bluuebunny/crossref_metadata_2025_split huggingface dataset:
On the multifractal properties of the energy dissipation derived from turbulence data
Authors: Aurell E. , Frisch U. , Lutsko J. , Vergassola M. 
Published: April 2006

Various difficulties can be expected in trying to extract from experimental data the distribution of singularities, the f(α) function, of the energy dissipation. One reason is that the multifractal model of turbulence implies a dependence of the viscous cutoff on the singularity exponent. It is an open question if current hot-wire probes can resolve the scales implied by exponents a significantly less than 1.Two exactly soluble models are used to show how spurious scaling can occur, due to finite Reynolds number effects. In the Gaussian model the true velocity signal is replaced by independent Gaussian random variables. The dissipation, defined as the square of the difference of successive variables, has trivial scaling in so far as all the moments of spatial averages of the dissipation behave asymptotically as a uniform dissipation. Still, contamination by subdominant terms requires that scaling exponents for high-order moments be identified over an increasingly large range of scales. If the available range is limited by the Reynolds number, scaling exponents for high orders will be systematically underestimated and spurious intermittency will be inferred. Burgers’ model is used to highlight further problems. At finite Reynolds numbers, regions with no small-scale activity (away from shocks) have a residual dissipation which contributes a spurious point (α = 1,f(α) = 1). In addition, when the f(α) function is obtained by Legendre transform techniques, convex hull effects generate an entire spurious segment.Finally, Burgers’ model also indicates that the relation between exponents of structure functions and exponents of local dissipation moments, which goes back to Kolmogorov's (1962) work, leads to an inconsistency for structure functions of low positive order.
Almost symmetric solitary eddies in a two-layer ocean
Authors: Sutyrin G. G. , Dewar W. K. 
Published: April 2006

An asymptotic theory of two-dimensional planetary solitary eddies is presented. Previous studies in one-and-a-half layer models have discovered special classes of radially symmetric structure which are associated with eddies of permanent form. We generalize these studies by including an active lower layer and by considering the effects of azimuthal structure. Accordingly, we stress two main results; namely, (i) permanent-form two-layer eddies with essentially arbitrary radial structure exist, provided that the eddy includes a weak imbedded dipolar asymmetry and an appropriate counter-rotating deep flow, and (ii) fluid trapped under an eddy in Taylor columns can significantly affect eddy properties if the trapped fluid possesses non-trivial potential vorticity.The structural permanency in our solutions arises from a balance between nonlinear steepening, driven by the continuity equation, and planetary dispersion. The structural asymmetries affect eddy propagation, either by dipole interaction within the layer (as occurs in modons) or by pressure forces acting between layers. The primary role of the deep counter-rotating flow is to balance the net upper-layer transport. The interesting layer-layer interaction, however, involves higher-order dynamics and is sensitive to the continuity of the potential-vorticity field. In general, these eddies trap fluid both in the upper thermocline and in the lower layer.The dominance of oceanic anticyclones over cyclones is relatively well known. A main conclusion of this study is that the class of long-lived anticyclones is considerably broader than previously realized. This may help explain the observed bias toward anticyclonic eddies. A second conclusion is that estimates of material transport by eddies may need to account for the movement of fluid outside the main bowl of the eddies.
Free-surface cusps associated with flow at low Reynolds number
Authors: Jeong Jae-Tack , Moffatt H. K. 
Published: April 2006

When two cylinders are counter-rotated at low Reynolds number about parallel horizontal axes below the free surface of a viscous fluid, the rotation being such as to induce convergence of the flow on the free surface, then above a certain critical angular velocity Ωc, the free surface dips downwards and a cusp forms. This paper provides an analysis of the flow in the neighbourhood of the cusp, via an idealized problem which is solved completely: the cylinders are represented by a vortex dipole and the solution is obtained by complex variable techniques. Surface tension effects are included, but gravity is neglected. The solution is analytic for finite capillary number [Cscr ], but the radius of curvature on the line of symmetry on the free surface is proportional to exp (−32π[Cscr ]) and is extremely small for [Cscr ] [gsim ] 0.25, implying (in a real fluid) the formation of a cusp. The equation of the free surface is cubic in (x, y) with coefficients depending on [Cscr ], and with a cusp singularity when [Cscr ] = ∞.The influence of gravity is considered through a stability analysis of the free surface subjected to converging uniform strain, and a necessary condition for the development of a finite-amplitude disturbance of the free surface is obtained.An experiment was carried out using the counter-rotating cylinders as described above, over a range of capillary numbers from zero to 60; the resulting photographs of a cross-section of the free surface are shown in figure 13. For Ω < Ωc, a rounded crest forms in the neighbourhood of the central line of symmetry; for Ω > Ωc, the downward-pointing cusp forms, and its structure shows good agreement with the foregoing theory.
The leading edge of an oil slick, soap film, or bubble stagnant cap in Stokes flow
Authors: Harper J. F. 
Published: April 2006

Trace impurities often collect on the upstream side of an obstacle in the surface of flowing liquid. The transition from practically free surface to surface sufficiently clogged to be treated as stationary can be quite sharp. The viscous flow underneath is nonlinearly coupled to the convective mass transfer of surface-active material. For two-dimensional flow at high Reynolds number the first observations were due to Thoreau, Langton and Reynolds over 100 years ago, and the theory was given by Harper & Dixon in 1974. If the whole problem is considered from a frame of reference moving with the stream instead of fixed to the downstream surface film, the solution refers to the leading edge of a slowly spreading oil slick.The present work gives the theory corresponding to Harper & Dixon's for low Reynolds numbers (Stokes flow), for which there is a very simple leading approximation near the transition for a soluble surfactant, and a more complicated one, which can still be found exactly, for an insoluble surfactant which spreads onto clear liquid by surface diffusion. In both cases the surface remains flat: the ridge often observed is not a Stokes flow phenomenon.The results are used to clarify the circumstances in which Savic's stagnant-cap approximation is useful for a bubble rising in a viscous liquid: the rear stagnation point now plays the role of the obstacle in the surface, and the flow near the surface transition can be treated locally as if it were two-dimensional instead of axisymmetric.
Fixed-flux convection in a tilted slot
Authors: Cessi Paola , Young W. R. 
Published: April 2006

We study fixed-flux convection in a long, narrow slot which is inclined to the horizontal. (Gravity is in the vertical direction, and horizontal is perpendicular to this.) Because of the fixed-flux boundary conditions the convective modes have much larger lengthscales in the along-slot direction than in the transverse direction. In the case of a horizontal slot this disparity in scales has been previously exploited to obtain an amplitude equation for the single mode which first becomes unstable as the Rayleigh number is increased above critical. When the slot is tilted we show that there is a distinguished limit in which there are two active modes in the slightly supercritical regime. This new limit is when the horizontal wavenumber, the supercriticality, and the tilt of the slot away from vertical, are all small. A modification of the well-known expansion for fixed flux convection in a horizontal slot leads to a coupled system of partial differential equations for the amplitudes of the two modes.Numerical solution of this system suggests that all initial conditions eventually evolve into one of the two states, both of which consist of a single, steady roll in the cavity. The states are distinguished by the direction of circulation of the roll, and by the buoyancy fields, which are quite different in the two cases.
Boundary-layer separation of rotating flows past surface-mounted obstacles
Authors: Richards K. J. , Smeed D. A. , Hopfinger E. J. , D'Hières G. Chabert 
Published: April 2006

This paper describes laboratory experiments on the flow over a three-dimensional hill in a rotating fluid. The experiments were carried out in towing tanks, placed on rotating tables. Rotation is found to have a strong influence on the separation behind the hill. The topology of the separation is found to be the same for all the flows examined. The Rossby number R in the experiments is of order 1, the maximum value being 6. The separated flow is dominated by a single trailing vortex. In the majority of cases the surface stress field has a single separation line and there are no singular points. In a few experiments at the highest Rossby numbers the observations suggest more complex stress fields but the results are inconclusive.A criterion for flow separation is sought. For values of D/L > 1, where D is the depth of the flow and L the lengthscale of the hill, separation is found to be primarily dependent on R. At sufficiently small values of R separation is suppressed and the flow remains fully attached.Linear theory is found to give a good estimate for the critical value of R for flow separation. For hills with a moderate slope (slope ≤ 1) this critical value is around 1, decreasing with increasing slope. It is postulated that the existence of a single dominant trailing vortex is due to the uplifting and subsequent turning of transverse vorticity generated by surface pressure forces upstream of the separation line.
The asymptotic theory of hypersonic boundary-layer stability
Authors: Grubin S. E. , Trigub V. N. 
Published: April 2006

In this paper the linear stability of the hypersonic boundary layer is considered in the local-parallel approximation. It is assumed that the Prandtl-number ½ < σ < 1 and the viscosity-temperature law is a power function: μ/μ∞ = (T/T∞)ω. The asymptotic theory in the limit M∞ → ∞ is developed.Smith & Brown found for the Blasius base flow and Balsa & Goldstein for the mixing layer that, in this limit, the disturbances of the vorticity mode are located in the thin region between the boundary layer and the external flow. The gas model with σ = 1, ω = 1 was exploited in these studies. Here it is demonstrated that the vorticity mode also exists for gas with ½ < σ 1, ω < 1, but its structure and characteristics are considerably different. The nomenclature is discussed, i.e. what an acoustic mode and a vorticity mode are. The numerical solution of the inviscid instability problem for the vorticity mode is obtained for helium and compared with the solution of the complete Rayleigh equation at finite Mach numbers.The limit M∞ → ∞ in the local-parallel approximation for the Blasius base flow is considered so as to understand the viscous structure of the vorticity mode. The viscous stability problem for the vorticity mode is formulated under these assumptions. The problem contains only a single similarity parameter which is a function of the Mach and Reynolds numbers, the temperature factor and wave inclination angle. This problem is numerically solved for helium. The universal upper branch of the neutral curve is obtained as a result. The asymptotic results are compared with the numerical solutions of the complete problem.
The plane Symmetric sudden-expansion flow at low Reynolds numbers
Authors: Durst F. , Pereira J. C. F. , Tropea C. 
Published: April 2006

Detailed velocity measurements and numerical predictions are presented for the flow through a plane nominally two-dimensional duct with a Symmetric sudden expansion of area ratio 1:2. Both the experiments and the predictions confirm a symmetry-breaking bifurcation of the flow leading to one long and one short Separation zone for channel Reynolds numbers above 125, based on the upstream channel height and the maximum flow velocity upstream. With increasing Reynolds numbers above this value, the short separated region remains approximately constant in length whereas the long region increases in length.The experimental data were obtained using a one-component laser-Doppler anemometer at many Reynolds number values, with more extensive measurements being performed for the three Reynolds numbers 70, 300 and 610. Predictions were made using a finite volume method and an explicit quadratic Leith type of temporal discretization. In general, good agreement was found between measured and predicted velocity profiles for all Reynolds numbers investigated.
On Faraday waves
Authors: Miles John 
Published: April 2006

The standing waves of frequency ω and wavenumber κ that are induced on the surface of a liquid of depthdthat is subjected to the vertical displacementaocos 2wtare determined on the assumptions that: the effects of lateral boundaries are negligible; ε =ka0tanhkd[Lt ] 1 and 0 < ε−δ = O(δ3), where δ is the linear damping ratio of a free wave of frequency ω; the waves form a square pattern (which follows from observation). This problem, which goes back to Faraday (1831), has recently been treated by Ezerskiiet al.(1986) and Milner (1991) in the limit of deep-water capillary waves (kd, kl*[Gt ] 1, wherel*is the capillary length). Ezerskiiet al.show that the square pattern is unstable for sufficiently large ε—δ, and Milner shows that nonlinear damping is necessary for equilibration of the square pattern. The present formulation extends those of Ezerskiiet al.and Milner to capillary–gravity waves and finite depth and incorporates third-order parametric forcing, which is neglected in these earlier formulations but is comparable with third-order damping. There are quantitative differences in the resulting evolution equations (forkd, kl*[Gt ] 1), which appear to reflect errors in the earlier work.These formulations determine a locus of admissible waves, but they do not select a particular wave. The hypothesis that the selection process maximizes the energy-transfer rate to the Faraday wave selects the maximum of the resonance curve in a frequency-amplitude plane.
Experimental studies of the deformation and breakup of a synthetic capsule in steady and unsteady simple shear flow
Authors: Chang K. S. , Olbricht W. L. 
Published: April 2006

An experimental study is reported of the motion, deformation, and breakup of a synthetic capsule that is freely suspended in Couette flow. The capsule is a liquid drop surrounded by a thin polymeric membrane. The shape and orientation of the capsule are measured in steady flow and following the start-up of Couette flow. Results are compared with predictions of the small-deformation theory of Barthes-Biesel and co-workers. The data suggest that the capsule membrane is viscoelastic, and comparisons with theory yield values of the membrane elastic modulus and the membrane viscosity. The values of the elastic modulus of the capsule membrane deduced from the flow data are compared with independent measurements for the same capsule.When the flow-induced deformation becomes sufficiently large, the capsules break. Breakup begins at points on the membrane surface near the principal strain axis of the undisturbed flow. By examining the local deformation within the membrane, it is shown that breakup is correlated with local thinning of the membrane and is initiated at points where the thickness is a minimum.
Direct numerical simulation of isotropic turbulence interacting with a weak shock wave
Authors: Lee Sangsan , Lele Sanjiva K. , Moin Parviz 
Published: April 2006

Interaction of isotropic quasi-incompressible turbulence with a weak shock wave was studied by direct numerical simulations. The effects of the fluctuation Mach number Mt of the upstream turbulence and the shock strength M21 — 1 on the turbulence statistics were investigated. The ranges investigated were 0.0567 ≤ Mt ≤ 0.110 and 1.05 ≤ M1 ≤ 1.20. A linear analysis of the interaction of isotropic turbulence with a normal shock wave was adopted for comparisons with the simulations.Both numerical simulations and the linear analysis of the interaction show that turbulence is enhanced during the interaction with a shock wave. Turbulent kinetic energy and transverse vorticity components are amplified, and turbulent lengthscales are decreased. The predictions of the linear analysis compare favourably with simulation results for flows with M2t < a(M21 — 1) with a ≈ 0.1, which suggests that the amplification mechanism is primarily linear. Simulations also showed a rapid evolution of turbulent kinetic energy just downstream of the shock, a behaviour not reproduced by the linear analysis. Investigation of the budget of the turbulent kinetic energy transport equation shows that this behaviour can be attributed to the pressure transport term.Shock waves were found to be distorted by the upstream turbulence, but still had a well-defined shock front for M2t < a(M21— 1) with a ≈ 0.1). In this regime, the statistics of shock front distortions compare favourably with the linear analysis predictions. For flows with M2t > a(M21— 1 with a ≈ 0.1, shock waves no longer had well-defined fronts: shock wave thickness and strength varied widely along the transverse directions. Multiple compression peaks were found along the mean streamlines at locations where the local shock thickness had increased significantly.
Impingement of an unsteady two-phase jet on unheated and heated flat plates
Authors: Özdemir İ. Bedii , Whitelaw J. H. 
Published: April 2006

This paper is concerned with an experimental investigation of the oblique impingement of an unsteady, axisymmetric two-phase jet on heated surfaces. Size and velocity were measured simultaneously with a phase-Doppler velocimeter, and the spatial distributions over the wall jet were found to be correlated with the interfacial activities as inferred from vertical velocity measurements in the vicinity of the wall. These results are discussed together with size measurements by a laser-diffraction technique to quantify the effect of the approach conditions of the inflowing jet droplet field and wall temperature in relation to mechanisms of secondary atomization.Two mechanisms of secondary atomization were identified; the first did not involve direct wall contact and was due to the strain acting on the droplets by the continuous phase within the impingement region and was enhanced by thermal effects from the wall to cause breakup. The approaching velocity of the inflowing droplets to the plate was important to this process so that higher velocities increased the rate of strain within the impingement region and, consequently, the wall temperature promoting the secondary atomization shifted towards lower values. The second mechanism required direct wall contact and involved atomization of the film deposited on the wall by the impingement of the inflowing two-phase jet. With the penetration of high-speed inflowing droplets into the film, liquid mass was raised into the two-phase medium due to splashes from the film so that a new size class with larger droplets was generated. The resulting large droplets tended to stay close to the wall within the impingement region with small vertical velocitiesIn between the injections, the suspended droplet field above the film oscillated normal to the plate as a cloud so that the impact of large droplets on the film resulted in coalescence with the film and the ejection of smaller numbers of small droplets. The unsteady wall jet flow, caused by the arrival of the spray at the plate, swept the vertically oscillating droplet cloud radially outwards so that the resulting radial transport caused the dynamics of the unsteady film to be correlated with the size characteristics of the unsteady wall jet. Based on this phenomenological description, a radial droplet transport equation is derived.The correlation suggests that the secondary atomization with direct wall contact is the dominant process for the generation of a new size class within the wall flow and initiates the mutual interaction between the unsteady film and wall jet droplet field.
Internal wave generation in uniformly stratified fluids. Part 2. Moving point sources
Authors: Voisin Bruno 
Published: April 2006

The Green's function method is applied to the generation of internal gravity waves by a moving point mass source. Arbitrary motion of a source of arbitrary time dependence is treated using the impulsive Green's function, while ‘classical’ approaches of uniform motion of a steady or oscillatory source are recovered using the monochromatic Green's function. Waves have locally the structure of impulsive waves, emitted at the retarded time tr, and having propagated with the group velocity; at each position and time an implicit equation defines tr, in terms of which the waves are written. A source both oscillating and moving generates two systems of waves, with respectively positive and negative frequencies, and when oscillations vanish these systems merge into one.Three particular cases are considered: the uniform horizontal and vertical motions of a steady source, and the uniform horizontal motion of an oscillatory source. Waves spread downstream of the steady source. For the oscillatory source they can extend both upstream and downstream, depending on the ratio of the source frequency to the buoyancy frequency, and are contained inside conical wavefronts, parts of which are caustics. For horizontal motion, moreover, the steady analysis (based on the monochromatic Green's function) reveals the presence of two insignificant contributions overlooked by the unsteady analysis (based on the impulsive Green's function), but which for an extended source may become of the same order as the main contribution. Among those is an upstream columnar disturbance associated with blocking.