bluuebunny/crossref_metadata_2025 huggingface dataset:
Turbulent channel flow with large-amplitude velocity oscillations
Authors: Tardu Sedat F. , Binder Gilbert , Blackwelder Ron F.
Published: April 2006

Measurements in turbulent channel flow with forced oscillations covering a wide range of frequencies (ω+ = 0.03–0.0005) and amplitudes (10–70% of centreline velocity) are presented and discussed. Phase averages of the velocity  across the flow, and of the wall shear stress <τ>, as well as the turbulent fluctuations  and  are obtained with LDA and hot-film techniques. The time-mean quantities, except u’2, are only slightly affected by the imposed oscillations whatever their frequency and amplitude. It is shown that the appropriate similarity parameter for the oscillating quantities ũ and ĩ is the non-dimensional Stokes length l+s (or the frequency ω+ = 2/l+2s). In the regime of high-frequency forcing (l+s < 10) the oscillating flow ũ and ĩ are governed by purely viscous shear forces although the time-mean flow is fully turbulent. This behaviour may be explained by the physical significance of l+s. At lower frequency l+s 10, the oscillating flow is influenced by the turbulence, in particular the amplitude of ĩ increases with respect to the Stokes amplitude and becomes proportional to l+s. The relative amplitude of  and  decreases sharply with increasing forcing frequency once l+s < 25. This decay of the turbulence response is faster for the wall shear stress. For forcing frequencies such that l+s > 12,  and  lag behind  and <τ> by respectively about 75 and 130 viscous time units. These lags decrease by a factor 2 at higher forcing frequencies. It is shown that in the log layer, the turbulence modulation diffuses away from the wall with a diffusivity equal to that of the time-mean turbulence. The imposed oscillations are felt down to the small scales of the turbulence as may be evidenced from the cyclic modulation of the Taylor microscale, the skewness and the flatness factors of δu′/δt. The modulations of the skewness and the flatness go through a maximum around l+s = 12.
Turbulent mixing at an inversion layer
Authors: Perera M. J. A. M. , Fernando H. J. S. , Boyer D. L.
Published: April 2006

A series of laboratory experiments was carried out to examine the interaction between stratification and turbulence at an inversion layer, with the objective of gaining insight into certain wave–turbulence encounters in the atmosphere. A three-layer stratified fluid system, consisting of a (thick) strongly stratified inversion layer, sandwiched between an upper turbulent layer and a lower non-turbulent weakly stratified layer, was employed. Oscillating-grid-induced shear-free turbulence was used in the upper layer. During the experiments, a fourth (interfacial) layer developed in the region between the inversion and the turbulent layer, and most of the wave–turbulence interactions were confined to this layer. Detailed measurements of the vertical velocity structure, internal-wave parameters and mixing characteristics were made in the stratified layers and, whenever possible, the results were compared to available theoretical predictions.
The dispersion zone between fluids with different density and viscosity in a heterogeneous porous medium
Authors: Kempers L. J. T. M. , Haas H.
Published: April 2006

A shock front in the concentration between two miscible fluids flowing through a porous medium becomes dispersed owing to the heterogeneous structure of the porous medium. If the fluids have equal viscosity and density and the heterogeneity of the porous medium is statistically homogeneous, the length of the dispersion zone between the fluids is known to increase as (βX)½, where β is the dispersivity andXis the average displacement distance. At present the dispersivity is considered to be a property of only the porous medium. For the case where the fluids differ in density and/or in viscosity we have investigated the effect of the dynamics of the fluid flow on the magnitude of the dispersivity β and on the validity of theX½dependence of the dispersion zone's length. First, we measured the dispersivity in a 1.8 m long sandstone core with brine displacing water and with gas displacing oil. The measurements demonstrate that the dispersivity does indeed depend on the displacement velocity. Second, we monitored the expansion of the dispersion zone using detailed numerical simulations of the flow in a porous medium with statistically homogeneous heterogeneity. We found that the dispersion zone does grow asX½in the presence of a density contrast and a viscosity contrast, in spite of the nonlinearity of the governing equations. Third, we quantified the magnitude of the dispersivity by means of a random-walk model and tested the model against the experiments and the numerical simulations. Experiments, simulations and the model show that the dispersivity is strongly dependent on the displacement velocity in the conditionally stable flow regime. They also show that a nearly non-dispersive development of the shock front between the fluids occurs when gravity segregation dominates the dispersive effect of the porous medium. Even a very small difference in density, such as that between water and brine, can suppress the dispersivity significantly.
Liquid metal flow in a U-bend in a strong uniform magnetic field
Authors: Molokov S. , Bühler L.
Published: April 2006

Magnetohydrodynamic flows in a U-bend and in a right-angle bend are considered with reference to the toroidal concepts of self-cooled liquid-metal blankets. The ducts composing the bends have rectangular cross-sections. The applied magnetic field is aligned with the toroidal duct and perpendicular to ducts supplying liquid metal. For high Hartmann numbers the flow region is divided into cores and boundary layers of different types. The magnetohydrodynamic equations are reduced to a system of partial differential equations governing wall electric potentials and the core pressure. The system is solved numerically. The results show that the flow is very sensitive to variations of certain parameters, such as the wall conductance ratio and the aspect ratio of the toroidal duct cross-section. Depending on these parameters, the flow exhibits a variety of qualitatively different flow patterns. In particular, structures of helical and vortex type are obtained. A high-velocity jet occurs at the plasma-facing first wall and there is mixing of the fluid in the toroidal duct. These factors lead to desirable heat-transfer conditions.
The flapping shear layer formed by flow separation from the forward corner of a square cylinder
Authors: Lyn D. A. , Rodi W.
Published: April 2006

The turbulent shear layer and the associated recirculation region on the sidewall formed in flow separation from the forward corner of a square cylinder have been studied with one-component laser-Doppler velocimetry. Because of vortex shedding, the flow is approximately periodic, and is treated as a separated flow undergoing largeamplitude forcing at the shedding frequency. Phase (ensemble)-averaged velocities and turbulence intensities were obtained, and a close relationship in phase and amplitude between phase-averaged turbulence intensities and gradients of phase-averaged velocity is found in much of the flow region. The similarity behaviour of the phase-averaged profiles in the shear layer as well as the streamwise growth of the shear layer are investigated. While phase-averaged velocity profiles collapse well in similarity coordinates, normalized turbulence intensities exhibit systematic deviations from similarity. Shear-layer growth also departs markedly from the linear growth law of unforced plane mixing layers. The effect of the recirculation is suggested as a possible explanation for some of these deviations. Similarities to and differences from steady and forced mixing layers, steady separated flows with recirculation, and unsteady boundary layers are discussed.
Crossflow disturbances in three-dimensional boundary layers: nonlinear development, wave interaction and secondary instability
Authors: Malik M. R. , Li F. , Chang C.-L.
Published: April 2006

Nonlinear stability of a model swept-wing boundary layer, subject to crossflow instability, is investigated by numerically solving the governing partial differential equations. The three-dimensional boundary layer is unstable to both stationary and travelling crossflow disturbances. Nonlinear calculations have been carried out for stationary vortices and the computed wall vorticity pattern results in streamwise streaks which resemble quite well the surface oil-flow visualizations in swept-wing experiments. Other features of the stationary vortex development (half-mushroom structure, inflected velocity profiles, vortex doubling, etc.) are also captured in these calculations. Nonlinear interaction of the stationary and travelling waves is also studied. When initial amplitude of the stationary vortex is larger than the travelling mode, the stationary vortex dominates most of the downstream development. When the two modes have the same initial amplitude, the travelling mode dominates the downstream development owing to its higher growth rate. It is also found that, prior to laminar/turbulent transition, the three-dimensional boundary layer is subject to a high-frequency secondary instability, which is in agreement with the experiments of Poll (1985) and Kohama, Saric & Hoos (1991). The frequency of this secondary instability, which resides on top of the stationary crossflow vortex, is an order of magnitude higher than the frequency of the most-amplified travelling crossflow mode.
Linear stability of free shear flow of viscoelastic liquids
Authors: Azaiez J. , Homsy G. M.
Published: April 2006

The effects of viscoelasticity on the hydrodynamic stability of plane free shear flow are investigated through a linear stability analysis. Three different rheological models have been examined: the Oldroyd-B, corotational Jeffreys, and Giesekus models. We are especially interested in possible effects of viscoelasticity on the inviscid modes associated with inflexional velocity profiles. In the inviscid limit, it is found that for viscoelasticity to affect the instability of a flow described by the Oldroyd-B model, the Weissenberg number, We, has to go to infinity in such a way that its ratio to the Reynolds number, G ∞ We/Re, is finite. In this special limit we derive a modified Rayleigh equation, the solution of which shows that viscoelasticity reduces the instability of the flow but does not suppress it. The classical Orr–Sommerfeld analysis has been extended to both the Giesekus and corotational Jeffreys models. The latter model showed little variation from the Newtonian case over a wide range of Re, while the former one may have a stabilizing effect depending on the product ςWe where ς is the mobility factor appearing in the Giesekus model. We discuss the mechanisms responsible for reducing the instability of the flow and present some qualitative comparisons with experimental results reported by Hibberd et al. (1982), Scharf (1985 a, b) and Riediger (1989).
Theory and computations for breakup of unsteady subsonic or supersonic separating flows
Authors: Vickers I. P. , Smith F. T.
Published: April 2006

This study of flow just beyond a breakaway-separation point presents a description of planar nonlinear unsteady effects over a fairly wide parameter range, for a subsonic or supersonic boundary layer at large Reynolds numbers. The inviscid model thus produced essentially contains a vortex sheet near the smooth solid surface, with local inner–outer interaction. The governing equations couple the eddy velocity and pressure with the thicknesses of the detached boundary layer and the eddy. The computational method presented here uses a new adaptive gridding technique intended to capture accurately the spiky solution behaviour that develops and to compare with theory. Analysis and computations point to a breakup in the solution, suggesting an explanation for the start of transition and possible turbulent reattachment as found experimentally. The influence of the detached boundary-layer thickness proves crucial. The type of finite-time breakup encountered is studied analytically and the criterion for its occurrence is highlighted. This is guided by a characteristic analysis for a special case. The finite-time breakup is similar in spirit to, although different in detail from, a nonlinear breakup proposed earlier by one of the authors for general unsteady interactive boundary layers and it suggests a wide application of that nonlinear breakup theory and its criterion. Comparisons between computations and theory are found to be supportive.
Fully developed turbulent pipe flow: a comparison between direct numerical simulation and experiment
Authors: Eggels J. G. M. , Unger F. , Weiss M. H. , Westerweel J. , Adrian R. J. , Friedrich R. , Nieuwstadt F. T. M.
Published: April 2006

Direct numerical simulations (DNS) and experiments are carried out to study fully developed turbulent pipe flow at Reynolds numberRec≈ 7000 based on centreline velocity and pipe diameter. The agreement between numerical and experimental results is excellent for the lower-order statistics (mean flow and turbulence intensities) and reasonably good for the higher-order statistics (skewness and flatness factors). To investigate the differences between fully developed turbulent flow in an axisymmetric pipe and a plane channel geometry, the present DNS results are compared to those obtained from a channel flow simulation. Beside the mean flow properties and turbulence statistics up to fourth order, the energy budgets of the Reynolds-stress components are computed and compared. The present results show that the mean velocity profile in the pipe fails to conform to the accepted law of the wall, in contrast to the channel flow. This confirms earlier observations reported in the literature. The statistics on fluctuating velocities, including the energy budgets of the Reynolds stresses, appear to be less affected by the axisymmetric pipe geometry. Only the skewness factor of the normal-to-the-wall velocity fluctuations differs in the pipe flow compared to the channel flow. The energy budgets illustrate that the normal-to-the-wall velocity fluctuations in the pipe are altered owing to a different ‘impingement’ or ‘splatting’ mechanism close to the curved wall.
Local fluid and heat flow near contact lines
Authors: Anderson D. M. , Davis S. H.
Published: April 2006

We consider steady two-dimensional fluid flow and heat transfer near contact lines in single-phase and two-phase systems. Both single- and double-wedge geometries admit separable solutions in plane polar coordinates for both thermal and flow fields. We consider the class of functions which have bounded temperatures and velocities at the corner. When free surfaces are present, we seek local solutions, those that satisfy all local boundary conditions, and partial local solutions, those that satisfy all but the normal-stress boundary condition. Our aim in this work is to describe local fluid and heat flow in problems where these fields are coupled by determining for which wedge angles solutions exist, identifying singularities in the heat flux and stress which are present at contact lines, and determining the dependence of these singularities on the wedge angles. For thermal fields in two phases we identify two modes of heat transfer that are analogous to the two modes identified by Proudman & Asadullah (1988) for two-fluid flow. For non-isothermal flow, locally, convection does not play a role but coupling through thermocapillary effects on non-isothermal free surfaces can arise. We find that under non-isothermal conditions a planar free surface must leave a planar rigid boundary at an angle of π, the same angle found by Michael (1958) for an isothermal rigid/free wedge, in order to satisfy all local boundary conditions. Finally, we find that situations arise where no coupled solutions of the form sought can be found; we discuss means by which alternative solutions can be obtained.
A new roll-type instability in an oscillating fluid plane
Authors: Bolton Edward W. , Maurer J.
Published: April 2006

A new roll-type instability has been discovered experimentally. When fluid between two closely spaced, parallel plates is oscillated about an axis midway between the plates, it exhibits an instability that takes the form of longitudinal rolls aligned perpendicular to the axis of rotation. The basic-state oscillatory shear flow, before the onset of rolls, may be viewed as driven by the $\dot{\bm \Omega}\times \hat{\bm r}$ term of the Navier–Stokes equation in the oscillatory reference frame. A regime diagram is presented in a parameter space defined by the maximum amplitude of angular oscillation, α, and the non-dimensional frequency, Φ = ωd2/ν. The equilibrium wavelength of the rolls scales with d, the gap spacing between the plates, and it increases as Φ increases. Supercritical to a weak-roll onset, an abrupt transition to stronger roll amplitude occurs. Photographs of the cell after an impulsive start show the roll development and initial increase in roll wavelength. A variety of phenomena are observed, including wavelength selection via defect creation and elimination, front propagation, secondary wave instabilities, and the transition to turbulence. We also present solutions of the Navier–Stokes equation for the basic-state shear flow in a near-axis approximation. We develop a simple resonance model which shows some promise in understanding the low-α, high-Φ behaviour of strong rolls. A theoretical analysis of this instability is presented by Hall (1994).
On the instability of the flow in an oscillating tank of fluid
Authors: Hall Philip
Published: April 2006

The instability of a viscous fluid inside a rectangular tank oscillating about an axis parallel to the largest face of the tank is investigated in the linear regime. The flow is shown to be unstable to both longitudinal roll and standing wave instabilities. The particular cases of low and high oscillation frequencies are discussed in detail. The relationship between the roll instability and convective or centrifugal instabilities in unsteady boundary layers is discussed. The eigenvalue problems associated with the roll and standing wave instabilities are solved using Floquet theory and a combination of numerical and asymptotic methods. The results obtained are compared to the recent experimental investigation of Bolton & Maurer (1994) which indeed provided the stimulus for the present investigation.
The flow structure in the lee of an inclined 6:1 prolate spheroid
Authors: Fu T. C. , Shekarriz A. , Katz J. , Huang T. T.
Published: April 2006

Particle displacement velocimetry is used to measure the velocity and vorticity distributions around an inclined 6: 1 prolate spheroid. The objective is to determine the effects of boundary-layer tripping, incidence angle, and Reynolds number on the flow structure. The vorticity distributions are also used for computing the lateral forces and rolling moments that occur when the flow is asymmetric. The computed forces agree with results of direct measurements. It is shown that when the flow is not tripped, separation causes the formation of a pair of vortex sheets. The size of these sheets increases with increasing incidence angle and axial location. Their orientation and internal vorticity distribution also depend on incidence. Rollup into distinct vortices occurs in some cases, and the primary vortex contains between 20 % and 50 % of the overall circulation. The entire flow is unsteady and there are considerable variations in the instantaneous vorticity distributions. The remainder of the lee side, excluding these vortex sheets, remains almost vorticity free, providing clear evidence that the flow can be characterized as open separation. Boundary-layer tripping causes earlier separation on part of the model, brings the primary vortex closer to the body, and spreads the vorticity over a larger region. The increased variability in the vorticity distribution causes considerable force fluctuations, but the mean loads remain unchanged. Trends with increasing Reynolds number are conflicting, probably because of boundary-layer transition. The separation point moves towards the leeward meridian and the normal force decreases when the Reynolds number is increased from 0.42 × 106 to 1.3 × 106. Further increase in the Reynolds number to 2.1 × 106 and tripping cause an increase in forces and earlier separation.
Theoretical analysis of inertially irrotational and solenoidal flow in two-dimensional radial-flow pump and turbine impellers with equiangular blades
Authors: Visser F. C. , Brouwers J. J. H. , Badie R.
Published: April 2006

Using the theory of functions of a complex variable, in particular the method of conformal mapping, the irrotational and solenoidal flow in two-dimensional radialflow pump and turbine impellers fitted with equiangular blades is analysed. Exact solutions are given for the fluid velocity along straight radial pump and turbine impeller blades, while for logarithmic spiral pump impeller blades solutions are given which hold asymptotically as (r1/r2)n→0, in whichr1is impeller inner radius,r2is impeller outer radius andnis the number of blades. Both solutions are given in terms of a Fourier series, with the Fourier coefficients being given by the (Gauss) hypergeometric function and the beta function respectively. The solutions are used to derive analytical expressions for a number of parameters which are important for practical design of radial turbomachinery, and which reflect the two-dimensional nature of the flow field. Parameters include rotational slip of the flow leaving radial impellers, conditions to avoid reverse flow between impeller blades, and conditions for shockless flow at impeller entry, with the number of blades and blade curvature as variables. Furthermore, analytical extensions to classical one-dimensional Eulerian-based expressions for developed head of pumps and delivered work of turbines are given.
On the dynamics of gravity currents in a channel
Authors: Klemp Joseph B. , Rotunno Richard , Skamarock William C.
Published: April 2006

We attempt to clarify the factors that regulate the propagation and structure of gravity currents through evaluation of idealized theoretical models along with two-dimensional numerical model simulations. In particular, we seek to reconcile research based on hydraulic theory for gravity currents evolving from a known initial state with analyses of gravity currents that are assumed to be at steady state, and to compare these approaches with both numerical simulations and laboratory experiments. The time-dependent shallow-water solution for a gravity current propagating in a channel of finite depth reveals that the flow must remain subcritical behind the leading edge of the current (in a framework relative to the head). This constraint requires that hf/d ≤ 0.347, where hf is the height of the front and d is the channel depth. Thus, in the lock-exchange problem, inviscid solutions corresponding to hf/d = 0.5 are unphysical, and the actual currents have depth ratios of less than one half near their leading edge and require dissipation or are not steady. We evaluate the relevance of Benjamin's (1968) well-known formula for the propagation of steady gravity currents and clarify discrepancies with other theoretical and observed results. From two-dimensional simulations with a frictionless lower surface, we find that Benjamin's idealized flow-force balance provides a good description of the gravity-current propagation. Including surface friction reduces the propagation speed because it produces dissipation within the cold pool. Although shallow-water theory over-estimates the propagation speed of the leading edge of cold fluid in the ‘dam-break’ problem, this discrepancy appears to arise from the lack of mixing across the current interface rather than from deficiencies in Benjamin's front condition. If an opposing flow restricts the propagation of a gravity current away from its source, we show that the propagation of the current relative to the free stream may be faster than predicted by Benjamin's formula. However, in these situations the front propagation remains dependent upon the specific source conditions and cannot be generalized.
Instability of strongly nonlinear waves in vortex flows
Authors: Kribus A. , Leibovich S.
Published: April 2006

Weakly nonlinear descriptions of axisymmetric cnoidal and solitary waves in vortices recently have been shown to have strongly nonlinear counterparts. The linear stability of these strongly nonlinear waves to three-dimensional perturbations is studied, motivated by the problem of vortex breakdown in open flows. The basic axisymmetric flow varies both radially and axially, and the linear stability problem is therefore nonseparable. To regularize the generalization of a critical layer, viscosity is introduced in the perturbation problem. In the absence of the waves, the vortex flows are linearly stable. As the amplitude of a wave constituting the basic flow increases owing to variation in the level of swirl, stability is first lost to non-axisymmetric ‘bending’ modes. This instability occurs when the wave amplitude exceeds a critical value, provided that the Reynolds number is larger enough. The critical wave amplitudes for instability typically are large, but not large enough to create regions of closed streamlines. Examination of the most-amplified eigenvectors shows that the perturbations tend to be concentrated downstream of the maximum streamline displacement in the wave, in a position consistent with the observed three-dimensional perturbations in the interior of a bubble type of vortex breakdown.
Equation of motion of a diffusing vortex sheet
Authors: Dhanak M. R.
Published: April 2006

Moore's (1978) equation for following the evolution of a thin layer of uniform vorticity in two dimensions is extended to the case of a non-uniform, instantaneously known, vorticity distribution, using the method of matched asymptotic expansions. In general, the vorticity distribution satisfies a boundary-layer equation. This has a similarity solution in the case of a vortex layer of small thickness in a viscous fluid. Using this solution, an equation of motion of a diffusing vortex sheet is obtained. The equation retains the simplicity of Birkhoff's integro-differential equation for a vortex sheet, while incorporating the effect of viscous diffusion approximately. The equation is used to study the growth of long waves on a Rayleigh layer.
Supercooling in hypersonic nitrogen wind tunnels
Authors: Griffith Wayland C. , Yanta William J. , Ragsdale William C.
Published: April 2006

Recent experimental observation of supercooling in large hypersonic wind tunnels using pure nitrogen identified a broad range of non-equilibrium metastable vapour states of the flow in the test cell. To investigate this phenomenon a number of real-gas effects are analysed and compared with predictions made using the ideal-gas equation of state and equilibrium thermodynamics. The observed limit on the extent of supercooling is found to be at 60% of the temperature difference from the sublimation line to Gibbs’ absolute limit on phase stability. The mass fraction then condensing is calculated to be 12–14%. Included in the study are virial effects, quantization of rotational and vibrational energy, and the possible role of vibrational relaxation and freezing in supercooling. Results suggest that use of the supercooled region to enlarge the Mach–Reynolds number test envelope may be practical. Data from model tests in supercooled flows support this possibility.
Faraday waves: rolls versus squares
Authors: Miles John
Published: April 2006

Weakly nonlinear capillary—gravity waves of frequency ω and wavenumber k that are induced on the surface of a liquid in a square cylinder that is subjected to the vertical displacement a0 cos 2ωt are studied on the assumptions that: 0 < δ < ka0, where δ is the linear damping ratio; the dominant modes are cos kx and cos ky, where x and y are Cartesian coordinates in a horizontal plane. The formulation extends those of Simonelli & Gollub (1989), Feng & Sethna (1989), Nagata (1989, 1991) and Umeki (1991) by incorporating capillarity, cubic forcing and cubic damping. The results are also applicable to a laterally unbounded fluid, but the basic symmetry then is hypothetical rather than imposed by the boundaries. Canonical evolution equations for the modal amplitudes are determined from an average Lagrangian. The fixed points of the evolution equations comprise: (i) the null solution; (ii) an orthogonal pair of rolls described by either cos kx or cos ky; (iii) an orthogonal pair of squares described by either cos kx + cos ky or cos kx – cos ky; (iv) coupled-mode solutions for which both modes are active and neither in phase nor in antiphase. The solutions for squares are isomorphic to those for rolls through a linear transformation of the coefficients in the Hamiltonian. The fixed points for rolls and squares lie on separate loci in an energy–frequency plane that intersect the null solution at a pair of pitchfork bifurcations, one of which is definitely supercritical and the other of which may be either subcritical or supercritical. The parametric domain of the various solutions includes subdomains in which squares/rolls are stable/unstable and conversely. In the limiting case of deep-water capillary waves in the threshold domain 0 < ka0 — δ < 8δ3/9 all of the rolls and coupled-mode solutions are unstable, while squares are stable except for fixed points between the subcritical bifurcation (if it exists) and the corresponding turning point.
Modulation of the growth rate of short surface capillary–gravity wind waves by a long wave
Authors: Troitskaya Yu. I.
Published: April 2006

Modulation of the growth rate of short capillary–gravity surface wind waves in the presence of a long wave with steepness much smaller than the maximum is studied theoretically. The Miles (1962) mechanism taking into account the viscous wave stresses in the air flow is considered to be the main process of short-wave generation. The short-wave growth rate is defined by the wind velocity gradient in the viscous sublayer of the logarithmic boundary layer. The long wave propagating on the wave surface induces an additional component of the wind velocity gradient oscillating with the length and time periods of the long wave, which results in modulation, with the same period, of the growth rate of the short wave riding on the long one. The growthrate modulation amplitude depends on the parameter M being of the order of the relation between the oscillating and the mean wind velocity gradients in the viscous sublayer \[M=\frac{2kac}{u^2_*}(ckv_{\alpha})^{1/2} \] (where c, k, a are the phase velocity, the wavenumber and the elevation amplitude of the long wave; va is the viscosity coefficient in the air; u* is the wind friction velocity). When M = O(1) (weak winds and long waves) the oscillating component of the shortwave growth rate is of the same order as the mean one. If M is much smaller than unity, then the relative amplitude of the growth rate is of the same order as the steepness of the long wave.
The effect of torsion on the motion of a helical vortex filament
Authors: Ricca Renzo L.
Published: April 2006

In this paper we analyse in detail, and for the first time, the rôle of torsion in the dynamics of twisted vortex filaments. We demonstrate that torsion may influence considerably the motion of helical vortex filaments in an incompressible perfect fluid. The binormal component of the induced velocity, asymptotically responsible for the displacement of the vortex filament in the fluid, is closely analysed. The study is performed by applying the prescription of Moore & Saffman (1972) to helices of any pitch and a new asymptotic integral formula is derived. We give a rigorous proof that the Kelvin régime and its limit behaviour are obtained as a limit form of that integral asymptotic formula. The results are compared with new calculations based on the re-elaboration of Hardin's (1982) approach and with results obtained by Levy & Forsdyke (1928) and Widnall (1972) for helices of small pitch, here also re-elaborated for the purpose.
Ventilated oscillatory boundary layers
Authors: Conley Daniel C. , Inman Douglas L.
Published: April 2006

Boundary layers arising from flows which oscillate parallel to a permeable bed, and are subject to oscillating percolation of the same frequency as the bed parallel flow, referred to here as ‘ventilated oscillatory boundary layers’, are the subject of this laboratory study. These boundary layers are intended to approximate naturally occurring wave boundary layers over permeable beds. Measurements of boundary-layer velocities, bed stress and turbulent flow properties are presented. It is observed that suction (flow into the bed) enhances the near-bed velocities and bed stress while injection (flow out of the bed) leads to a reduction in these quantities. As the ventilated oscillatory boundary layer experiences both these phenomenon in one full cycle, the result is a net stress and a net boundary-layer velocity in an otherwise symmetric flow. While production of turbulence attributable to injection is enhanced, the finite time required for this to occur leads to a greater vertically averaged turbulence in the suction half-cycle. Turbulence generated in the suction half-cycle is maintained in a compact layer much closer to the bed. These effects appear to hold for$\widetilde{Re}$ranging from 105to 106and for oscillations other than sinusoidal.
Evolution and breakup of vortex rings in straining and shearing flows
Authors: Marshall J. S. , Grant J. R.
Published: April 2006

A study of the effect of external straining and shearing flows on the evolution and form of breakup of vortex rings has been performed. Two orientations each of straining and shearing flows are considered. A theoretical analysis of the ring motion for small strain and shear rates is performed, and it is found that for shearing and straining flows in the plane of the ring, the ring may oscillate periodically. For a straining flow with compression normal to the initial plane of the ring, the linear theory predicts that the ring radius will expand with time. For shearing flow normal to the initial plane of the ring, the linear theory predicts tilting of the ring in the direction of the shear flow rotation.

Numerical calculations are performed with both single vortex filaments and with a three-dimensional discrete vortex element method. The numerical calculations confirm the predictions of the linear theory for values of strain and shear rates below a certain critical value (which depends on the ratio R/σ0 of initial ring to core radii), whereas for strain and shear rates above this value the ring becomes very elongated with time and eventually pinches off. Three distinct regimes of long-time behaviour of the ring have been identified. Regime selection depends on initial ring geometry and orientation and on values of strain and shear rates. These regimes include (i) periodic oscillations with no pinching off, (ii) pinching off at the ring centre, and (iii) development of an elongated vortex pair at the ring centre and wider ‘heads’ near the ends (with pinching off just behind the heads). The boundaries of these regimes and theoretical reasons for the vortex behaviour in each case are described. It is also shown that the breakup of stretched vortex rings exhibits a self-similar behaviour, in which the number and size of ‘offspring’ vortices, at the point of pinching-off the ring, may be scaled by the product of the strain rate e (or shear rate s) and the oscillation period τ of a slightly elliptical ring with mean radius R.
Electrohydrodynamic stability of a slightly viscous jet
Authors: Mestel A. J.
Published: April 2006

Many electro-spraying devices raise to a high electric potential a pendant drop of weakly conducting fluid, which may adopt a conical shape from whose apex a thin, charged jet is emitted. Such a jet eventually breaks up into fine droplets, but often displays surprising longevity. This paper examines the stability of an incompressible cylindrical jet carrying surface charge in a tangential electric field, allowing for the finite rate of charge relaxation. The viscosity is assumed to be small so that the shear resulting from the tangential surface stress can be large, even for relatively small fields. This shear can suppress surface tension instabilities, but if too large, it excites electrical ones. For imperfect conductors, surface charge is redistributed by the rapid fluid reaction to variations in tangential stress as well as by conduction. Phase differences between the effects due to the tangential field and the surface charge lead to charge ‘over-relaxation’ instabilities, but the maximum growth rate can still be lower than in the absence of electric effects.
Finite-size effects in forced two-dimensional turbulence
Authors: Smithr Leslie M. , Yakhot Victor
Published: April 2006

A new mechanism for the creation of structures in two-dimensional turbulence is investigated. The forced Navier-Stokes equations are solved numerically in a periodic square in the limit of zero viscosity. The force is a white-in-time random noise acting in a narrow band of high wavenumbers. The inverse-cascade process and the presence of the boundary lead ultimately to a pile-up of energy in the lowest wavenumber (Bose condensation). In the asymptotic limit where the enstrophy cascade range is negligible, Bose condensation is solely responsible for the generation of coherent vortices and intermittency in the system. We present the evolution of the velocity and vorticity fields through the later stages of the condensate state, and explore the possible implications for atmospheric turbulence constrained by the periodic domain about the earth.
Resonantly generated internal waves in a contraction
Authors: Clarke S. R. , Grimshaw R. H. J.
Published: April 2006

The near-resonant flow of a stratified fluid through a localized contraction is considered in the long-wavelength weakly nonlinear limit to investigate the transient development of nonlinear internal waves and whether these might lead to local steady hydraulic flows. It is shown that under these circumstances the response of the fluid will fall into one of three categories, the first governed by a forced Korteweg–de Vries equation and the latter two by a variable-coefficient form of this equation. The variable-coefficient equation is discussed using analytical approximations and numerical solutions when the forcing is of the same (positive) and of opposite (negative) polarity to that of free solitary waves in the fluid. For positive and negative forcing, strong and weak resonant regimes will occur near the critical point. In these resonant regimes for positive forcing the flow becomes locally steady within the contraction, while for negative forcing it remains unsteady within the contraction. The boundaries of these resonant regimes are identified in the limits of long and short contractions, and for a number of common stratifications.
Hypersonic boundary-layer separation on a cold wall
Authors: Kerimbekov R. M. , Ruban A. I. , Walker J. D. A.
Published: April 2006

An asymptotic theory of laminar hypersonic boundary-layer separation for large Reynolds number is described for situations when the surface temperature is small compared with the stagnation temperature of the inviscid external gas flow. The interactive boundary-layer structure near separation is described by well-known tripledeck concepts but, in contrast to the usual situation, the displacement thickness associated with the viscous sublayer is too small to influence the external pressure distribution (to leading order) for sufficiently small wall temperature. The present interaction takes place between the main part of the boundary layer and the external flow and may be described as inviscid–inviscid. The flow in the viscous sublayer is governed by the classical boundary-layer equations and the solution develops a singularity at the separation point. A main objective of this study is to show how the singularity may be removed in different circumstances.
Dynamics of a drop in a constricted capillary tube
Authors: Tsai T. M. , Miksis Michael J.
Published: April 2006

Here we study the dynamics of a bubble or drop as it is driven by a pressure gradient through a capillary tube. For the case of a straight capillary, the drop can either approach a steady-state shape or the rear of the drop develops a re-entrant cavity. Also, depending on the initial conditions, the drop can break apart into smaller drops. For flow through a constricted capillary tube, depending on the physical parameters of the problem, the drop can either move through the constriction or break into two or more pieces as it moves past the constriction. We study this snap-off process numerically and determine the effect of the physical parameters on the dynamics of the drop.
Tidal excitation of hydromagnetic waves and their damping in the Earth
Authors: Kerswell R. R.
Published: April 2006

We examine the possibility that the Earth's outer core, as a tidally distorted fluid-filled rotating spheroid, may be the seat of an elliptical instability. The instability mechanism is described within the framework of a simple Earth-like model. The preferred forms of wave disturbance are explored and a likely growth rate supremum deduced. Estimates are made of the Ohmic and viscous decay rates of such hydromagnetic waves in the outer core. Rather than a conclusive disparity of scales, we find that typical elliptical growth rates, Ohmic decay rates and viscous decay rates all have the same order for plausible core fields and core-to-mantle conductivities. This study is all the more timely considering the recent realization that the Earth's precession may also drive similar instabilities at comparable strengths in the outer core.
Applications of exact solutions to the Navier–Stokes equations: free shear layers
Authors: Varley Eric , Seymour Brian R.
Published: April 2006

A family of exact solutions to the Navier—Stokes equations is used to analyse unsteady three-dimensional viscometric flows that occur in the vicinity of a plane boundary that translates and rotates with time-varying velocities. Such flows are important in the study of flows that are produced by rotating machinery. They are also useful in describing local behaviour in more complex global flows, such as that produced in a shear layer by the passage of a disturbance in the mainstream. An example is the flow produced in a turbulent shear layer by the passage of the core of a Rankine vortex. When the effect of viscosity is unimportant, the use of Lagrangian coordinates reduces the mathematical problem to that of solving a set of linear ordinary differential equations.
Steep solitary waves in water of finite depth with constant vorticity
Authors: Vanden-Broeck J.-M.
Published: April 2006

Solitary waves with constant vorticity in water of finite depth are calculated numerically by a boundary integral equation method. Previous calculations are confirmed and extended. It is shown that there are branches of solutions which bifurcate from a uniform shear current. Some of these branches are characterized by a limiting configuration with a 120° angle at the crest of the wave. Other branches extend for arbitrary large values of the amplitude of the wave. The corresponding solutions ultimately approach closed regions of constant vorticity in contact with the bottom of the channel. A numerical scheme is presented to calculate directly these closed regions of constant vorticity. In addition, it is shown that there are branches of solutions which do not bifurcate from a uniform shear flow.
The boundary-layer flow due to a vortex approaching a cylinder
Authors: Affes H. , Xiao Z. , Conlisk A. T.
Published: April 2006

The three-dimensional unsteady boundary layer induced by a vortex filament moving outside a circular cylinder is considered. In the present paper, we focus attention on the situation where the inviscid flow is fully three-dimensional but is symmetric with respect to the top centreline of the cylinder. The motion of the vortex toward the cylinder leads to separation of the boundary layer; in the present work a large unsteady adverse pressure gradient develops as well. Results for the three-dimensional streamlines, the vorticity distribution, and the velocity component normal to the cylinder indicate the presence of a region of unsteady three-dimensional secondary flow structure of rather complex shape located deep within the boundary layer. Within this three-dimensional secondary flow the fluid is progressively squeezed into a narrow region under the main vortex and it is expected that a local three-dimensional jet will develop sending boundary-layer fluid out into the main stream. It is pointed out that such three-dimensional eruptive behaviour has been observed in experiments. The results indicate the development of a three-dimensional singularity in the boundary-layer equations.
Critical points in a turbulent near wake
Authors: Zhou Y. , Antonia R. A.
Published: April 2006

Velocity data were obtained in the turbulent wake of a circular cylinder with an orthogonal array of sixteen X-wires, eight in the (x, y)-plane and eight in the (x, z)-plane. By applying the phase-plane technique to these data, three types of critical points (where the velocity is zero and the streamline slope is indeterminate) were identified. Of these, foci and saddle points occurred most frequently, although a significant number of nodes was also found. Flow topology and properties associated with these points were obtained in each plane. Saddle-point regions associated with spanwise vortices provide the dominant contribution to the Reynolds shear stress and larger contributions to the normal stresses than focal regions. The topology was found to be in close agreement with that obtained from other methods of detecting features of the organized motion. The inter-relationship between critical points simultaneously identified in the two planes can provide some insight into the three-dimensionality of the organized motion. Foci in the (x, z)-plane correspond, with relatively high probability and almost negligible streamwise separation, to saddle points in the (x, y)-plane and are interpreted in terms of ribs aligned with the diverging separatrix between consecutive spanwise vortex rolls. Foci in the (x, z)-plane which correspond, with relatively weak probability, to foci in the (x, y)-plane seem consistent with a distortion of the vortex rolls in the (y, z)-plane.