bluuebunny/crossref_metadata_2025_split huggingface dataset:
Wall region of a relaxing three-dimensional incompressible turbulent boundary layer
Authors: Hebbar K. S. , Melnik W. L. 
Published: April 2006

An experimental investigation was conducted at selected locations in the wall region of a three-dimensional turbulent boundary layer relaxing in a nominally zero external pressure gradient behind a transverse hump (in the form of a 30° swept, 5 ft chord, wing-type model) faired into the side wall of a low-speed wind tunnel. The boundary layer (approximately 3·5 in. thick near the first survey station, where the length Reynolds number was 5·5 × 106) had a maximum cross-flow velocity ratio of 0·145 and a maximum cross-flow angle of 21·9° close to the wall. The hot-wire data indicated that the apparent dimensionless velocity profiles in the viscous sublayer are universal and that the wall influence on the hot wire is negligible beyond y+= 5. The existence of wall similarity in the relaxing flow field was confirmed in the form of a log law based on the resultant mean velocity and resultant friction velocity (obtained from the measured skin friction).The smallest collateral region extended from the point nearest to the wall (y+≈ 1) up to y+= 9·7, corresponding to a resultant mean velocity ratio (local to free-stream) of 0·187. The unusual feature of these profiles was the presence of a narrow region of slightly decreasing cross-flow angle (1° or less) that extended from the point of maximum cross-flow angle down to the outer limit of the collateral region. A sublayer analysis of the flow field using the measured local transverse pressure gradient slightly overestimated the decrease in cross-flow angle. It is concluded that, in the absence of these gradients, the skewing of the flow could have been much more pronounced practically down to the wall (limited only by the resolution of the sensor), implying a near-wallnon-collateralflow field consistent with the equations of motion in the neighbourhood of the wall.The streamwise relaxation of the mean flow field based on the decay of the cross-flow angle was much faster in the inner layer than in the outer layer. Over the stream-wise distance covered, the mean flow in the inner layer and the wall shear-stress vector relaxed to a two-dimensional state in approximately 10 boundary-layer thicknesses whereas the relaxation of the turbulence was slower and was not complete over the same distance.
Towards an optimum yacht sail
Authors: Wood C. J. , Tan S. H. 
Published: April 2006

This paper contains a simple and entirely conventional application of lifting-line theory to a close-hauled, high aspect ratio sail, set upright on a flat water surface. In seeking an optimum spanwise loading distribution however, an unconventional criterion is used, which leads to an unexpected result.By seeking to maximize the forward thrust for a given rolling moment, rather than maximizing the lift-drag ratio, an optimum loading distribution is obtained which departs dramatically from elliptic loading. It offers the prospect of a significant improvement in extreme yacht performance if the associated mechanical and control problems can ever be solved.
Effect of free-stream turbulence on large structure in turbulent mixing layers
Authors: Chandrsuda C. , Mehta R. D. , Weir A. D. , Bradshaw P. 
Published: April 2006

Flow-visualization investigations and correlation measurements show that the essentially two-dimensional structures which dominated the turbulent mixing layer of Brown & Roshko (1974) are formed only if the free-stream turbulence is low. If free-stream disturbances are significant, as is likely in most practical cases, including a mixing layer entraining ‘still air’ from the surroundings, three-dimensionality develops at an early stage in transition. Other recent experiments strongly suggest that the Brown-Roshko structure will not form if the initial mixing layer is turbulent or subject to instability modes other than spanwise vortices. Therefore the Brown-Roshko structure will be rare in practice. The alternative large structure in a mixing layer, found by several workers, is intense, but fully three-dimensional and thus less orderly than the Brown-Roshko structure.The balance of evidence suggests that if the Brown-Roshko structure does appear it will eventually relax into the alternative fully three-dimensional form: the Kármán vortex street behind a bluff body provides a precedent for slow development of three-dimensionality. However the Brown-Roshko structure, if formed, may well relax so slowly as to be identifiable for the full length of a practical flow.
Theory of the almost-highest wave. Part 2. Matching and analytic extension
Authors: Longuet-Higgins M. S. , Fox M. J. H. 
Published: April 2006

Most methods of calculating steep gravity waves (of less than the maximum height) encounter difficulties when the radius of curvature R at the crest becomes small compared with the wavelength L, or some other typical length scale. This paper describes a new method of calculation valid when R/L is small.For deep-water waves, a parameter ε is defined as equal to q/2½c0, where q is the particle speed at the wave crest, in a frame of reference moving with the phase speed c. Hence ε is of order (R/L)½. Three zones are distinguished: (1) an inner zone of linear dimensions ε2L near the crest, where the flow is described by the inner solution found previously by Longuet-Higgins & Fox (1977); (2) an outer zone of dimensions O(L) where the flow is given by a perturbed form of Michell's solution for the highest wave; and (3) a matching zone of width O(L). The matching procedure involves complex powers of ε.The resulting expression for the square of the phase velocity is found to be
\[
c^2 = (g/k)\{1.1931-1.18\epsilon^3\cos(2.143\ln \epsilon + 2.22)\}
\]
(see figures 5a, b), which is in remarkable agreement with independent calculations based on high-order series. In particular, the existence of turning-points in the phase velocity as a function of wave height is confirmed.Similar expressions, valid to order ε3, are found for the wave height, the potential and kinetic energies and the momentum flux or impulse of the wave.The velocity field is extended analytically across the free surface, revealing the existence of branch-points of order ½, as predicted by Grant (1973).
Experiments on centrifugally driven thermal convection in a rotating cylinder
Authors: Hudson J. L. , Tang Daniel , Abell Steven 
Published: April 2006

Heat-transfer measurements have been carried out in a right circular cylinder of fluid which is heated from above and rotated steadily about its vertical axis. Convection is produced relative to solid-body rotation through the coupling of the centrifugal acceleration and density variations in the fluid. Two silicone oils having kinematic viscosities of 350 cS and 0·65 cS were used in the experiments. In the former case viscous forces are important throughout the cylinder whereas in the latter case Ekman layers form and the Coriolis acceleration controls the interior flow.With the 350 cS oil the Nusselt number for heat transfer from the top to the bottom of the cylinder is a function ofGrωandr0, whereGrωis a Grashof number defined by employing the centrifugal acceleration evaluated at the outer edge of the cylinder in place of the gravitational acceleration, andr0is the cylinder aspect ratio.The behaviour is quite different for the 0·65 cS oil. Ekman layers form on the horizontal surfaces and heat is convected by Ekman suction. The Nusselt number is given by\[ Nu = 4.16\beta^{0.822}\epsilon^{-0.499}r_0^{0.173},\quad Ac\leqslant 0.025,\quad\sigma\beta\epsilon^{-\frac{1}{2}} > 0.7, \]where β is the thermal Rossby number, ε is the Ekman number, σ is the Prandtl number, andAcis the ratio of gravitational to centrifugal accelerations. This is consistent with previous theories which indicate that the system should depend on the parameters σβε−½andr0in the limit as ε and β approach zero.
Symmetrical flow past a double wedge at high subsonic Mach numbers
Authors: Chattot Jean-Jacques 
Published: April 2006

Symmetrical flow past a double wedge is studied for a high subsonic Mach number. The main features of the flow field are discussed in the physical and the hodograph plane. It is shown how a regular solution to the hodograph equation exhibits limit lines in the physical plane, which are eliminated through a ‘cut’ corresponding to the shock wave. In the case of the wedge it is assumed that the shock which is likely to be the most stable is the weakest possible.The boundary-value problem is solved in the hodograph plane using Telenin's method, which has proved to be successful when dealing with equations of mixed type. The bounded analytic solution which is thus constructed is regular in the hodograph plane but presents three folds in the physical plane.The computation is carried out for flow past a 4·5° half-angle wedge at a Mach numberM∞= 0·89. These figures are chosen so that the problem may be justifiably treated by potential theory, the entropy gradient behind the shock being negligible. In this case the mapping of the solution into the physical plane gives the pressure distribution along the double wedge, the sonic line and the shock wave. Of particular interest is the point where the sonic line meets the shock. This configuration is in agreement with the hypothesis of Nocilla, according to which the shock terminates in the supersonic domain. Experimental evidence cannot be obtained, however, because of the lack of resolution in this region.
The uniform distortion of thermal and velocity mixing layers
Authors: Keffer J. F. , Kawall J. G. , Hunt J. C. R. , Maxey M. R. 
Published: April 2006

Two similar problems are considered: what is the effect of applying a uniform and constant rate of strain (i) to the two-dimensional thermal mixing region in a homogeneous grid-generated turbulent field, and (ii) to the two-dimensional velocity mixing region formed between two uniform streams moving with different mean velocities? The imposed strain field is orientated so as to compress or separate the isothermal and isokinetic surfaces in the plane of interest.Two theoretical models are presented; in the first, the profiles of temperature and velocity are assumed to be self-preserving and an assumption is made about the velocity scales; in the second, the statistical, rapid-distortion approach to dispersion due to Hunt & Mulhearn (1973) is applied. The circumstances in which these models differ and those where the simpler self-preserving model can be applied are determined. The measurements presented here indicate that the widths of both mixing layers decrease within the strain field, the width of the thermal mixing layer decreasing at a greater rate than that of the velocity mixing layer. However, the measured length scales were found to be 5% larger than the scales predicted by either of the analyses, which differed from each other by 5%. It is suggested that selective amplification of the energy-containing eddies by the strain field is responsible.
Absorption of sound by homogeneous turbulence
Authors: Noir D. T. , George A. R. 
Published: April 2006

The following problem is treated: given a plane acoustic wave propagating through an unbounded field of turbulence, calculate the amount of acoustic energy converted into turbulent kinetic energy. The fluid velocities due to the acoustic waves and the turbulence are assumed to be small compared with the speed of sound. Thus the sound-turbulence interaction is weak and the turbulent field may be considered to be incompressible. The analysis is based on the interaction of two opposite effects: the acoustic distortion of the turbulence (producing anisotropic Reynolds stresses) and the redistribution of the kinetic energy among components (tendency towards isotropy) and among wavenumbers (energy cascade and dissipation). These phenomena are described using semi-empirical turbulence arguments. It is seen that the simplest model for the redistribution among components is not sufficient for unsteady flows. A more complete model is used which is modified to agree with the exact instantaneous distortion analysis of Ribner [map ] Tucker to first order. Owing to the two redistribution effects, the Reynolds stress behaves inelastically and is out of phase with the acoustic field. Thus there is an average production of turbulent energy corresponding to the absorption of acoustic energy and attenuation of the incident wave. For nearly isotropic turbulence, the attenuation coefficient is found to be proportional to the rate of viscous dissipation and independent of the frequency.In order to compare the theory with experiment several constants involved in the semi-empirical model of the turbulence must be found. Owing to the lack of better information these constants are estimated here by order-of-magnitude considerations. No existing experiments correspond to the homogeneous turbulence assumed by the theory. Comparison with the few reasonably applicable experiments shows qualitative agreement though the importance of the turbulent absorption is generally of nearly the same order as the measurement error. Several discrepancies between jet noise experiments and aerodynamic noise predictions may be roughly explained using the above analysis.
Deformation and breakup of a single slender drop in an extensional flow
Authors: Acrivos Andreas , Lo T. S. 
Published: April 2006

The deformation and conditions for breakup of a single slender drop placed symmetrically in a uniaxial extensional flow are examined theoretically. For the case of an inviscid drop in zero-Reynolds-number flow, Buckmaster (1972) showed, using slender-body analysis, that the shape of the drop is given byr≡εR(z)=ε(1−|z|ν)/2ν, where εεγ/Gμland γ is the interfacial tension,Gthe strength of the extensional flow, μ the viscosity of the suspending fluid andlthe drop half-length; alsov= ½P− 1, wherePis the unknown constant pressure inside the drop rendered dimensionless with respect toGμ. By requiring thatRbe analytic atz= 0, Buckmaster then concluded thatvhad to be an even integer and thereby obtained a countably infinite set of slender profiles for any (large) value of the flow strengthG. In the present work, the expression forR(z)shown above is obtained readily using the method of inner and outer expansions, the method failing when |z|[les ]O(ε) and ν is not an even integer. Thus, in general, a new solution is needed to describe the shape within the ‘singular’ region |z|[les ]O(ε). The requirement that the two solutions match in their domain of overlap then leads to the conclusion thatvcan be either equal to 2 or greater than or equal to 3. However, a stability analysis reveals that only the solution withv= 2 is stable, and hence a unique shape exists.Next, drops of low viscosity μi=O(ε2μ) are examined in zero-Reynolds-number flow. Here, again, a unique solution is obtained according to which a steady shape cannot exist if (Gμa/γ) (μi/μ)⅙> 0·148, where$a \equiv(3V4\pi)^{\frac{1}{3}}$andVis the volume of the drop. This breakup criterion is identical to that found by Taylor (1964). A similar analysis for the case of an inviscid drop in a flow with non-zero Reynolds number shows that drop breakup will occur if$(G\mu a/\gamma) (\rho a\gamma/\mu^2)^{\frac{1}{5}} > 0.284$, where ρ is the density of the suspending fluid. Finally, when μi=O(ε2μ) and inertial effects are neglected within the drop but retained in the surrounding fluid, the critical value of$(G\mu a/\gamma) (\rho a\gamma/\mu^2)^{\frac{1}{5}}$required for drop breakup is found as a function of the dimensionless group\[ (\rho a\gamma/\mu^2)^{\frac{1}{5}}(\mu/\mu_i)^{\frac{1}{6}}, \]which depends only on the physical properties of the system and the size of the drop. These last two results are the first which take into account inertial effects in determining the deformation and breakup conditions of a drop placed in a shear field.
The linear stability of the flow in a narrow spherical annulus
Authors: Walton I. C. 
Published: April 2006

The flow of a fluid in a narrow spherical annulus is considered. When the outer sphere remains fixed and the angular velocity of the inner one is increased beyond a critical value an instability resembling Taylor vortices appears. This instability is investigated by expanding the solution in powers of the small parameter ε, the ratio of the gap thickness to the radius, and assuming that two length scales, O(1) and O(ε), are important in the latitudinal direction.The perturbation then takes the form of cells which are of roughly square cross-section, at least near the equator, but whose amplitude decays rapidly with latitude; it is also subject to a slow spatial modulation. The critical value of the Taylor number at which the instability first appears is shown to be that for infinite concentric cylinders plus a correction O(ε) due to secondary motions and a correction not greater than O(ε) due to the domain being bounded.
On Itoh's finite amplitude stability theory for pipe flow
Authors: Davey A. 
Published: April 2006

In two recent papers Itoh has developed a finite amplitude stability theory which indicates that nonlinearity increases the damping rate of a small but finite amplitude disturbance to flow in a circular pipe when the disturbance is concentrated near the axis of the pipe. For such a centre mode, which is the only mode considered by Itoh, Davey & Nguyen found, in an earlier paper, the opposite result that nonlinearity decreases the damping rate. We examine the reasons for this discrepancy and we explain the subtle difference between Itoh's method and the method of Reynolds & Potter, which was used by Davey & Nguyen.We suggest that for the centre mode of pipe flow neither Itoh's result nor Davey & Nguyen's result is a reliable guide to the true situation. However, for the wall mode of pipe flow, and especially for plane Couette flow, both methods give very similar results and we suggest that this similarity indicates that in these cases the damping rate is decreased by nonlinearity. For a particular problem we believe that it is only when the results of the two methods are very similar that either method is likely to be useful.
The effects of eccentricity on torque and load in Taylor-vortex flow
Authors: Eagles P.M. , Stuart J. T. , Diprima R. C. 
Published: April 2006

This paper extends two earlier papers in which DiPrima & Stuart calculated first (1972b) the critical Taylor number to order ε2, where the eccentricity ε is proportional to the displacement of the axes of the circular cylinders, and second (1975) the torque and load to order ε associated with nonlinear effects of Taylor vortices. In the latter paper, it was shown that to order ε the torque arising from the Taylor vortices is identical with that for the concentric problem, which was first calculated, by a perturbation method, by Davey (1962). This deficiency is remedied in the present paper, where the calculation is taken to order ε2. It is found that, as ε rises, the torque associated with the Taylor vortices falls slightly when we keep constant the percentage elevation of the Taylor number above the ε-dependent critical value. This result is in accordance with experimental observations by Vohr (1967, 1968). In addition, results of calculations of the pressure field developed by the Taylor-vortex flow in association with the eccentric geometry are presented; this is larger than in the concentric case owing to a Reynolds lubrication effect. Also given are the associated components of the load on the inner cylinder, but only for Taylor numbers close to the critical value.One additional observation by Vohr, for cylinders with a mean ratio of the gap to the inner radius of 0·099, was that the maximum Taylor-vortex strength with ε = 0·475 occurred some 50° downstream of the maximum gap for a 20% elevation of the Taylor number above the critical value. Calculations in the two earlier papers (1972b, 1975) gave 90 and 76°, respectively, for that angle. Note that in the 1975 paper a geometrical correction of order ε was included. Here, with an additional modification of order ε due to the flow, this result is improved to 49° by the extended analysis presented, although the ‘small’ parameters are somewhat outside the range for which perturbation theory is expected to be valid.
Stability of thin, radially moving liquid sheets
Authors: Weihs Daniel 
Published: April 2006

An analysis of the stability of thin viscous liquid sheets, such as those emitted from industrial spraying nozzles, is presented. These sheets are in the form of a circular sector whose thickness reduces as the distance from the nozzle increases.The Kelvin-Helmholtz type of instability usually observed causes the breakup and atomization of the sheet, as required in most industrial spraying processes. Waviness, like that of a flapping flag, is produced and increasing amplitudes finally cause breakup.An analytical solution in the form of hypergeometric functions for the shape of the sheet and the waves is obtained. This solution includes, as special cases, analyses existing in the literature, in addition to establishing the possibility of a new type of instability dependent on the distance from the nozzle. Also, the classical type of instability, in which the waves increase with time, is examined and relations for unstable waves as a function of parameters such as the fluid viscosity, surface tension and sheet velocity are obtained. It is shown that there is no single wave that has a maximum growth rate, but that the wavenumber for maximum instability increases with the distance from the nozzle orifice.
Two-dimensional turbulence on the surface of a sphere
Authors: Tang Cha-Mei , Orszag Steven A. 
Published: April 2006

Large-scale atmospheric flow shares certain attributes with two-dimensional turbulence. In this paper, we study the effect of spherical geometry on two-dimensional turbulence.Energy transfer is multi-component in spherical geometry in contrast to energy transfer among triads of wave vectors in Cartesian geometry. It follows that energy transfer is more local in spherical than in Cartesian geometry. Enstrophy transfer to higher wavenumbers in spherical geometry is less than enstrophy transfer to higher wavenumbers in Cartesian geometry. Since both energy and enstrophy are inviscid constants of motion, the back transfer of energy is also less in spherical than in Cartesian geometry. Therefore, with a finite viscosity, enstrophy decays more slowly in spherical geometry than in Cartesian geometry. Here these conjectures are tested numerically by spectral methods. The numerical results agree well with the conjectures.