulent structures found in a zero pressure gradient boundary layer and a boundary layer subjected to a strong adverse pressure gradient is presented. The pressure gradient reverses the direction of the dominant turbulent diffusion, resulting in considerable turbulent transport towards the wall. Two‐point space–time correlations and the invariants show that this reduces the anisotropy in the near wall region and indicate an important reflection of the turbulent motion from the wall back into the outer layer. This is verified by a quadrant analysis [Lu and Willmarth, J. Fluid Mech. 60, 481 (1973)] which demonstrates that the strong events near the wall are totally dominated by motions in the first and fourth quadrants.

An experimental study of a three-dimensional pressure-driven turbulent boundary layer

Abstract: A three-dimensional, pressure-driven turbulent boundary layer created by an idealized wing-body junction flow was studied experimentally. The data presented include time-mean static pressure and directly measured skin-friction magnitude on the wall. The mean velocity and all Reynolds stresses from a three-velocity-component fibre-optic laser-Doppler anemometer are presented at several stations along a line determined by the mean velocity vector component parallel to the wall in the layer where the u 2 kinematic normal stress is maximum (normal-stress coordinate system). This line was selected by intuitively reasoning that overlap of the near-wall flow and outer-region flow occurs at the location where u 2 is maximum. Along this line the flow is subjected to a strong crossflow pressure gradient, which changes sign for the downstream stations. The shear-stress vector direction in the flow lags behind the flow gradient vector direction. The flow studied here differs from many other experimentally examined three-dimensional flows in that the mean flow variables depend on three spatial axes rather than two axes, such as flows in which the three-dimensionality of the flow has been generated either by a rotating cylinder or by a pressure gradient in one direction only throughout the flow.

Pressure recovery in bileaflet heart valve prostheses. Localized high velocities and gradients in central and side orifices with implications for Doppler-catheter gradient relation in aortic and mitral position.

Abstract: Background We investigate pressure recovery in central and side orifices of St Jude valves and the effect of mitral versus aortic position on the relation between Doppler- and catheter-derived pressure gradients. Methods and Results Maximum, transvalvular, and net pressure gradients are calculated and compared with Doppler-derived gradients in an in vitro model. Pressure recovery and pressure loss coefficients are calculated. Simultaneous Doppler and catheter gradients are obtained intraoperatively in five patients undergoing mitral valve replacement. Centerline Doppler gradients correspond closely with maximum catheter gradients but are higher than transvalvular and net pressure gradients. Thirty-six percent of the initial pressure drop is recovered between the valve leaflets and is independent of valve size or configuration. A variable amount of postvalvular pressure recovery is observed depending on aortic or mitral configuration. Side orifice velocities are 85±4% of the centerline velocities. Incorpor...

Upwelling Circulation on the Oregon Continental Shelf. Part II: Simulations and Comparisons with Observations

Abstract: Sixty-day simulations of flow on the Oregon continental shelf are performed using the Blumberg and Mellor sigma coordinate, primitive equation model. The model is two-dimensional (an across-shelf section) with high spatial resolution and realistic shelf topography. Forcing consists of surface heat flux, either hourly or low-pass filtered wind stress, and in one case, a constant alongshore pressure gradient. Model results are compared with current and hydrographic measurements from the CUE-2 program. The horizontal scale of the alongshore coastal jet is significantly influenced by the structure of the initial density and velocity fields. The model successfully reproduces the vertical shear in the alongshore velocity field v, but the model's mean v field is too strongly southward, and the variance in both the vvu and v fields is underpredicted. Inclusion of the alongshore pressure gradient, while improving prediction of the mean alongshore velocities, does not improve the model-data correlation. Th...

Pressure structure functions and spectra for locally isotropic turbulence

Abstract: Beginning with the known relationship between the pressure structure function and the fourth-order two-point correlation of velocity derivatives, we obtain a new theory relating the pressure structure function and spectrum to fourth-order velocity structure functions. This new theory is valid for all Reynolds numbers and for all spatial separations and wavenumbers. We do not use the joint Gaussian assumption that was used in previous theory. The only assumptions are local homogeneity, local isotropy, incompressibility, and use of the Navier-Stokes equation. Specific formulae are given for the mean-squared pressure gradient, the correlation of pressure gradients, the viscous range of the pressure structure function, and the pressure variance. Of course, pressure variance is a descriptor of the energy-containing range. Therefore, for any Reynolds number, the formula for pressure variance requires the more restrictive assumption of isotropy. For the case of large Reynolds numbers, formulae are given for the inertial range of the pressure structure function and spectrum and of the pressure-gradient correlation; these are valid on the basis of local isotropy, as are the formulae for mean-squared pressure gradient and the viscous range of the pressure structure function. Using the experimentally verified extension to fourth-order velocity structure functions of Kolmogorov’s theory, we obtain r4I3 and kp7/3 laws for the inertial range of the pressure structure function and spectrum. The modifications of these power laws to account for the effects of turbulence intermittency are also given. New universal constants are defined; these require experimental evaluation. The pressure structure function is sensitive to slight departures from local isotropy, implying stringent conditions on experimental data, but applicability of the previous theory is likewise constrained. The results are also sensitive to compressibility.

On improving a one-layer ocean model with thermodynamics

Abstract: A popular method used to incorporate thermodynamic processes in a shallow water model (e.g. one used to study the upper layer of the ocean) is to allow for density variations in time and horizontal position, but keep all dynamical fields as depth independent. This is achieved by replacing the horizontal pressure gradient by its vertical average. These models have limitations, for instance they cannot represent the ‘thermal wind’ balance (between the horizontal density gradient and the vertical shear of the velocity) which dominates at low frequencies. A new model is now proposed which uses velocity and density fields varying linearly with depth, with coefficients that are functions of horizontal position and time. This model can explicitly represent the thermal wind balance, but its use is not restricted to low- frequency dynamics.Volume, mass, buoyancy variance, energy and momentum are conserved in the new model. Furthermore, these integrals of motion have the same dependence on the dynamical fields as the exact (continuously stratified) case. The evolution of the three components of the absolute vorticity field are correctly represented. Conservation of density–potential vorticity is not fulfilled, though, owing to artificial removal of the vertical curvature of the velocity field.The integrals of motion are used to construct a ‘free energy’ [Escr ]f, which is quadratic to the lowest order in the deviation from a steady state with (at most) a uniform velocity field. [Escr ]f is positive definite, and therefore the free evolution of the system cannot lead to an ‘explosion’ of the dynamical fields. (This is not the case if the velocity shear and/or the density vertical gradient is excluded in the model, which results in a non-negative definite free energy.)In a model with one active layer, linear waves on top of a steady state with no currents are, to a very good approximation, those of the first two vertical modes of the continuously stratified model. These are the familiar geophysical gravity and vortical waves (e.g. Poincare, Rossby, and coastal Kelvin waves at mid-latitudes, equatorial waves, etc.).Finally, baroclinic instability is well represented in the new model. For long perturbations (wavelengths of the order of the deformation radius of the first mode) the agreement with more precise calculations is excellent. On the other hand, the comparison with the eigenvalues of Eady's problem (which corresponds to wavelengths of the order of the deformation radius of the second mode) shows differences of the order of 40%. Nevertheless, the new model does have a high-wavenumber cutoff, even though it is constrained to linear profiles in depth and therefore cannot reproduce the exponential trapping of Eady's problem eigensolutions.In sum, the integrals of motion, vorticity dynamics, free waves and baroclinic instability results all give confidence in the new model. Its main novelty, however, lies in the ability to incorporate thermodynamic processes.

Unsteady axial viscoelastic pipe flows

Abstract: The main objective of this work is to examine in detail basic unsteady pipe flows and to investigate any new physical phenomena. We take the viscoelastic upper-convected Maxwell fluid as our non-Newtonian model and consider the flow of such a fluid in pipes of uniform circular cross-section in the following three cases: 1. (a) when the pressure gradient varies exponentially with time; 2. (b) when the pressure gradient is pulsating; 3. (c) a starting flow under a constant pressure gradient. In the first problem we looked separately at the pressure gradient rising exponentially with time and falling exponentially with time, i.e. the pressure gradient is proportional to e±α2τ. The behaviour of the flow field depends to a large extent on β where β2 = α2(1 ± Hα2) with H being the quotient of the Weissenberg and Reynolds numbers. In both cases for small |βη|, η being the radial distance from the axis, the velocity profiles are seen to be parabolic. However, for large |βη| the flows are vastly different. In the case of increasing pressure gradient the flow depicts boundary-layer characteristics while for decreasing pressure gradient the velocity depends on the wall distance. The case of a pulsating pressure gradient is investigated in the second problem. Here the pressure gradient is proportional to cos nτ. Again the flow depends to a large extent on a parameter β (β2 = in − n2H). For small values of |βη| the velocity profile is parabolic. However, it is found that, unlike Newtonian fluids, the velocity distribution for the upper-convected Maxwell fluid is not in phase with the exciting pressure distribution. In the case of large |βη| the solution displays a boundary-layer characteristic and the phase of the motion far from the wall is shifted by half a period. The final problem examines a flow that is initially at rest and then set in motion by a constant pressure gradient. A closed form solution has been obtained with the aid of a Fourier-Bessel series. The variation of the velocity across the pipe has been sketched and comparison made with the classical solution.

Dynamics of spatiotemporally propagating transport barriers

Abstract: A simple dynamic model of spatiotemporally propagating transport barriers and transition fronts from low (L) to high (H) confinement regimes is presented. The model introduces spatial coupling (via transport) into the coupled evolution equations for flow shear and fluctuation intensity, thus coupling the supercritical L to H bifurcation instability to turbulent transport. Hence, fast spatiotemporal front propagation and evolutionary behavior result. The theory yields expressions for the propagation velocity and termination point of an L–H transition front and transport barrier. When the evolution of the pressure gradient, ∇Pi, and the contribution of ∇Pi to sheared electric field, Er′, is included, the ambient pretransition pressure gradient acts as a local source term that drives the evolution of the poloidal velocity shear. The transition may then evolve either as a spatiotemporally propagating front or as a uniform (i.e., nonlocal) fluctuation reduction or quench. The precise route to transition adopte...

Droplet deposition and momentum transfer in annular flow

Abstract: Entrainment and deposition in gas-liquid annular upflow are known to account for as much as 20% of the pressure gradient, through droplet accelerations in the core region. Momentum is transferred from the core when droplets decelerate upon impact with the liquid film. It is usually assumed that all of this momentum is transferred to the film, essentially driving the film upward in conjunction with interfacial friction. New data, obtained for annular gas-liquid upflow in a 5.08-cm-ID tube, are used in a momentum balance analysis to determine the mechanism of momentum transfer from depositing droplets. Measurements include the liquid film thickness, wall shear stress, pressure gradient, entrained liquid fraction, droplet deposition rate, droplet centerline axial velocity, and mass-average drop size for two gas-liquid systems. This analysis supports the idea that large droplets displace the film locally and decelerate primarily at the wall, effectively transferring negligible momentum to the liquid film.

Flow dynamics in thin slab caster moulds

Abstract: This study investigated the dynamic fluid flow phenomena that occurred in water models of a thin slab caster mould. The flow of fluid caused significant surface waves and was observed to be strongly oscillatory. The magnitude and the period of oscillation of these waves represent potential quality constraints in thin slab casting. The oscillation mechanism is explained in terms of the dynamic balance/imbalance between the pressure gradient across the jet emerging from the SEN and the opposing momentum of the recirculating, entrained flow.

A Numerical Study of the Stratiform Region of a Fast-Moving Squall Line. Part II: Relationship between Mass, Pressure, and Momentum Fields

Abstract: In a companion paper, a two-dimensional simulation of a fast-moving tropical squall line was successfully compared to observations performed during the COPT81 experiment over West Africa. The full ice phase parameterization is shown to be crucial in the simulation of trailing anvil precipitation. Different diagnostic tools are applied to the simulated fields to further our understanding of the scale interactions within a squall line-type mesoscale convective system. The pressure organization is characterized by two marked features important for explaining the inner circulation: first, a front-to-rear midlevel pressure gradient and, second. the surface pressure mesohigh extending from the gust front to the rear of the most active part of the trailing stratiform region. Based on the hydrostatic approximation, an original method of decomposition of the pressure field is proposed, whereby dynamical and buoyant contributions depend only on the horizontal and vertical, respectively. The mean pressure i...

Transition Length Prediction for Flows With Rapidly Changing Pressure Gradients

Abstract: A new method for calculating intermittency in transitional boundary layers with changing pressure gradients is proposed and tested against standard turbomachinery flow cases. It is based on recent experimental studies which show the local pressure gradient parameter to have a significant effect on turbulent spot spreading angles and propagation velocities (and hence transition length). This can be very important for some turbomachinery flows. On a turbine blade suction surface for example, it is possible for transition to start in a region of favorable pressure gradient and finish in a region of adverse pressure gradient. Calculation methods which estimate the transition length from the local pressure gradient parameter at the start of transition will seriously overestimate the transition length under these conditions. Conventional methods based on correlations of zero pressure gradient transition data are similarly inaccurate. The new calculation method continuously adjusts the spot growth parameters in response to changes in the local pressure gradient through transition using correlations based on data given in the companion paper by Gostelow, Melwani and Walker (1995). Recent experimental correlations of Gostelow, Blunden and Walker (1994) are used to estimate the turbulent spot generation rate at the start of transition. The method has been incorporated in a linear combination integral computation and tested with good results on cases which report both the intermittency and surface pressure distribution data. It has resulted in a much reduced sensitivity to errors in predicting the start of the transition zone, and can be recommended for engineering use in calculating boundary layer development on axial turbomachine blades.Copyright © 1995 by ASME

Observations of the transverse structure and dynamics of the low frequency flow through the North Channel of the Irish Sea

Abstract: During March–June 1985 an array of moored current meters was maintained across the North Channel of the Irish Sea, providing the first comprehensive cross-channel measurements of the low frequency flow (<0.4 cph). This flow was at up to 0.2 m s−1 and orientated parallel to the axis of the channel. The mean volume transport was northward at 0.11 Sv (1 Sv = 1 x 106m3 s−1) prior to servicing of the array in late April and 0.14 Sv subsequently. Underlying this was a partitioning of residual flow pattern across the channel, with persistent southward flow (0.05 and 0.03 Sv) on the west of the channel and northward flow in the east. An examination of the momentum balance indicated the large scale wind field to be a principal control of the along-channel flow variability, both as a consequence of the generation of an along-channel pressure gradient and direct forcing. On the western side, an additional relationship was observed between along-channel wind stress and Coriolis. In the east, along-channel flow was associated with a cross-channel surface slope, implying a geostrophic balance. However, the unaccounted momentum balance resembled the pressure gradient time series, implying the balance was not truly geostrophic. Application of a simple correlation model suggested that the mean current structure could not be fully described in terms of wind. The partitioning of the mean flow regime is consistent with linearized bottom friction balancing the large scale horizontal density differential between the Irish Sea and Atlantic waters. The regional significance of this persistent flow regime is considered.

Aerodynamic low drag structure

Abstract: Boundary layer separation at the boundary surface of an intake duct (18) of a turbofan aeroengine nacelle (12) at conditions of high incidence and high engine mass flow arises from shockwave induced pressure gradients in the boundary layer. To control separation, gaseous fluid is withdrawn from a high pressure region of the boundary layer at a downstream region of the boundary surface, conveyed within the intake duct structure (19) and discharged at an upstream region of the boundary surface into a low pressure region of the boundary layer. The intake duct (18) embodies a noise attenuation panel (19), and fluid is withdrawn from the high pressure region of the boundary layer into a modified panel section (191) by passage through apertures (30) in the front face of the panel section (191) at a downstream region of the panel section, conveyed along a fluid communication path within the panel section (191) and discharged into the low pressure region of the boundary layer by passage through apertures (30) in the front face of the panel section (191) at an upstream region of the panel section (191). Gaseous fluid is conveyed solely as a consequence of the difference in pressures in the boundary layer at the downstream and upstream regions.

Dynamics of premelted films: Frost heave in a capillary.

Abstract: Due either to van der Waals or to short range interactions, some materials will interfacially premelt against a foreign substrate. We present a theoretical study of this phenomenon for a situation in which the material is confined within a deformable capillary tube. At a temperature below the bulk melting transition an annulus of premelted liquid separates the solid from the capillary walls. For an isothermal capillary, at finite reduced temperature, the film is of uniform thickness and is static. On imposition of an axial temperature gradient the thickness of the film varies with position along the axis. A thermomolecular pressure gradient transports fluid towards regions of colder temperatures, where it solidifies and deforms the confining capillary. For the case of van der Waals interactions we formulate a mathematical model and solve it numerically and by matched asymptotic expansions. The main result is the temporal and spatial deformation of the capillary tube; a measurable quantity. In the case of a transient thermal field, we find that the deformation of the capillary is small and that it is uniform over most of its length. For a steady thermal field, large deformation occurs in a region of small reduced temperature and grows towards the cold end of the capillary. We focus on ice monocrystals, and offer our theory as a model for frost-heave phenomena, with the advantage of having exposed the essential physics of the problem in the absence of impurity and curvature effects. The experiments conducted by Wilen and Dash [Bull. Am. Phys. Soc. 38, 747 (1993); Phys. Rev. Lett. (to be published)] provide information that is unavailable using equilibrium techniques, and form the relevant test of this theoretical approach.

Stable and Unstable Accretion Flows with Angular Momentum near a Point Mass

Abstract: The properties of axisymmetric accretion flows of cold adiabatic gas with zero total energy in the vicinity of a Newtonian point mass are characterized by a single dimensionless parameter, the thickness of incoming flow. In the limit of thin accretion flows with vanishing thickness, we show that the governing equations become self-similar, involving no free parameters. We study numerically thin accretion flows with finite thickness as well as those with vanishing thickness. Mass elements of the incoming flow enter the computational regime as thin rings. In the case with finite thickness, after a transient period of initial adjustment, an almost steady-state accretion shock with a small oscillation amplitude forms, confirming the previous work by Molteni, Lanzafame, \& Chakrabarti (1994). The gas in the region of vorticity between the funnel wall and the accretion shock follows closed streamlines, forming a torus. This torus, in turn, behaves as an effective barrier to the incoming flow and supports the accretion shock which reflects the incoming gas away from the equatorial plane. The postshock flow, which is further accelerated by the pressure gradient behind the shock, goes through a second shock which then reflects the flow away from the symmetry axis to form a conical outgoing wind. As the thickness of the inflowing layer decreases (or if the ratio of the half thickness to the distance to the funnel wall along the equatorial plan is smaller than $\sim0.1$), the flow becomes unstable. In the case with vanishing thickness, the accretion shock formed to stop the incoming flow behind the funnel wall oscillates quasi-periodically with an amplitude comparable to the thickness. The structure between the funnel wall and the accretion shock is destroyed as the shock moves inwards toward the central mass and re-generated

A Windstorm in the Lee of a Gap in a Coastal Mountain Barrier

Abstract: This paper describes a localized windstorm that struck some areas of northwest Washington State on 28 December 1990 with winds exceeding 45 m s−1, resulting in extensive property damage, treefalls, and power outages. Arctic air, originating within the interior of British Columbia, descended into a mesoscale gap in the Coast/Cascade Mountains and then accelerated ageostrophically to the west. This gap acceleration is explained quantitatively by a three-way balance among the pressure gradient force, friction, and inertia. The flow maintained its integrity as a narrow current of high-speed air as it exited the gap and subsequently accelerated over water. Troughing in the lee of the Cascade Mountains enhanced the horizontal pressure gradient over northwest Washington; this pressure gradient approximately balanced frictional drag resulting in only minimal acceleration. Farther south the flow decelerated as the current spread out horizontally.

Two-dimensional weak shock-vortex interaction in a mixing zone

Abstract: The interaction between a vortex or a pair of vortices and a shock is studied by using two-dimensional direct numerical simulation. The deformation of the shock structure is analyzed and the mechanisms leading to the formation of triple points are underscored. It is shown that they are related to the appearance of pressure gradients in the direction parallel to the shock resulting from the shock-vortex interaction. A distribution of an inert chemical species, i.e., mixture fraction, is prescribed within the vortex. From its time evolution, one analyzes the coupling between the response of the shock to the disturbance and the change in mixing rate. Modifications of the maximum of the scalar gradient are observed in the direction perpendicular to the shock and also, to a smaller extent, in the direction parallel to the shock. Nomenclature A(s) = stretching function of the mesh a,b,c,d = coefficients of the FADE scheme D = diffusion coefficient of the inert chemical species L = reference length of the problem M = Mach number N = total number of grid points in streamwise direction P = pressure Pr = Prandtl number q, qr = mesh stretching ratio and stretching rate R = radius of the vortex Re = acoustic Reynolds number (r, ft) = polar coordinates s = position on the uniform mesh