bluuebunny/crossref_metadata_2025 huggingface dataset:
Mechanics of collisional motion of granular materials. Part 3. Self-similar shock wave propagation
Authors: Goldshtein A. , SHAPIRO M. , Gutfinger C.
Published: April 2006

Shock wave propagation arising from steady one-dimensional motion of a piston in a granular gas composed of inelastically colliding particles is treated theoretically. A self-similar long-time solution is obtained in the strong shock wave approximation for all values of the upstream gas volumetric concentration v0. Closed form expressions for the long-time shock wave speed and the granular pressure on the piston are obtained. These quantities are shown to be independent of the particle collisional properties, provided their impacts are accompanied by kinetic energy losses. The shock wave speed of such non-conservative gases is shown to be less than that for molecular gases by a factor of about 2.

The effect of particle kinetic energy dissipation is to form a stagnant layer (solid block), on the surface of the moving piston, with density equal to the maximal packing density, vM. The thickness of this densely packed layer increases indefinitely with time. The layer is separated from the shock front by a fluidized region of agitated (chaotically moving) particles. The (long-time, constant) thickness of this layer, as well as the kinetic energy (granular temperature) distribution within it are calculated for various values of particle restitution and surface roughness coefficients. The asymptotic cases of dilute (v0 [Lt ] 1) and dense (v0 ∼ vM) granular gases are treated analytically, using the corresponding expressions for the equilibrium radial distribution functions and the pertinent equations of state. The thickness of the fluidized region is shown to be independent of the piston velocity.

The calculated results are discussed in relation to the problem of vibrofluidized granular layers, wherein shock and expansion waves were registered. The average granular kinetic energy in the fluidized region behind the shock front calculated here compared favourably with that measured and calculated (Goldshtein et al. 1995) for vibrofluidized layers of spherical granules.
Disturbance growth in an unstable three-dimensional boundary layer and its dependence on environmental conditions
Authors: Deyhle H. , Bippes H.
Published: April 2006

Experimental investigations in the three-dimensional boundary layer of a swept flat plate with the pressure gradient induced from outside are aimed at enhancing knowledge of the transition process in the presence of pure crossflow instability. The development of disturbances is characterized by the occurrence of both stationary and travelling instability modes, by early nonlinear development and by complex dependence upon the environmental conditions. Experiments under natural conditions of transition showed a good correspondence of the identified modes with those predicted by local linear stability theory. The disturbance growth, however, is generally overpredicted. Controlled excitation of crossflow vortices allowing measurements closer to the linear range of amplification confirmed this result. Nonlinear effects such as interaction between stationary disturbances and base flow and between travelling and stationary modes have already been observed when the naturally excited instabilities become of measurable size.

The most striking feature of the disturbance development is the complex dependence on initial conditions. Experiments under systematically varied environments showed that surface roughness represents the key parameter responsible for the initiation of stationary crossflow vortices. In contrast to two-dimensional boundary layers, free-stream turbulence influences the transition process indirectly. Only for turbulence levels Tu > 0.2% and smooth surfaces do the travelling instability waves dominate. The location of the final breakdown of laminar flow is clearly determined by the saturation amplitude of crossflow vortices. The receptivity to sound, two-dimensional surface roughness and non-uniformities of the test-section mean flow was found to be very weak.
Topological interpretation of the surface flow visualization of conical viscous/inviscid interactions
Authors: Van Oudheusden B. W. , Nebbeling C. , Bannink W. J.
Published: April 2006

The asymptotic flow structure is considered for a viscous–inviscid conical interaction, in particular that between a swept shock wave and a boundary layer. A flow model is devised based on the three-layer interaction concept. Assuming conicity of the inviscid flow regions, a viscous layer structure is established that is compatible with the inviscid outer flow, and which produces a geometrically conical surface flow pattern. This result is obtained from a dimensional analysis, which reveals similarity of the viscous layer in cross-flow planes at different radial distances from the conical origin. The results of this analysis provide a tool for the quantitative interpretation of surface flow visualizations in terms of the related topological structure of the flow in the cross-flow plane. This method is illustrated by application to the surface flow visualization of a Mach 3 shock-wave/boundary-layer interaction.
A random-flight evaluation of the constants of relative dispersion in idealized turbulence
Authors: Faller Alan J.
Published: April 2006

In the idealized problem of homogeneous isotropic stationary inertial-range turbulence the rate of relative dispersion of an ensemble of tracer pairs can be characterized by a constantC0. In order to compute this constant with random-flight equations, however, it is necessary first to know the values of two other constants,C1andC2, that occur in the two-particle velocity-component relations of Lagrangian tracers (Faller 1992).

C1andC2are found by an elaborate trial and error procedure in a new two-tracer random-flight model of dispersion that matches input and output values of these two variates. The constantC0is then computed using the Lagrangian relations and is found to be significantly smaller than when the Eulerian Kármán/Howarth correlations are used.

The probability density distribution of tracer separations has a kurtosis slightly larger than that of a comparable Gaussian distribution. At small spacings the frequency of tracer spacings is six to ten times larger than would be expected from a Gaussian distribution. The distribution function for the speed of separation of the Lagrangian tracers has a negative skewness similar to that found for two-point Eulerian velocities.
Oblique wind waves generated by the instability of wind blowing over water
Authors: Morland L. C.
Published: April 2006

The growth rates of gravity waves are computed from linear, inviscid stability theory for wind velocity profiles that are representative of the mean flow in a turbulent boundary layer. The energy transfer to the waves is largely concentrated in an angle (to the wind) interval that broadens with increasing wind speed and narrows with increasing wavelength. At sufficiently high wind speeds and sufficiently short wavelengths, the waves of maximum growth rate propagate at an oblique angle to the wind. The connection with bimodal directional distributions of observed spectra is discussed.
An analysis of aerodynamic forces on a delta wing
Authors: Chang Chien-Cheng , Lei Sheng-Yuan
Published: April 2006

The present study aims at relating lift and drag to flow structures around a delta wing of elliptic section. Aerodynamic forces are analysed in terms of fluid elements of non-zero vorticity and density gradient. The flow regime considered is Mα = 0.6 ∼ 1.8 and α = 5° ∼ 19°, where Mα denotes the free-stream Mach number and α the angle of attack. Let ρ denote the density, u velocity, and ω vorticity. It is found that there are two major source elements Re(x) and Ve(x) which contribute about 95% or even more to the aerodynamic forces for all the cases under consideration,
\[R_e({\bm x})=-\frac{1}{2} {\bm u}^2 \nabla\rho \cdot \nabla\phi\quad {\rm and}\quad V_e ({\bm x}) = -\rho{\bm u}\times {\bm \omega}\cdot \nabla\phi,\]
where θ is an acyclic potential, generated by the delta wing moving with unit velocity in the negative direction of the force (lift or drag). All the physical quantities are non-dimensionalized. Detailed force contributions are analysed in terms of the flow structures and the elements Re(x) and Ve(x). The source elements Re(x) and Ve(x) are concentrated in the following regions: the boundary layer in front of (below) the delta wing, the primary and secondary vortices over the delta wing, and a region of expansion around the leading edge. It is shown that Ve(x) due to vorticity prevails as the source of forces at relatively low Mach number, Mα < 0.7. Above about Mα = 0.75, Re(x) due to compressibility generally becomes the dominating contributor to the lift, while the overall contribution from Ve(x) decreases with increasing Mα, and even becomes negative at Mα = 1.2 for the lift, and at a higher Mα for the drag. The analysis is carried out with the aid of detailed numerical results by solving the Reynolds-averaged Navier–Stokes equations, which are in close agreement with experiments in comparisons of the surface pressure distributions.
Chaotic advection in three-dimensional unsteady incompressible laminar flow
Authors: Cartwright Julyan H. E. , Feingold Mario , Piro Oreste
Published: April 2006

We discuss chaotic advection in three-dimensional unsteady incompressible laminar flow, and analyse in detail the most important novel advection phenomenon in these flows: the global dispersion of passive scalars in flows with two slow and one fast velocity components. We make a comprehensive study of the first model of an experimentally realizable flow to exhibit this resonance-induced dispersion: biaxial unsteady spherical Couette flow is a three-dimensional incompressible laminar flow with periodic time dependence derived analytically from the Navier–Stokes equations in the low-Reynolds-number limit.
Horizontal fractionation of rising and sinking particles in wind-affected currents
Authors: Smith Ronald
Published: April 2006

The different rise or sinking velocity for different sizes or types of particles gives different vertical sampling of a wind-affected shallow-water flow. This paper derives a mathematical model for the consequent horizontal fractionation of a dilute suspension of particles when the flow is a wind-influenced perturbation from the classical logarithmic open-channel flow. Simple approximations are given for the effective horizontal velocity and for the shear dispersion tensor which preserve the perfect duality between the sensitivity of sinking particles to bed stress and the sensitivity of rising particles to surface stress.
Interaction of phase-locked modes: a new mechanism for the rapid growth of three-dimensional disturbances
Authors: Wu Xuesong , Stewart Philip A.
Published: April 2006

In this paper, we have identified a new mechanism which can promote rapid growth of three-dimensional disturbances. The mechanism involves the interaction between a planar mode and an oblique mode, or a pair of oblique modes, which are phase-locked in the sense that they have the same phase speed. This allows a powerful nonlinear interaction to take place within the common critical layer(s). The disturbance is not required to form a subharmonic resonant triad, and hence the mechanism operates under much less restrictive conditions than does subharmonic resonance (although it is somewhat less powerful). We show that the quadratic interaction between the planar mode and the oblique modes drives an exceptionally large forced mode with the difference frequency, which in turn interacts with the planar mode to contribute the dominant nonlinear effect. This interaction can cause the oblique modes to grow super-exponentially provided that their magnitude is sufficiently small. As a result of the super-exponential growth, the oblique mode may soon become strong enough to produce a feedback effect on the planar mode, so that the interactions eventually become fully coupled. This subsequent stage takes slightly different forms depending on whether a single or a pair of oblique modes is present. Both cases are investigated. Particular attention is paid to symmetric plane shear layers, e.g. a planar wake or jet, for which subharmonic resonance of sinuous modes is inactive.
Asymptotic theory for the almost-highest solitary wave
Authors: Longuet-Higgins M. S. , Fox M. J. H.
Published: April 2006

The behaviour of the energy in a steep solitary wave as a function of the wave height has a direct bearing on the breaking of solitary waves on a gently shoaling beach. Here it is shown that the speed, energy and momentum of a steep solitary wave in water of finite depth all behave in an oscillatory manner as functions of the wave height and as the limiting height is approached. Asymptotic formulae for these and other wave parameters are derived by means of a theory for the ‘almost-highest wave’ similar to that formulated previously for periodic waves in deep water (Longuet-Higgins & Fox 1977, 1978). It is demonstrated that the theory fits very precisely some recent calculations of solitary waves by Tanaka (1995).
Hydrodynamics of scallop locomotion: unsteady fluid forces on clapping shells
Authors: Cheng J.-Y. , DeMont M. E.
Published: April 2006

A potential flow model has been formulated for scallop swimming. Under the smalldisturbance approximation, the problem of the unsteady flow past the wing-like configuration of a scallop is separated into two linear sub-problems: the steady lifting problem and the unsteady symmetric thickness problem. The latter is associated with the expansion and contraction of the boundary surface of the scallop due to the shell opening and closing. A quasi-two-dimensional analytical solution of the thickness problem was obtained to give the time-dependent fluid forces acting on the outer surfaces of the shells. In addition to the added-mass effect, which has been widely accepted in the hydrodynamics of aquatic locomotion, there are two other mechanisms in the fluid reaction: flow-induced pseudo-elasticity and pseudo-viscosity. The pseudoelasticity provides a force proportional to the gape angle displacement, and will assist shell opening but resist shell closing. The pseudo-viscosity force is proportional to the angular velocity of the gape, and benefits both shell opening and closing. Their roles are discussed through comparison with those of shell inertia, hinge ligament elasticity and hinge damping. At 10 °C the hinge damping in the scallop was found to be almost compensated by the flow pseudo-viscosity. The unsteady fluid reaction may have a significant effect on the operation of the dynamic swimming system of scallops.
Rendering a subcritical Hopf bifurcation supercritical
Authors: Yuen Po Ki , Bau Haim H.
Published: April 2006

It is demonstrated experimentally and theoretically that through the use of a nonlinear feedback controller, one can render a subcritical Hopf bifurcation supercritical and thus dramatically modify the nature of the flow in a thermal convection loop heated from below and cooled from above. In particular, we show that the controller can replace the naturally occurring chaotic motion with a stable, periodic limit cycle. The control strategy consists of sensing the deviation of fluid temperatures from desired values at a number of locations inside the loop and then altering the wall heating to counteract such deviations.
Simple cases of the streamline-curvature instability in three-dimensional boundary layers
Authors: Itoh Nobutake
Published: April 2006

A new instability of the centrifugal type due to the curvature of external streamlines was theoretically predicted in a recent study on boundary layers along a swept wing. It is, however, not clear how this instability relates to already-known instability phenomena in various three-dimensional flows. So the basic idea developed in the analysis of boundary layers is applied to the simpler problems of the flow on a rotating disk and along the leading edge of a yawed circular cylinder, and the resulting eigenvalue problems are numerically solved to show multiple stability characteristics of the flows. Computational results confirm that the streamline-curvature instability does appear in the rotating-disk flow and that it is in fact identical with the instability called the ‘parallel’ or ‘type 2’ mode in the atmospheric literature. This instability is also found to occur in the steady flow near the attachment line and to give the lowest values of the critical Reynolds number except for a very narrow region close to the attachment line, where the viscous and cross-flow instabilities are dominant. These facts provide evidence to show that the same mode of instability as the classical one observed in rotating flows can appear in general three-dimensional boundary layers without rotation.
Turbulence characteristics of a boundary layer over a swept bump
Authors: Webster D. R. , Degraaff D. B. , Eaton J. K.
Published: April 2006

The evolution of the turbulent boundary layer over a bump defined by three tangential circular arcs and swept at 45° was examined. The flat-plate boundary layer approaching the swept bump had a momentum thickness Reynolds number of approximately 3800. The ratios of upstream boundary-layer thickness to bump height and convex radius of curvature were 1.5 and 0.06, respectively. The boundary layer was influenced by alternating signs of streamwise pressure gradient, wall curvature, and mean crossflow, which resulted in a complex boundary-layer flow that grew rapidly on the downstream side of the bump. The mean flow profiles deviated significantly from typical logarithmic layer behaviour, but the flow remained attached. The evolution of the Reynolds stress components was explained by the growth of two internal layers triggered by discontinuities in wall curvature near the leading and trailing edges of the bump. The shear stress vector was found to lag the velocity gradient vector, despite the spanwise flow changing direction above the bump. The measurements were compared to the previous results from a two-dimensional bump with the same profile shape and Reynolds number. Contrary to previous studies, the addition of mean crossflow to this complex flow field did not reduce the vertical mixing relative to the turbulent kinetic energy.
Magnetic structures in a dynamo simulation
Authors: Brandenburg A. , Jennings R. L. , Nordlund Å. , Rieutord M. , Stein R. F. , Tuominen I.
Published: April 2006

We use three-dimensional simulations to study compressible convection in a rotating frame with magnetic fields and overshoot into surrounding stable layers. The, initially weak, magnetic field is amplified and maintained by dynamo action and becomes organized into flux tubes that are wrapped around vortex tubes. We also observe vortex buoyancy which causes upward flows in the cores of extended downdraughts. An analysis of the angles between various vector fields shows that there is a tendency for the magnetic field to be parallel or antiparallel to the vorticity vector, especially when the magnetic field is strong. The magnetic energy spectrum has a short inertial range with a slope compatible with k+1/3 during the early growth phase of the dynamo. During the saturated state the slope is compatible with k−1. A simple analysis based on various characteristic timescales and energy transfer rates highlights important qualitative ideas regarding the energy budget of hydromagnetic dynamos.
Stability and nonlinear dynamics of one-dimensional overdriven detonations in gases
Authors: Clavin Paul , He Longting
Published: April 2006

The purpose of this analytical work is twofold: first, to clarify the physical mechanisms triggering the one-dimensional instabilities of plane detonations in gases; secondly to provide a nonlinear description of the longitudinal dynamics valid even far from the bifurcation. The fluctuations of the rate of heat release result from the temperature fluctuations of the shocked gas with a time delay introduced by the propagation of entropy waves. The motion of the shock is governed by a mass conservation resulting from the gas expansion across the reaction zone whose position fluctuates relative to the inert shock. The effects of longitudinal acoustic waves are quite negligible in pistonsupported detonations at high overdrives with a small difference of specific heats. This limit leads to a useful quasi-isobaric approximation for enlightening the basic mechanism of galloping detonations. Strong nonlinear effects, free from the spurious singularities of the square-wave model, are picked up by considering two different temperature sensitivities of the overall reaction rate: one governing the induction length, another one the thickness of the exothermic zone. A nonlinear integral equation for the longitudinal dynamics of overdriven detonations is obtained as an asymptotic solution of the reactive Euler equations. The analysis uses a distinguished limit based on an infinitely large temperature sensitivity of the induction kinetics and a small difference of specific heats. Comparisons with numerical calculations show a satisfactory agreement even outside the limits of validity of the asymptotic solution.
Oscillations of liquid drops: results from USML-1 experiments in Space
Authors: Wang T. G. , Anilkumar A. V. , Lee C. P.
Published: April 2006

Oscillations of low-viscosity drops were studied in the microgravity environment of a Space shuttle flight. From the damped oscillation data, the inviscid frequency shift, due to nonlinearity, has been extracted using a central-averaging scheme. For the classical case of the oscillations of a free low-viscosity drop, it has been found that the frequency shift agrees well with the predictions of the inviscid nonlinear theory of Tsamopoulos & Brown (1983) for ε < 0.3. But for the oscillations of a rotating low-viscosity drop, under acoustic levitation, the frequency shift is smaller, and the percentage of time spent in prolate displacement is significantly less than that for the classical case.
Stability of bounded rapid shear flows of a granular material
Authors: Wang Chi-Hwa , Jackson R. , Sundaresan S.
Published: April 2006

This paper presents a linear stability analysis of a rapidly sheared layer of granular material confined between two parallel solid plates. The form of the steady base-state solution depends on the nature of the interaction between the material and the bounding plates and three cases are considered, in which the boundaries act as sources or sinks of pseudo-thermal energy, or merely confine the material while leaving the velocity profile linear, as in unbounded shear. The stability analysis is conventional, though complicated, and the results are similar in all cases. For given physical properties of the particles and the bounding plates it is found that the condition of marginal stability depends only on the separation between the plates and the mean bulk density of the particulate material contained between them. The system is stable when the thickness of the layer is sufficiently small, but if the thickness is increased it becomes unstable, and initially the fastest growing mode is analogous to modes of the corresponding unbounded problem. However, with a further increase in thickness a new mode becomes dominant and this is of an unusual type, with no analogue in the case of unbounded shear. The growth rate of this mode passes through a maximum at a certain value of the thickness of the sheared layer, at which point it grows much faster than any mode that could be shared with the unbounded problem. The growth rate of the dominant mode also depends on the bulk density of the material, and is greatest when this is neither very large nor very small.
Stability of thermoviscous Hele-Shaw flow
Authors: Morris S. J. S.
Published: April 2006

Viscous fingering can occur as a three-dimensional disturbance to plane flow of a hot thermoviscous liquid in a Hele-Shaw cell with cold isothermal walls. This work assumes the principle of exchange of stabilities, and uses a temporal stability analysis to find the critical viscosity ratio and finger spacing as functions of channel length, Lc. Viscous heating is taken as negligible, so the liquid cools with distance (x) downstream. Because the base flow is spatially developing, the disturbance equations are not fully separable. They admit, however, an exact solution for a liquid whose viscosity and specific heats are arbitrary functions of temperature. This solution describes the neutral disturbances in terms of the base flow and an amplitude, A(x). The stability of a given (computed) base flow is determined by solving an eigenvalue problem for A(x), and the critical finger spacing. The theory is illustrated by using it to map the instability for variable-viscosity flow with constant specific heat. Two fingering modes are predicted, one being a turning-point instability. The preferred mode depends on Lc. Finger spacing is comparable with the thermal entry length in a long channel, and is even larger in short channels. When applied to magmatic systems, the results suggest that fingering will occur on geological scales only if the system is about freeze.
Concerning marginal singularities in the boundary-layer flow on a downstream-moving surface
Authors: Timoshin S. N.
Published: April 2006

The formation of separation singularities in solutions of the classical boundary-layer equations is studied numerically and analytically for the case of a two-dimensional incompressible steady flow near a solid surface moving in the direction of the main stream. Unlike the previously studied regime of the incipient separation located at the maximum point in the external pressure distribution, the breakdown in this work occurs under an adverse pressure forcing and involves a regular flow field upstream of the Moore-Rott-Sears point with an algebraic non-analyticity downstream. Small deviations from the precisely regular approach to the singular point are shown to result in an exponential amplification of linear disturbances; in the subsequent nonlinear stage the solution terminates in a finite-distance blow-up singularity or, alternatively, continues in a regular fashion across the singular station. The case of asymptotically small slip velocities is considered and a connection with marginal separation on a fixed wall is discussed.
Effects of compressibility, pitch rate, and Reynolds number on unsteady incipient leading-edge boundary layer separation over a pitching airfoil
Authors: Choudhuri P. Ghosh , Knight D. D.
Published: April 2006

The effects of compressibility, pitch rate and Reynolds number on the initial stages of two-dimensional unsteady separation of laminar subsonic flow over a pitching NACA-0012 airfoil have been studied numerically. The approach involves the simulation of the flow by solving the two-dimensional unsteady compressible laminar Navier-Stokes equations employing the implicit approximate-factorization algorithm of Beam & Warming and a boundary-fitted C-grid. The algorithm has been extensively validated through comparison with analytical and previous numerical results. The computations display several important trends for the ‘birth’ of the primary recirculating region which is a principal precursor to leading-edge separation. Increasing the non-dimensional pitch rate from 0.05 to 0.2 at a fixed Reynolds number and Mach number delays the formation of the primary recirculating region. The primary recirculating region also forms closer to the leading edge. Increasing the Mach number from 0.2 to 0.5 at a fixed Reynolds number and pitch rate causes a delay in the formation of the primary recirculating region and also leads to its formation farther from the airfoil top surface. The length scale associated with the recirculating regions increases as well. Increasing the Reynolds number from 104 to 105 at a fixed Mach number and pitch rate hastens the appearance of the primary recirculating region. A shock appears on the top surface at a Reynolds number of 105 along with the simultaneous formation of multiple recirculating regions near the leading edge.
Linear dynamics of wind waves in coupled turbulent air–water flow. Part 2. Numerical model
Authors: Harris J. A. , Belcher S. E. , Street R. L.
Published: April 2006

We develop a numerical model of the interaction between wind and a small-amplitude water wave. The model first calculates the turbulent flows in both the air and water that would be obtained with a flat interface, and then calculates linear perturbations to this base flow caused by a travelling surface wave. Turbulent stresses in the base flow are parameterized using an eddy viscosity derived from a low-turbulent-Reynolds-number κ – ε model. Turbulent stresses in the perturbed flow are parameterized using a new damped eddy viscosity model, in which the eddy viscosity model is used only in inner regions, and is damped exponentially to zero outside these inner regions. This approach is consistent with previously developed physical scaling arguments. Even on the ocean the interface can be aerodynamically smooth, transitional or rough, so the new model parameterizes the interface with a roughness Reynolds number and retains effects of molecular stresses (on both mean and turbulent parts of the flow).

The damped eddy viscosity model has a free constant that is calibrated by comparing with results from a second-order closure model. The new model is then used to calculate the variation of form drag on a stationary rigid wave with Reynolds number, R. The form drag increases by a factor of almost two as R drops from 2 × 104 to 2 × 103 and shows remarkably good agreement with the value measured by Zilker & Hanratty (1979). These calculations show that the damped eddy viscosity model captures the physical processes that produce the asymmetric pressure that leads to form drag and also wave growth.

Results from the numerical model show reasonable agreement with profiles measured over travelling water waves by Hsu & Hsu (1983), particularly for slower moving waves. The model suggests that the wave-induced flow in the water is irrotational except in an extremely thin interface layer, where viscous stresses are as likely to be important as turbulent stresses. Thus our study reinforces previous suggestions that the region very close to the interface is crucial to wind-wave interaction and shows that scales down to the viscous length may have an order-one effect on the development of the wave.

The energy budget and growth rate of the wave motions, including effects of the sheared current and Reynolds number, will be examined in a subsequent paper.
Entrainment into two-dimensional and axisymmetric turbulent gravity currents
Authors: Hallworth Mark A. , Huppert Herbert E. , Phillips Jeremy C. , Sparks R. Stephen J.
Published: April 2006

Entrainment of ambient fluid into both two-dimensional and axisymmetric gravity currents is investigated experimentally using a novel neutralization technique. The technique involves the titrative neutralization of an alkaline gravity current which intrudes into and entrains an acidic ambient, and is visualized using a pH indicator solution. Using this technique, we can determine quantitative results for the amount of dilution in the head of the current. The head of the current is able to entrain ambient fluid both by shear instabilities on the current/ambient interface and by over-riding (relatively light) ambient fluid. Guided by our experimental observations, we present two slightly different theoretical models to determine the entrainment into the head of the current as a function of distance from the source for the instantaneous release of a constant volume of fluid in a two-dimensional geometry. By dimensional analysis, we determine from both models that the dimensionless entrainment or dilution ratio, E, defined as the ratio of the volumes of ambient and original fluid in the head, is independent of the initial reduced gravity of the current; and this result is confirmed by our experiments in Boussinesq situations. Our theoretical evaluation of E in terms of the initial cross-sectional area of the current agrees very well with our experimental measurements on the incorporation of an entrainment coefficient α, evaluated experimentally to be 0.063 ± 0.003. We also obtain experimental results for constant-volume gravity currents moving over horizontal surfaces of varying roughness. A particularly surprising result from all the experiments, which is reflected in the theoretical models, is that the head remains essentially unmixed – the entrainment is negligible – in the slumping phase. Thus the heads of gravity currents with identical initial cross-sectional areas but different initial aspect ratios (lock lengths) will begin to be diluted by ambient fluid at different positions and hence propagate at different rates. A range of similar results is determined, both theoretically and experimentally, for the instantaneous release of a fixed volume of (heavy) fluid in an axisymmetric geometry. By contrast, the results of our experiments with gravity currents fed by a constant flux exhibit markedly different entrainment dynamics due to the continual replenishment of the fluid in the head by the constant input of undiluted fluid from the tail.
Manifestations of bottom topography on the ocean surface: the physical mechanism for large scales
Authors: Shrira Victor I. , Annenkov Sergei Yu.
Published: April 2006

The paper is a first attempt at theoretical investigation of the experimentally observed enigmatic phenomenon of surface manifestations of bottom topography reproducing well the image of the relief despite several kilometres of ocean depth. Both satellite observations and direct measurements have been repeatedly reported in the last two decades. We suggest a possible mechanism for these manifestations in a large scale range (of the order 5 × 101–103 km), based on the hydrodynamic theory of quasi-geostrophic stratified flow over topography on a β-plane.

The classical theories of quasi-geostrophic flow over topography on a β-plane do not include vertical shear, and it is well-known that the disturbance caused by topography cannot reach the surface of a stratified ocean unless the stratification or current velocity is unrealistic. The new element changing the situation qualitatively is the taking into account of the influence of near-bottom and near-surface boundary layers, where flow velocities, velocity gradients and stratification can significantly exceed the corresponding values for the flow in the main body. The asymptotic solution derived shows the considerable increase of the normal mode amplitude towards the boundaries. Thus, this specific distortion of the eigenmode structure results in effective forcing of the modes by topography and, on the other hand, leads to pronounced disturbances in the fields of near-surface characteristics. The mechanism effectiveness is demonstrated by the fact that the surface disturbance amplitude normally significantly exceeds the corresponding value for the barotropic current equal to the maximum of the shear flow. A remarkable feature of the solution is that the Green's function is strongly localized in the horizontal plane for a wide range of relevant parameters, thus leading to the close resemblance of surface patterns and bottom relief. To get a better understanding of the quantitative characteristics of the mechanism, the dependence of the effect on the parameters of an N-layer model was studied in detail. The amplification of the surface manifestations due to the presence of boundary layers can reach several orders of magnitude and thus make the manifestations easily observable. The surface temperature anomalies due to topography were estimated and found to be observable under favourable conditions.
Supersonic cooling by shock–vortex interaction
Authors: Fox M. D. , Kurosaka M.
Published: April 2006

The subject of total temperature separation in jets was treated in Fox et al. (1993) for subsonic jets. When we extended this study to the case of supersonic jets, we found the presence of a different mechanism of cooling, an effect which does not appear to have been known in the past. Named the ‘shock-induced total temperature separation’, this cooling can be of much greater magnitude than the subsonic cooling treated previously; it is caused by the interaction of convected vortical structures near the jet exhaust with the shock structure of the supersonic jet.

In studying this phenomenon, we focus our attention on overexpanded jets exiting a convergent-divergent nozzle. The theoretical results for the shock-induced cooling which are based on a linearized, unsteady supersonic analysis are shown to agree favourably with experiments.

When an impingement plate is inserted, the shock-induced cooling would manifest itself as wall cooling, whose magnitude is significantly larger than the subsonic counterpart. This has implications for heat transfer not only in jets, but wherever vortical structures may interact with shock waves.
Resonant interaction of a linear array of supersonic rectangular jets: an experimental study
Authors: Raman Ganesh , Taghavi Ray
Published: April 2006

This paper examines a supersonic multi-jet interaction problem that we believe is likely to be important for mixing enhancement and noise reduction in supersonic mixer-ejector nozzles. We demonstrate that it is possible to synchronize the screech instability of four rectangular jets by precisely adjusting the inter-jet spacing. Our experimental data agree with a theory that assumes that the phase-locking of adjacent jets occurs through a coupling at the jet lip. Although synchronization does not change the frequency of the screech tone, its amplitude is augmented. The synchronized multi- jets exhibit higher spreading than the unsynchronized jets, with the single jet spreading the least. We compare the near-field noise of the four jets with synchronized screech to the noise of the sum of four jets operated individually. Our noise measurements reveal that the more rapid mixing of the synchronized multi-jets causes the peak jet noise source to move upstream and to radiate noise at larger angles to the flow direction. Based on our results, we have grounds to believe that screech synchronization is advantageous for noise reduction internal to a mixer-ejector nozzle, since the noise can now be suppressed by a shorter acoustically lined ejector.
The contraction of liquid filaments
Authors: Schulkes R. M. S. M.
Published: April 2006

In this paper the evolution of a free liquid filament of arbitrary viscosity, contracting under the action of surface tension forces, is studied by numerical means. A finite- element discretization procedure is used to obtain approximate solutions to the Navier-Stokes equations. A Lagrangian approach is employed to deal with the large domain deformations which occur during the evolution of the filament. Typically we find that during the contraction a bulbous region forms at the end of the filament. The character of the evolution of the filament is found to be crucially dependent on the value of the Ohnesorge number Oh (a measure of viscous and surface tension forces). For large Ohnesorge numbers (Oh [Gt ] O(1)) it is found that the liquid filament remains stable during contraction, even when the initial length of the filament is much longer than the Rayleigh stability limit. The bulbous end becomes more localized with decreasing Ohnesorge number while at the same time a clear neck forms in front of the bulbous end. In addition we find that the region in which the pressure is minimum moves towards the neck. For sufficiently small Ohnesorge numbers (Oh [Lt ] O(0.01)) the filament becomes unstable with the radius of the neck decreasing and, eventually, the bulbous end breaking away from the filament.
The effects of excitation on the coherent and random motion in a plane wall jet
Authors: Zhou M. D. , Heine C. , Wygnanski I.
Published: April 2006

Three components of velocity fluctuations were measured in a plane turbulent wall jet which was modulated periodically by a sinusoidal pressure fluctuation in its settling chamber. The experiment was carried out in a closed-loop wind tunnel in the absence of an external stream at Reynolds numberRej=Ujb/v= 6900 and Strouhal numberStj=fb/Uj= 9.5 × 10−3, wherebis the width of the slot from which the jet emerges at an efflux velocityUj. A detailed comparison is provided with similar measurements made in a natural, unexcited turbulent wall jet. One of the purposes of this experiment was to establish the kinetic energy transfers which take place in the wall jet under controlled perturbations. More specifically, we were interested in determining the interactions occurring between the steady mean flow, the coherent eddies and the ‘random’ turbulent fluctuations. We used the triple decomposition of the equations of motion as suggested by Hussain (1983) and quickly observed that the usefulness of this decomposition depends on the definition of coherent motion, which is ambiguous in the presence of phase jitter. Two such definitions were considered and the results are discussed in the experimental case-study provided. An attempt is made to define quantitatively the intensities of the coherent motion in externally excited, wallbounded flows. It is a case-study and not a parametric investigation aimed at maximizing the effects of period oscillations on the wall jet.
Convection in a long box driven by heating and cooling on the horizontal boundaries
Authors: Sturman J. J. , Ivey G. N. , Taylor J. R.
Published: April 2006

Convection driven by spatially variable heat transfer across the water surface is an important transport mechanism in many geophysical applications. This flow is modelled in a rectangular tank with an aspect ratio, H/L, of 0.1 (where H and L are the tank height and length, respectively). Heat fluxes are applied through horizontal copper plates of length 0.1 L located at the top of one end of the tank and at the bottom of the other end. Experimental flows have been forced with heating at the bottom of the tank and cooling at the top, which gives rise to unstable convection in the end regions. Using water and a glycerol/water mix as the experimental fluids, flow visualization studies and measurements of temperature, velocity and heat flux have been made. Flow visualization studies revealed that complex unsteady turbulent flows occupied the end regions, while cubic velocity profiles characterized the horizontal laminar flow in the interior of the tank. Simple scaling arguments were developed for steady-state velocity and temperature fields, which are in good agreement with the experimental data. In the current experiments the portion of the plates closest to the tank interior (and to the tank endwall in the case of the glycerol/water experiments) were occupied by laminar boundary layers, while the remainder of the plates were occupied by turbulent flow. An effective Rayleigh number Ra* was defined, based upon the portion of the plate occupied by turbulent flow, as was a corresponding modified Nusselt number Nu*. The heat transfer was well predicted by classical Rayleigh-Bénard scaling with the Nusselt number Nu* ∼ Ra*1/3. The range of Ra* was 4.3 × 105 ≤ Ra* ≤ 1.7 × 108. Scaling arguments predicted the triple occupancy of the plates by differing boundary layer regimes within the range of 105 ≤ Ra* ≤ 1014.
Topology of fine-scale motions in turbulent channel flow
Authors: Blackburn Hugh M. , Mansour Nagi N. , Cantwell Brian J.
Published: April 2006

An investigation of topological features of the velocity gradient field of turbulent channel flow has been carried out using results from a direct numerical simulation for which the Reynolds number based on the channel half-width and the centreline velocity was 7860. Plots of the joint probability density functions of the invariants of the rate of strain and velocity gradient tensors indicated that away from the wall region, the fine-scale motions in the flow have many characteristics in common with a variety of other turbulent and transitional flows: the intermediate principal strain rate tended to be positive at sites of high viscous dissipation of kinetic energy, while the invariants of the velocity gradient tensor showed that a preference existed for stable focus/stretching and unstable node/saddle/saddle topologies. Visualization of regions in the flow with stable focus/stretching topologies revealed arrays of discrete downstream-leaning flow structures which originated near the wall and penetrated into the outer region of the flow. In all regions of the flow, there was a strong preference for the vorticity to be aligned with the intermediate principal strain rate direction, with the effect increasing near the walls in response to boundary conditions.
On the time dependence of the wave resistance of a body accelerating from rest
Authors: Liu Yuming , Yue Dick K. P.
Published: April 2006

We consider the large-time behaviour of the disturbances associated with an initial acceleration of a body in or near a free surface. As a canonical problem, we study the case of a body starting impulsively from rest to a constant velocity U. For a constant-strength translating point source (or dipole) started impulsively, it is known that the unsteady part of the Green function oscillates at the critical frequency ωc=g/4U (g is the gravitational acceleration) with an amplitude that decays with time, t, as t−1/2 and t−1 for t [Gt ] 1 in two (Havelock 1949) and three (Wehausen 1964) dimensions respectively. These classical results turn out to be non-realistic in that for an actual body, the associated source strengths are in general time dependent and a priori unknown, and must together satisfy the kinematic condition on the body boundary. We consider such an initial-boundary-value problem using a transient wave-source distribution on the body surface. Through asymptotic analyses, the unsteady behaviour of the solution at large time is obtained explicitly. Specifically, we show that for a general class of bodies satisfying a simple geometric condition (Γ ≠ 0), the decay rate of the transient oscillations (at frequency ωc) in the wave resistance and velocity potential is an order of magnitude faster: as t−3/2 and t−2, as t → ∞, in two and three dimensions respectively. For body geometries satisfying T = 0, for which the single source is a special case, the classical Green function results are recovered. These results are confirmed by an analysis in the frequency domain and substantiated by direct time-domain numerical simulations.
Filling flows, cliff erosion and cleaning flows
Authors: Peregrine D. H. , Kalliadasis S.
Published: April 2006

The flows considered here are those where a container or confined region is being filled by a substantial flow of liquid. The case of especial interest is where the incoming flow fills a large part of the cross-section of the container, for example where a nearly full flowing conduit has one end suddenly closed and hence fills rapidly, or where a water wave propagates close to the under surface of a horizontal structure and then rapidly fills the available space. These flows are taken to be so rapid that gravity is unimportant and yet not so violent that compressibility effects become significant. Important features, such as the greatly enhanced pressures and a thin high-velocity return jet are evaluated. The calculated pressures are very significantly greater than those associated with the incoming flow velocity and can be especially large when there is little clearance between the flow and the container boundary. One of many possible applications is in the extension of cracks and openings in coastal cliffs and structures. The flows could also be relevant to estimating the forces on the underside of some marine structures. A simple two-dimensional irrotational free-surface solution is found for the flow, which is steady in a suitably moving frame of reference.

Reversing the direction of one of these filling flows gives the case of a narrow high-speed jet which may be used to flush liquid out of cavities and containers. The optimum size of jet is calculated.