bluuebunny/crossref_metadata_2025 huggingface dataset:
Internal temperature distributions of droplets vaporizing in high-temperature convective flows
Authors: Wong Shwin-Chung , Lin Ar-Cheng
Published: April 2006

Transient internal temperature distributions of vaporizing droplets have been carefully measured, using fine thermocouples at 1 atm. and 1000 K. Droplet diameters are fixed at 2000 ± 50 μm with Reynolds numbers being 17, 60 or 100. Fuels tested are JP-10, n-decane and JP-10 thickened with polystyrene. The effects of Reynolds number and liquid viscosity on internal temperature distribution and heating mechanism have been examined. Experimental results indicate that liquid viscosity or circulation intensity strongly affects the temperature distribution and heating mechanism. In contrast, the temperature distributions associated with the three different Reynolds numbers have shown little difference for both low- and high-viscosity cases. For the low-viscosity JP-10 droplets at Reynolds numbers up to 100, where the vortex model of Sirignano and coworkers (Prakash & Sirignano 1978; Tong & Sirignano 1983) has been claimed to be applicable, the vortex model appears qualitatively correct but quantitatively inaccurate. Physical reasons for the deviation have been discussed. Solutions of the full Navier-Stokes equations appear to accord better with the experimental temperature distributions. Circulative heat transport decreases progressively as liquid viscosity increases. A semi-empirical effective conductivity model for high-viscosity cases yields a very good simulation of the experimental temperature distributions at all the Reynolds numbers when proper effective conductivity factors are chosen. A discussion on internal droplet dynamics and heating mechanisms in physical terms has been provided.
An experimental study of vortex shedding behind linearly tapered cylinders at low Reynolds number
Authors: Piccirillo Paul S. , Van Atta C. W.
Published: April 2006

Experiments were performed to study vortex shedding behind a linearly tapered cylinder. Four cylinders were used, with taper ratios varying from 50:1 to 100:1. The cylinders were each run at four different velocities, adjusted to cover the range of laminar vortex shedding for a non-tapered cylinder. The flow was confirmed to consist of discrete shedding cells, each with a constant frequency. For a centrespan Reynolds number greater than 100, the dimensionless mean cell length was found to be a constant. Individual cell size was found to be roughly self-similar. New shedding cells were created on the ends of the cylinders, or in regions adjacent to areas not shedding. Successful scalings were found for both the cell shedding frequencies and their differences, the modulation frequencies. The modulation frequencies were found to be constant along the cylinder span. The shedding frequency Strouhal number versus Reynolds number curve was found to have a slightly steeper slope than the Strouhal number curve for a non-tapered cylinder. Vortex shedding was found to begin at a local Reynolds number of about 60, regardless of any other factors. End effects were found to be of little importance.

The vortex splits, which form the links between shedding cells, were found to be similar in some respects to those found by earlier investigators. Amplitude results suggested that the splits at different spanwise locations are temporally sequenced by an overall flow mechanism, a supposition confirmed by flow visualization. Wavelet analysis results showed that while the behaviour of the shedding frequencies in time was relatively unaffected by changing taper ratio, the behaviour of the modulation frequency in time was greatly affected. Comparisons with other experiments point out the universality of vortex splitting phenomena.
On the transient motion of ordered suspensions of liquid drops
Authors: Pozrikidis C.
Published: April 2006

The transient motion of ordered suspensions of liquid drops, initially arranged on a cubic lattice, is studied as a model of suspension rheology. An asymptotic three-term expansion for the effective stress tensor of a dilute suspension of spherical drops is derived based on the Faxén law for the stresslet. Comparisons with available exact results for cubic lattices suggests that the expansion is remarkably accurate even at concentrations close to maximum packing. The behaviour of suspensions with recurrent structure evolving under the influence of a simple shear flow is investigated, and the results show that the time-averaged behaviour may differ substantially from the instantaneous behaviour. Transient normal stress differences may vanish in the mean, but make appreciable contributions to the instantaneous dynamics. The effect of particle deformation is assessed by numerically computing the motion of initially spherical drops arranged on a cubic lattice. At large times, the suspension is shown to exhibit periodic motions in which the drops oscillate about a mean shape with a phase shift which depends on the geometry of the lattice and the physical properties of the fluids. It is shown that drop deformations cause shear thinning and some type of elastic behaviour, and may lower the effective viscosity of the suspension below that corresponding to the dilute limit.
Hydrodynamics of electrophoretic motion in an alternating electric field
Authors: Sawatzky R. P. , Babchin A. J.
Published: April 2006

Electrophoresis in an alternating electric field is the basis for electroacoustical measurements. These measurements provide new means of investigating the electrokinetic properties of colloidal systems. In order to relate electroacoustical signals to the charge and the size of colloidal particles, an expression is required for the dynamic electrophoretic mobility of colloidal particles in a continuous fluid. In this paper, an exact analytical solution to the problem is given for an arbitrary ratio between the particle radius and the electric double-layer thickness, in the case where the electrokinetic potential of the uniformly charged particle is small and unaffected by the alternating field.
Temperature dependence of rotational relaxation in shock waves of nitrogen
Authors: Boyd I. D.
Published: April 2006

Computations are presented for one-dimensional Shockwaves of diatomic nitrogen. The direct simulation Monte Carlo method (DSMC) is employed. A model which allows the use of the Sutherland viscosity model in the DSMC technique is further developed to include the modelling of rotational relaxation. This is achieved by employing a temperature-dependent expression for the rotational collision number to simulate the rate of relaxation, in contrast to earlier DSMC studies which employed a constant value for the collision number. The behaviour of the new model is first considered for rotational relaxation in a heat bath. Comparison is made with the more traditional DSMC collision model termed the variable hard sphere (VHS) model in which the viscosity has a fixed temperature exponent. These two models are then applied to a number of shock-wave cases for which experimental data exist. These have Mach numbers ranging from 1.5 to 26, yet the enthalpies involved are sufficiently low to allow omission of vibrational relaxation. It is found that both the VHS and Sutherland viscosity models give excellent agreement with the experimental data for shock-wave thickness, and for profiles of density, rotational temperature, and velocity. The most significant finding of the study is that the reciprocal shock thickness varies with the upstream temperature condition. This variation is observed in the experimental data, and is simulated numerically by employing the temperature-dependent expression for the rotational collision number.
The long-wave limit in the asymptotic theory of hypersonic boundary-layer stability
Authors: Grubin S. E. , Trigub V. N.
Published: April 2006

This paper discusses the long-wave limit of the asymptotic theory of hypersonic boundary-layer stability for a gas with the Prandtl number ½ < σ < 1 and with the viscosity–temperature law being a power function. The investigation is confined to the local-parallel approximation.

In the long-wave limit the vorticity mode starts to interact with the acoustic disturbances in the boundary-layer region. The general solution of the linear problem in the boundary-layer inner region is analysed numerically and analytically. This solution is matched with the long-wave vorticity-mode solution near the transition layer. As a result, the inviscid instability problem for a hypersonic boundary layer is formulated. The analytical solution of this problem is found and analysed. The different limits of the solution are considered and the universal forms of the dependence are obtained. A similarity parameter is found which is a function of the Prandtl number and the power in the viscosity–temperature law. A significant change of the solution behaviour is noticed when this parameter passes a critical value. The asymptotic structure of the amplification rate, as a function of the wavenumber, is described and discussed.
Orbital flow around a circular cylinder. Part 2. Attached flow at larger amplitudes
Authors: Chaplin John R.
Published: April 2006

A time-stepping numerical model of uniform circular orbital flow around a cylinder provides results which are compared with the steady-state predictions of a boundary-layer solution by Riley. At small amplitudes of motion excellent agreement is found in most respects, but in the numerical model the outer recirculating flow and related components of loading do not reach a steady state after any finite time. At a Stokes parameter β of 500, the boundary-layer approach remains reasonably accurate for amplitudes of motion up to about 8 % of the cylinder diameter; for amplitudes up to twice this at the same value of β the flow remains largely attached. The strength of the outer recirculating flow is enhanced by nonlinear interactions, but the computed nonlinear loading exceeds that observed in experiments. Flow visualization shows a three-dimensional structure in the flow, and it is argued that this has an important effect on the loading that cannot yet be predicted. A computed force component at a frequency of about 30 % of that of the ambient flow is related to the retrogressive motion of vortex structures around the cylinder.
Mixed mode convection in an inclined slot
Authors: Fujimura K. , Kelly R. E.
Published: April 2006

Nonlinear interaction between transverse disturbances and longitudinal rolls has been investigated for flow in an inclined slot with a heated lower wall when both modes of instability occur at nearly the same value of the control parameter. This condition is shown to be possible for a fluid with Prandtl number greater than 0.263 897, For slightly supercritical values of the Rayleigh number (R) when the critical Rayleigh number for longitudinal rolls RLC is somewhat less than that for transverse stationary rolls, RSC, and for transverse travelling waves, RTC, longitudinal rolls occur first and then remain stable as R is increased beyond RSC or RTC; no mixed mode state occurs. In contrast, if RSc or RTc is slightly below RLC, pure transverse modes exist for only a relatively small range of R beyond RSC or RTC. Thereafter, a three-dimensional mixed mode state occurs well before RLC is reached, i.e. three-dimensionality sets in on a subcritical basis. As R approaches RLC the contribution of the transverse mode decreases continuously until a pure longitudinal roll state emerges for R slightly greater than RLC. Mixed mode convection is also investigated for a special choice of parameters when three modes, namely transverse stationary rolls, transverse travelling waves and longitudinal rolls, become unstable simultaneously. Longitudinal rolls again emerge as the stable supercritical state.
Flow in deformable porous media. Part 1 Simple analysis
Authors: Spiegelman Marc
Published: April 2006

Many processes in the Earth, such as magma migration, can be described by the flow of a low-viscosity fluid in a viscously deformable, permeable matrix. The purpose of this and a companion paper is to develop a better physical understanding of the equations governing these two-phase flows. This paper presents a series of analytic approximate solutions to the governing equations to show that the equations describe two different modes of matrix deformation. Shear deformation of the matrix is governed by Stokes equation and can lead to porosity-driven convection. Volume changes of the matrix are governed by a nonlinear dispersive wave equation for porosity. Porosity waves exist because the fluid flux is an increasing function of porosity and the matrix can expand or compact in response to variations in the fluid flux. The speed and behaviour of the waves depend on the functional relationship between permeability and porosity. If the partial derivative of the permeability with respect to porosity, ∂kϕ/∂ϕ, is also an increasing function of porosity, then the waves travel faster than the fluid in the pores and can steepen into porosity shocks. The propagation of porosity waves, however, is resisted by the viscous resistance of the matrix to volume changes. Linear analysis shows that viscous stresses cause plane waves to disperse and provide additional pressure gradients that deflect the flow of fluid around obstacles. When viscous resistance is neglected in the nonlinear equations, porosity shock waves form from obstructions in the fluid flux. Using the method of characteristics, we quantify the specific criteria for shocks to develop in one and two dimensions. A companion paper uses numerical schemes to show that in the full equations, viscous resistance to volume changes causes simple shocks to disperse into trains of nonlinear solitary waves.
The wake from a cylinder subjected to amplitude-modulated excitation
Authors: Nakano M. , Rockwell D.
Published: April 2006

Controlled, amplitude-modulated excitation of a cylinder at low Reynolds number (Re equals; 136) in the cross-stream direction generates several states of response of the near wake including: a locked-in wake structure, which is periodic at the modulation frequency; a period-doubled wake structure, which is periodic at a frequency half the modulation frequency; and a destabilized structure of the wake, which is periodic at the modulation frequency, but involves substantial phase modulations of the vortex formation relative to the cylinder displacement. The occurrence of each of these states depends upon the dimensionless modulation frequency, as well as the nominal frequency and amplitude of excitation. Transition through states of increasing disorder can be attained by either decreasing the modulation frequency or increasing the amplitude of excitation at a constant value of nominal frequency. These states of response in the near wake are crucial in determining whether the far wake is highly organized or incoherent. Both of these extremes are attainable by proper selection of the parameters of excitation.
Boundary interactions for two-dimensional granular flows. Part 2. Roughened boundaries
Authors: Campbell Charles S.
Published: April 2006

The global behaviour of a granular flow is critically dependent on its interaction with whatever solid boundaries with which it comes into contact, whether they be used to drive, retard or simply bound the flow field. This paper describes the results of a computer simulation study of the effects of roughening boundaries by ‘gluing’ particles to the surfaces. Roughness is commonly used in experimental devices as a way of approximating a no-slip condition between a granular material and the driving surfaces. On a microscopic level, this produces a boundary that extends out into the flow field to the limit of the roughness elements. This has a strong effect on the way that forces, and, in particular, torque, is transmitted to the particles in the neighbourhood of the boundary.
Hydrodynamic instabilities in cylindrical thermocapillary liquid bridges
Authors: Kuhlmann H. C. , Rath H. J.
Published: April 2006

The hydrodynamic stability of steady axisymmetric thermocapillary flow in a cylindrical liquid bridge is investigated by linear stability theory. The basic state and the three-dimensional disturbance equations are solved by various spectral methods for aspect ratios close to unity. The critical modes have azimuthal wavenumber one and the most dangerous disturbance is either a pure hydrodynamic steady mode or an oscillatory hydrothermal wave, depending on the Prandtl number. The influence of heat transfer through the free surface, additional buoyancy forces, and variations of the aspect ratio on the stability boundaries and the neutral mode are discussed.
The three-dimensional evolution of a plane mixing layer: pairing and transition to turbulence
Authors: Moser Robert D. , Rogers Michael M.
Published: April 2006

The evolution of three-dimensional temporally evolving plane mixing layers through as many as three pairings has been simulated numerically. All simulations were begun from a few low-wavenumber disturbances, usually derived from linear stability theory, in addition to the mean velocity. Three-dimensional perturbations were used with amplitudes ranging from infinitesimal to large enough to trigger a rapid transition to turbulence. Pairing is found to inhibit the growth of infinitesimal three-dimensional disturbances, and to trigger the transition to turbulence in highly three-dimensional flows. The mechanisms responsible for the growth of three-dimensionality and onset of transition to turbulence are described. The transition to turbulence is accompanied by the formation of thin sheets of spanwise vorticity, which undergo secondary rollups. The post-transitional simulated flow fields exhibit many properties characteristic of turbulent flows.
Spanwise scale selection in plane mixing layers
Authors: Rogers Michael M. , Moser Robert D.
Published: April 2006

Direct numerical simulations of temporally evolving plane mixing layers undergoing as many as three pairings have been examined for evidence of spanwise scale change. All simulations were begun from a few low-wavenumber disturbances, usually derived from linear stability theory, in addition to the mean velocity. The amplitude of the initial three-dimensional disturbances varied from infinitesimal to large enough to trigger a rapid transition to turbulence. The time required for a change of characteristic spanwise scale with infinitesimal three-dimensional disturbances was found to be very long, requiring three or more pairings to complete a doubling of the spanwise scale. Stronger three-dimensionality can produce more rapid scale changes, but it is also likely to trigger transition to turbulence. No evidence was found for a change from an organized array of rib vortices at one spanwise scale to a similar array at a larger spanwise scale.
The growth of large scales at defect sites in the plane mixing layer
Authors: Dallard T. , Browand F. K.
Published: April 2006

The evolution of vortex structure in the vicinity of a pattern defect or dislocation, generated experimentally by forcing a high Reynolds number mixing layer, is studied using a new two-dimensional wavelet transform called Arc. This transform localizes spectral information in physical space – as all wavelets do – but is not direction-specific in wavenumber space. Various types of forcing, including forcing at the fundamental and subharmonic wavenumbers, produce a range of mixing-layer responses. The most significant finding is that a dislocation site acts as a nucleus and initiates a rapid, localized evolution to larger scales. The area of the localized ‘patch’ grows approximately as the square of downstream distance. Defect-initiated patches bear generic similarities to the disturbed regions in cylinder wakes – commented upon recently by many researchers – and in particular to the Λ-structures described by Williamson (1992).
On the instability of hypersonic flow past a flat plate
Authors: Blackaby Nicholas D. , Cowley Stephen J. , Hall Philip
Published: April 2006

The instability of hypersonic boundary-layer flow over a flat plate is considered. The viscosity of the fluid is taken to be governed by Sutherland's formula, which gives a more accurate representation of the temperature dependence of fluid viscosity at hypersonic speeds than Chapman's approximate linear law. A Prandtl number of unity is assumed. Attention is focused on inviscid instability modes of viscous hypersonic boundary layers. One such mode, the ‘vorticity’ mode, is thought to be the fastest growing disturbance at high Mach numbers, M [Gt ] 1; in particular it is believed to have an asymptotically larger growth rate than any viscous instability. As a starting point we investigate the instability of the hypersonic boundary layer which exists far downstream from the leading edge of the plate. In this regime the shock that is attached to the leading edge of the plate plays no role, so that the basic boundary layer is non-interactive. It is shown that the vorticity mode of instability operates on a different lengthscale from that obtained if a Chapman viscosity law is assumed. In particular, we find that the growth rate predicted by a linear viscosity law overestimates the size of the growth rate by O((log M)½). Next, the development of the vorticity mode as the wavenumber decreases is described. It is shown, inter alia, that when the wavenumber is reduced to O(M-3/2) from the O(1) initial, ‘vorticity-mode’ scaling, ‘acoustic’ modes emerge.

Finally, the inviscid instability of the boundary layer near the leading-edge interaction zone is discussed. Particular attention is focused on the strong-interaction zone which occurs sufficiently close to the leading edge. We find that the vorticity mode in this regime is again unstable. The fastest growing mode is centred in the adjustment layer at the edge of the boundary layer where the temperature changes from its large, O(M2). value in the viscous boundary layer, to its O(1) free-stream value. The existence of the shock indirectly, but significantly, influences the instability problem by modifying the basic flow structure in this layer.
Mode interaction models for near-wall turbulence
Authors: Sanghi Sanjeev , Aubry Nadine
Published: April 2006

Intermittent bursting events, similar to those characterizing the dynamics of near-wall turbulence, have been observed in a low-dimensional dynamical model (Aubry et al. 1988) built from eigenfunctions of the proper orthogonal decomposition (Lumley 1967). In the present work, we investigate the persistency of the intermittent behaviour in higher - but still of relatively low-dimensional dynamical systems. In particular, streamwise variations which were not accounted for in an explicit way in Aubry et al.'s model are now considered. Intermittent behaviour persists but can be of a different nature. Specifically, the non-zero streamwise modes become excited during the eruptive events so that rolls burst downstream into smaller scales. When structures have a finite length, they travel at a convection speed approximately equal to the mean velocity at the top of the layer (y+ ≈ 40). In all cases, intermittency seems to be due to homoclinic cycles connecting hyperbolic fixed points or more complex (apparently chaotic) limit sets. While these sets lie in the zero streamwise modes invariant subspace, the connecting orbits consist of nonzero streamwise modes travelling downstream. Chaotic limit sets connected by quasi-travelling waves have also been observed in a spatio-temporal chaotic regime of the Kuramoto–Sivashinsky equation (Aubry & Lian 1992a). When the limit sets lose their steadiness, the elongated rolls become randomly active, as they probably are in the real flow. A coherent structure study in our resulting flow fields is performed in order to relate our findings to experimental observations. It is shown that streaks, streamwise rolls, horseshoe vortical structures and shear layers, present in our models, are all connected to each other. Finally, criteria to determine a realistic value of the eddy viscosity parameter are developed.
Effects of Görtler vortices, wall cooling and gas dissociation on the Rayleigh instability in a hypersonic boundary layer
Authors: Fu Yibin , Hall Philip
Published: April 2006

In a hypersonic boundary layer over a wall of variable curvature, the region most susceptible to Görtler vortices is the temperature adjustment layer sitting at the edge of the boundary layer. This temperature adjustment layer is also the most dangerous site for Rayleigh instability. In this paper, we investigate how the existence of large-amplitude Görtler vortices affects the growth rate of Rayleigh instability. The effects of wall cooling and gas dissociation on this instability are also studied. We find that all these mechanisms increase the growth rate of Rayleigh instability and are therefore destabilizing.
On a uniformly valid model for surface wave interaction
Authors: Agnon Yehuda
Published: April 2006

Nonlinear interaction of surface wave trains is studied. Zakharov's kernel is extended to include the vicinity of trio resonance. The forced wave amplitude and the wave velocity changes are then first order rather than second order. The model is applied to remove near-resonance singularities in expressions for the change of speed of one wave train in the presence of another. New results for Wilton ripples and the drift current and setdown in shallow water waves are readily derived. The ideas are applied to the derivation of forced waves in the vicinity of quartet and quintet resonance in an evolving wave field.
Properties of a bidisperse particle–gas suspension Part 1. Collision time small compared with viscous relaxation time
Authors: Kumaran V. , Koch Donald L.
Published: April 2006

The properties of a dilute bidisperse particle–gas suspension under low Reynolds number, high Stokes number conditions are studied in the limit τcτv using a perturbation analysis in the small parameter v, which is proportional to the ratio of timescales τc/τv. Here, τc is the time between successive collisions of a particle, and tv is the viscous relaxation time. The leading-order distribution functions for the two species are isotropic Gaussian distributions, and are identical to the molecular velocity distributions in a two-component gas at equilibrium. Balance equations are written for the mean and mean-square velocities, using a distribution function that is a small perturbation from the isotropic Gaussian. The collisional terms are calculated by performing an ensemble average over the relative configurations of the colliding particles, and the mean velocity and velocity variances are calculated correct to O(v2) by solving the balance equations. The difference in the mean velocities of the two species is O(v) smaller than the mean velocity of the suspension, and the fluctuating velocity is O(v½) smaller than the mean velocity.
Properties of a bidisperse particle–gas suspension Part 2. Viscous relaxation time small compared with collision time
Authors: Kumaran V. , Koch Donald L.
Published: April 2006

The properties of a dilute bidisperse particle–gas suspension under low Reynolds number, high Stokes number conditions are studied in the limit τv [Lt ] τc, where τc is the time between successive collisions of a particle, and τv is the viscous relaxation time. In this limit, the particles relax close to their terminal velocity between successive collisions, and we use a perturbation analysis in the small parameter ε, which is proportional to τv/τc, about a base state in which all the particles settle at their terminal velocities. The mean velocities of the two species are O(ε) different from their terminal velocities, and the mean-square velocities are O(ε) smaller than the square of the terminal velocity. The distribution functions for the two species, which incorporate the first effects of collisions between particles settling at their terminal velocities, are derived. The velocity distribution is highly anisotropic in this limit, and the mean-square velocity in the vertical direction is twice that in the horizontal plane. The distribution function for each species is singular at its terminal velocity, and the distributions are non-zero in a finite region in velocity space between the two terminal velocities.
Transonic flow around the leading edge of a thin airfoil with a parabolic nose
Authors: Rusak Z.
Published: April 2006

Transonic potential flow around the leading edge of a thin two-dimensional general airfoil with a parabolic nose is analysed. Asymptotic expansions of the velocity potential function are constructed at a fixed transonic similarity parameter (K) in terms of the thickness ratio of the airfoil in an outer region around the airfoil and in an inner region near the nose. These expansions are matched asymptotically. The outer expansion consists of the transonic small-disturbance theory and it second-order problem, where the leading-edge singularity appears. The inner expansion accounts for the flow around the nose, where a stagnation point exists. Analytical expressions are given for the first terms of the inner and outer asymptotic expansions. A boundary value problem is formulated in the inner region for the solution of a uniform sonic flow about an infinite two-dimensional parabola at zero angle of attack, with a symmetric far-field approximation, and with no circulation around it. The numerical solution of the flow in the inner region results in the symmetric pressure distribution on the parabolic nose. Using the outer small-disturbance solution and the nose solution a uniformly valid pressure distribution on the entire airfoil surface can be derived. In the leading terms, the flow around the nose is symmetric and the stagnation point is located at the leading edge for every transonic Mach number of the oncoming flow and shape and small angle of attack of the airfoil. The pressure distribution on the upper and lower surfaces of the airfoil is symmetric near the edge point, and asymmetric deviations increase and become significant only when the distance from the leading edge of the airfoil increases beyond the inner region. Good agreement is found in the leading-edge region between the present solution and numerical solutions of the full potential-flow equations and the Euler equations.
Initial and boundary value problems of internal gravity waves
Authors: Simakov Sergey T.
Published: April 2006

The paper considers the generation of Boussinesq internal waves in the framework of the Green's function method. For certain domains it is shown how to construct Green's functions using the fundamental solution of the equation. The behaviour of the solution at large times for an impulsively started monochromatic point source is studied, attention being focused on the growth rate of the oscillation amplitude on the characteristic surfaces of the steady-oscillation equation which are emitted from the point source. In addition a simple extended source is considered, for which a focusing singularity phenomenon is shown to take place.
Invariants in dissipationless hydrodynamic media
Authors: Tur A. V. , Yanovsky V. V.
Published: April 2006

We propose a general geometric method of derivation of invariant relations for hydrodynamic dissipationless media. New dynamic invariants are obtained. General relations between the following three types of invariants are established, valid in all models: Lagrangian invariants, frozen-in vector fields and frozen-in co-vector fields. It is shown that frozen-in integrals form a Lie algebra with respect to the commutator of the frozen fields. The relation between frozen-in integrals derived here can be considered as the Backlund transformation for hydrodynamic-type systems of equations. We derive an infinite family of integral invariants which have either dynamic or topological nature. In particular, we obtain a new type of topological invariant which arises in all hydrodynamic dissipationless models when the well-known Moffatt invariant vanishes.
Non-steady peristaltic transport in finite-length tubes
Authors: Li Meijing , Brasseur James G.
Published: April 2006

The classical lubrication-theory model of steady peristaltic transport of periodic sinusoidal waves in infinite-length tubes (Shapiro et al. 1969) is generalized to arbitrary wave shape and wavenumber in tubes of finite length. Whereas the classical model is steady in a frame of reference moving with the peristaltic waves, peristaltic transport in a finite-length tube is inherently non-steady. It may be shown, however, that pumping performance is independent of tube length if there exists an integral number of peristaltic waves in the tube. Three particularly interesting characteristics of non-steady peristalsis are described: (i) fluctuations in pressure and shear stress arise due to a non-integral number of waves in the finite-length tube; (ii) retrograde motion of fluid particles during peristaltic transport (reflux) has inherently different behaviour with single peristaltic waves as compared to multiple ‘train waves’, and (iii) finite tube length, the number of peristaltic waves and the degree of tube occlusion affect global pumping performance. We find that, whereas significant increases in pressure and shear stress result from the tube-to-wave length ratio being non-integral, global pumping performance is only slightly degraded by the existence of a non-integral number of waves in the tube during peristaltic transport. Furthermore, the extent of retrograde motion of fluid particles is much greater with single waves than with train waves. These results suggest that in the design and analysis of peristaltic pumps attention should be paid to the unsteady effects of finite tube length and to the differences between single and multiple peristaltic waves.
On equatorially trapped boundary inertial waves
Authors: Zhang K.
Published: April 2006

Solutions of the Poincaré equation describing equatorially trapped three-dimensional boundary travelling waves in rotating spherical systems are discussed. It is shown that the combined effects of Coriolis forces and spherical curvature enable the equatorial region to form an equatorial waveguide tube with characteristic latitudinal radius (2/m)1/2 and radial radius (1/m), where m is azimuthal wavenumber. Inertial waves with sufficiently simple structure along the axis of rotation and sufficiently small azimuthal wavelength must be trapped in the equatorial waveguide tube. The structure and frequency of the inertial waves are thus hardly affected by the presence of an inner sphere or by the condition of higher latitudes. Further calculations on rotating spherical fluid shells of finite internal viscosity and stressfree boundaries are also discussed.
Transient motion of a confined rarefied gas due to wall heating or cooling
Authors: Wadsworth Dean C. , Erwin Daniel A. , Muntz E. Phillip
Published: April 2006

The transient motion that arises in a confined rarefied gas as a container wall is rapidly heated or cooled is simulated numerically. The Knudsen number based on nominal gas density and characteristic container dimension is varied from near-continuum to highly rarefied conditions. Solutions are generated with the direct simulation Monte Carlo method. Comparisons are made with finite-difference solutions of the Navier–Stokes equations, the limiting free-molecular values, and (continuum) results based on a small perturbation analysis. The wall heating and cooling scenarios considered induce relatively large acoustic disturbances in the gas, with characteristic flow speeds on the order of 20% of the local sound speed. Steady-state conditions are reached after on the order of 5 to 10 acoustic time units, here based on the initial speed of sound in the gas and the container dimension. As rarefaction increases, the initial gas response time is decreased. For the case of a rapid increase in wall temperature, transient rarefaction effects near the wall greatly alter gas response compared to the continuum predictions, even at relatively small nominal Knudsen number. For wall cooling, the continuum solution agrees well with direct simulation at that same Knudsen number. A local Knudsen number, based on the mean free path and the scale length of the temperature gradient, is found to be a more suitable indicator of transient rarefaction effects.
The rollup of a vortex layer near a wall
Authors: Jiménez Javier , Orlandi Paolo
Published: April 2006

The behaviour of an inviscid vortex layer of non-zero thickness near a wall is studied, both through direct numerical simulation of the two-dimensional vorticity equation at high Reynolds numbers, and using an approximate ordinary nonlinear integro-differential equation which is satisfied in the limit of a thin layer under long-wavelength perturbations. For appropriate initial conditions the layer rolls up and breaks into compact vortices which move along the wall at constant speed. Because of the effect of the wall, they correspond to equilibrium counter-rotating vortex dipoles. This breakup can be related to the disintegration of the initial conditions of the approximate nonlinear dispersive equation into solitary waves. The study is motivated by the formation of longitudinal vortices from vortex sheets in the wall region of a turbulent channel.
Instability waves on the air–sea interface
Authors: Wheless G. H. , Csanady G. T.
Published: April 2006

We used a compound matrix method to integrate the Orr–Sommerfeld equation in an investigation of short instability waves (λ < 6 cm) on the coupled shear flow at the air–sea interface under suddenly imposed wind (a gust model). The method is robust and fast, so that the effects of external variables on growth rate could easily be explored. As expected from past theoretical studies, the growth rate proved sensitive to air and water viscosity, and to the curvature of the air velocity profile very close to the interface. Surface tension had less influence, growth rate increasing somewhat with decreasing surface tension. Maximum growth rate and minimum wave speed nearly coincided for some combinations of fluid properties, but not for others.

The most important new finding is that, contrary to some past order of magnitude estimates made on theoretical grounds, the eigenfunctions at these short wavelengths are confined to a distance of the order of the viscous wave boundary-layer thickness from the interface. Correspondingly, the perturbation vorticity is high, the streamwise surface velocity perturbation in typical cases being five times the orbital velocity of free waves on an undisturbed water surface. The instability waves should therefore be thought of as fundamentally different flow structures from free waves: given their high vorticity, they are akin to incipient turbulent eddies. They may also be expected to break at a much lower steepness than free waves.
A model of defect-induced pairing in mixing layers
Authors: Yang Ruixin , Browand Frederic K. , Coullet Pierre , Huerre Patrick
Published: April 2006

Experiment have shown that the well-known vortex pairing process may take place first in defect regions where the fundamental structure is weakest. A model is introduced here to describe this defect-induced pairing process. The model is constructed in such a way that, in a certain parameter range, a stable fundamental mode and a stable subharmonic mode may coexist. The numerical simulation demonstrates that, when initial conditions consist of a dominant fundamental with one or more defects, the subharmonic component is preferentially generated in the cores of these defects. Moreover, the results also indicate that pairing may first commence wherever the fundamental mode is weakest provided the white-noise level of the subharmonic is high enough. The numerical results are in good agreement with experimental observations.
Instability of rectangular jets
Authors: Tam Christopher K. W. , Thies Andrew T.
Published: April 2006

The instability of rectangular jets is investigated using a vortex-sheet model. It is shown that such jets support four linearly independent families of instability waves. Within each family there are infinitely many modes. A way to classify these modes according to the characteristics of their mode shapes or eigenfunctions is proposed. The stability equation for jets of this geometry is non-separable so that the traditional methods of analysis are not applicable. It is demonstrated that the boundary element method can be used to calculate the dispersion relations and eigenfunctions of these instability wave modes. The method is robust and efficient. A parametric study of the instability wave characteristics has been carried out. A sample of the numerical results is reported here. It is found that the first and third modes of each instability wave family are corner modes. The pressure fluctuations associated with these instability waves are localized near the corners of the jet. The second mode, however, is a centre mode with maximum fluctuations concentrated in the central portion of the jet flow. The centre mode has the largest spatial growth rate. It is anticipated that as the instability waves propagate downstream the centre mode would emerge as the dominant instability of the jet.
Boundary mixing in stratified reservoirs
Authors: Imberger J. , Ivey G. N.
Published: April 2006

We consider the steady flow driven by turbulent mixing in a benthic boundary layer along a sloping boundary in the general case of a non-uniform background density gradient. The velocity and density fields are decomposed into barotropic and baroclinic components, and a solution is obtained by taking an expansion in the small parameter A, the aspect ratio of the boundary layer defined as the thickness divided by the alongslope length. The flow in the boundary layer is governed by a balance between alongslope baroclinic and barotropic density fluxes. A number of flow regimes can exist, and we show that in the regimes relevant to lakes and reservoirs, the barotropic flow is divergent and drives an exchange flow between the boundary layer and the interior. This leads to changes in the interior density gradient which are significant when compared to field observations.
The sweeping decorrelation hypothesis and energy–inertial scale interaction in high Reynolds number flows
Authors: Praskovsky Alexander A. , Gledzer Evgeny B. , Karyakin Mikhail Yu. , Zhou And Ye
Published: April 2006

The random sweeping decorrelation hypothesis was analysed theoretically and experimentally in terms of the higher-order velocity structure functions $D_{u_i}^{(m)}(r) = \left< [u_i^m(x + r) - u_i^m(x)]^2\right>$. Measurements in two high Reynolds number laboratory shear flows were used: in the return channel (Rλ ≈ 3.2 × 103) and in the mixing layer (Rλ ≈ 2.0 × 103) of a large wind tunnel. Two velocity components (in the direction of the mean flow, u1, and in the direction of the mean shear, u2) were processed for m = 1−4. The effect of using Taylor's hypothesis was estimated by a specially developed method, and found to be insignificant. It was found that all the higher-order structure functions scale, in the inertial subrange, as r2/3. Such a scaling has been argued as supporting evidence for the sweeping hypothesis. However, our experiments also established a strong correlation between energy- and inertial-range excitation. This finding leads to the conclusion that the sweeping decorrelation hypothesis cannot be exactly valid.

The hypothesis of statistical independence of large- and small-scale excitation was directly checked with conditionally averaged moments of the velocity difference $\left< [u_i(x + r) - u_i(x)]^l\right>_{u_i^*}, l = 2-4$, at a fixed value of the large-scale parameter u*i. Clear dependence of the conditionally averaged moments on the level of averaging was found. In spite of a strong correlation between the energy-containing and the inertial-scale excitation, universality of the intrinsic structure of the inertial subrange was shown.
Scaling laws for fully developed turbulent shear flows. Part 1. Basic hypotheses and analysis
Authors: Barenblatt G. I.
Published: April 2006

The present work consists of two parts. Here in Part 1, a scaling law (incomplete similarity with respect to local Reynolds number based on distance from the wall) is proposed for the mean velocity distribution in developed turbulent shear flow. The proposed scaling law involves a special dependence of the power exponent and multiplicative factor on the flow Reynolds number. It emerges that the universal logarithmic law is closely related to the envelope of a family of power-type curves, each corresponding to a fixed Reynolds number. A skin-friction law, corresponding to the proposed scaling law for the mean velocity distribution, is derived.

In Part 2 (Barenblatt & Prostokishin 1993), both the scaling law for the velocity distribution and the corresponding friction law are compared with experimental data.
Scaling laws for fully developed turbulent shear flows. Part 2. Processing of experimental data
Authors: Barenblatt G. I. , Prostokishin V. M.
Published: April 2006

In Part 1 of this work (Barenblatt 1993) a non-universal scaling law (depending on the Reynolds number) for the mean velocity distribution in fully developed turbulent shear flow was proposed, together with the corresponding skin friction law. The universal logarithmic law was also discussed and it was shown that it can be understood, in fact, as an asymptotic branch of the envelope of the curves corresponding to the scaling law.

Here in Part 2 the comparisons with experimental data are presented in detail. The whole set of classic Nikuradze (1932) data, concerning both velocity distribution and skin friction, was chosen for comparison. The instructive coincidence of predictions with experimental data suggests the conclusion that the influence of molecular viscosity within the main body of fully developed turbulent shear flows remains essential, even at very large Reynolds numbers. Meanwhile, some incompleteness of the experimental data presented in the work of Nikuradze (1932) is noticed, namely the lack of data in the range of parameters where the difference between scaling law and universal logarithmic law predictions should be the largest.
A note on the distortion of a flat-plate boundary layer by free-stream vorticity normal to the plate
Authors: Goldstein M. E. , Leib S. J.
Published: April 2006

The purpose of this note is to construct a local solution that eliminates a residual velocity discontinuity in the inviscid portion of a solution obtained in a recent paper by Goldstein, Leib & Cowley (1992). This result is of importance because it shows that the solution obtained in that paper is entirely non-singular outside the viscous wall boundary layer and that any singularity in the problem will have to arise in the usual way through a breakdown in the viscous boundary layer.