bluuebunny/crossref_metadata_2025_split huggingface dataset:
The starting mechanism of wave-induced flow through a sharp-edged orifice
Authors: Evans R. A. , Bloor M. I. G. 
Published: April 2006

Following weak plane shock diffraction at a knife-edge situated in a duct, a two-dimensional vortex sheet springs from the salient edge. The method of ‘vortex discretization’ is used, in conjunction with a Schwarz-Christoffel transformation, to develop a two-dimensional potential model for this constrained form of vortex generation. The analysis is independent of empirical parameters and describes, qualitatively, the pattern of streamlines through the orifice.Flow-visualization photographs are presented which illustrate the spiral shape of the starting vortex. Although of a limited nature, quantitative experimental vortex growth rates have been obtained and are compared with initial growth rates predicted theoretically. The results are discussed together with other aspects of the problem, including the limitations of the theory.An extension of vortex discretization is developed whereby the pressure distribution remote from the vortex sheet can be calculated. The combination of flow separation and the associated static wall pressure distribution gives theoretical insight into the mechanism of flow through an orifice.
On choking flutter
Authors: Tanida Y. , Saito Y. 
Published: April 2006

The purpose of the present study is to assess the possibility of the so-called choking flutter in a transonic cascade operating under choking conditions. In the experiment, measurements of the unsteady aerodynamic moment acting on an aerofoil which is oscillating in pitch about the midchord in a transonic channel flow are performed for channel height-to-chord ratios H/c = 0·5−3 and oscillation frequencies up to 120 Hz. For a large channel height such as H/c = 3, the unsteady aerodynamic behaviour is similar to that of an isolated aerofoil, and the system will be aeroelastically stable in the transonic region as well as in the subsonic one. For smaller channel heights such as H/c = 0·5, however, the flow chokes and the aerodynamic behaviour becomes significantly different from that at large channel heights. As soon as a shock appears, i.e. in the incipient transonic region, the aerodynamic derivatives change discontinuously, so that the subsonic and transonic regions can be clearly separated. In this case, the aerodynamic damping becomes negative in the transonic region.In order to understand the transonic features, a one-dimensional unsteady analysis is undertaken for small channel heights H/c [les ] 0·5. The numerical results show good qualitative agreement with the experimental ones, predicting in the incipient transonic region a discontinuous variation of the aerodynamic moment which results in system instability.It is concluded that choking flutter may occur in transonic channel flow with a moderately small channel height when the passage is choked.
A note on the westward drift of the earth's magnetic field
Authors: Wood W. W. 
Published: April 2006

A model of the earth's liquid core is assumed in which the underlying magnetic field and velocity are zonal and axially symmetric. Alfvén waves that vary as ei(kϕ−σt) are considered, where ϕ is the angle of longitude. Buoyancy and Coriolis forces Ω × U are included.For a wide class of basic states and regions of flow, it is shown that roughly as many of the waves with a given k [ges ] 2 propagate eastwards as propagate westwards. All these waves are neutrally stable. The class of basic states is restricted by certain inequalities involving their velocity, magnetic field and entropy gradient.it is observed that the known equivalence (Malkus 1967) between Alfvén waves with frequencies σ [Lt ] Ω and inertial waves with frequencies σp which are O(Ω) still holds when buoyancy forces are present. The equivalence requires σp2 to be real. If σp is pure imaginary, as is possible (though perhaps uncommon) in an unstably stratified medium, then the corresponding Alfvén wave is not neutrally stable and travels westwards.
On the growth, limiting thickness and dominant eddy scale of turbulent shearing layers in the atmosphere
Authors: Lessen Martin , Barcilon Albert , Butler Thomas E. 
Published: April 2006

The growth of an unbounded, density-stratified, turbulent shearing layer in the presence of a gravity field is studied using the postulate of marginal instability. It is found, for a similarity mean velocity and density distribution, that after a rapid initial growth rate the growth slows asymptotically to zero as the Richardson number approaches a value of 1/4. Furthermore, the theory predicts a constant dominant turbulent eddy scale in all but the initial stages of growth of the turbulent shearing layer.Both the general growth characteristics and the constant dominant turbulent eddy scale predicted by the theory are confirmed by experimental data.
The accelerated fully rough turbulent boundary layer
Authors: Coleman Hugh W. , Moffat Robert J. , Kays William M. 
Published: April 2006

The behaviour of a fully rough turbulent boundary layer subjected to favourable pressure gradients both with and without blowing was investigated experimentally using a porous test surface composed of densely packed spheres of uniform size. Measurements of profiles of mean velocity and the components of the Reynolds-stress tensor are reported for both unblown and blown layers. Skin-friction coefficients were determined from measurements of the Reynolds shear stress and mean velocity.An appropriate acceleration parameterKrfor fully rough layers is defined which is dependent on a characteristic roughness dimension but independent of molecular viscosity. For a constant blowing fractionFgreater than or equal to zero, the fully rough turbulent boundary layer reaches an equilibrium state whenKris held constant. Profiles of the mean velocity and the components of the Reynolds-stress tensor are then similar in the flow direction and the skin-friction coefficient, momentum thickness, boundary-layer shape factor and the Clauser shape factor and pressure-gradient parameter all become constant.Acceleration of a fully rough layer decreases the normalized turbulent kinetic energy and makes the turbulence field much less isotropic in the inner region (forFequal to zero) compared with zero-pressure-gradient fully rough layers. The values of the Reynolds-shear-stress correlation coefficients, however, are unaffected by acceleration or blowing and are identical with values previously reported for smooth-wall and zero-pressure-gradient rough-wall flows. Increasing values of the roughness Reynolds number with acceleration indicate that the fully rough layer does not tend towards the transitionally rough or smooth-wall state when accelerated.
Convective instability of stably stratified water in the ocean
Authors: Leibovich S. 
Published: April 2006

A recent theoretical description of interactions between surface waves and currents in the ocean is extended to allow density stratification. The interaction leads to a convective instability even when the density stratification is statically stable. An unspecified random surface wave field is permitted provided that it is statistically stationary.The instability can be traced to torques produced by variations of a ‘vortex force’. Non-diffusive instabilities produced by this mechanism in water of infinite depth are explored in detail for arbitrary distributions of the destabilizing force. Stability is determined by an eigenvalue problem formally identical to that determining normal modes of infinitesimal internal waves in fluid with a density profile that is not monotone and thereby has a statically unstable region. Some tentative remarks are offered about the problem when dissipation is allowed.Application of the present theory to Langmuir circulations is discussed. Also, according to the present theory, internal wave propagation should be modified by the vortex force arising from the interaction between the surface waves and the current.
Internal gravity waves in a time-varying stratification
Authors: Rotunno Richard 
Published: April 2006

The influence of slow time variations of the Brun-Väisälä frequencyNupon the energy of internal gravity waves is investigated. It is found that, when time variations inNare produced by a mean deformation field (reversible mean state), the wave energy can vary in either direct or inverse proportion, depending on the wavenumber orientation. WhenNchanges owing to a certain type of irreversible process, the wave energy varies with only inverse proportionality.The nocturnal planetary boundary layer (NPBL) provides an example whereN=N(z, t). The full initial/boundary-value problem for anN(z, t) similar to the climatological mean for theNPBLis solved.
The motion of two-dimensional vortex pairs in a ground effect
Authors: Barker Steven J. , Crow Steven C. 
Published: April 2006

A new technique for generating a pair of line vortices in the laboratory has been developed. The mean flow of these vortices is highly two-dimensional, although most of the flow field is turbulent. This two-dimensionality permits the study of vortex motions in the absence of the Crow mutual induction instability and other three-dimensional effects. The vortices are generated in a water tank of dimensions 15 × 122 × 244 cm. They propagate vertically and their axes span the 15 cm width of the tank. One wall of the tank is transparent, and the flow is visualized using fluorescein dye. High speed photography is used to study both the transition to turbulence during the vortex formation process and the interaction of the turbulent vortices with a simulated ground plane.Transition occurs first in an annular region surrounding the core of each vortex, starting with a shear-layer instability on the rolled-up vortex sheet. The turbulent region then grows both radially inwards and radially outwards until the entire recirculation cell is turbulent. A ‘relaminarization’ of the vortex core appears to take place somewhat later.The interaction of the vortex pair with the ground plane does not follow the predictions of potential-flow theory for line vortices. Although the total circulation is apparently conserved, the vortices remain at a larger distance from the ground than is expected and eventually ‘rebound’ or move away from the ground. Differences between a free-surface boundary condition and a smooth or rough ground plane are discussed. The ground-plane interaction is qualitatively very similar to that of aircraft trailing vortices observed in recent flight tests.
Simple rotational flows
Authors: Shercliff J. A. 
Published: April 2006

The paper develops and discusses some new additions to the available stock of analytical solutions of the nonlinear equations of fluid motion. The motions are steady, two-dimensional and devoid of viscous or other rotational forces (although such forces must have been significant during any starting process). The fluid density is constant.The solutions are in two groups, referred respectively to Cartesian and polar co-ordinates. In both the stream function is of separable form, i.e. expressible as a product of two functions, each dependent on one co-ordinate. A remarkable variety of motions is revealed. Those that are most significant physically are described as bends (rapid transitions from one rectilinear flow to another) or as loops (closed, non-circular, vortex-type flows). The effects of boundary layers at walls or instability are not explored.The paper closes with a mention of some preliminary experiments on loop flows in which all streamlines are ellipses and some discussion of the applicability of bend flows. Generalizations to axisymmetric flows and compressible flows are also mentioned briefly.
Experiments on the structure of turbulence in fully developed pipe flow. Part 2. A statistical procedure for identifying ‘bursts’ in the wall layers and some characteristics of flow during bursting periods
Authors: Heidrick T. R. , Banerjee S. , Azad R. S. 
Published: April 2006

This paper is the second of a pair describing two-point velocity measurements in fully developed pipe flow. A method of processing hot-film anemometer signals to identify intervals of high energy production (‘bursts’) in wall turbulence is presented. The method uses filtered cross-stream spatial derivatives of the axial velocity fluctuations. It is demonstrated to be more sensitive to ‘bursts’ than several other methods of indentification. The bursts identified in this manner are shown to have similar characteristics to those observed in visual studies.The technique has been applied to the wall region of turbulent pipe flow. Mean burst rates have been obtained at various distances from the wall for three Reynolds numbers. It is shown that the mean burst rate cannot be reliably obtained from a previously used technique based on the autocorrelation of the axial velocity fluctuations.On the basis of our experiments, the mean burst rate and the turbulent shear stress have been found to vary similarly with distance from the wall. In the region near the wall where the shear stress is constant the mean burst rate is independent of the kinematic viscosity.Some characteristics of the velocity fluctuations during burst intervals have been studied. All the bursts began with a relative minimum in the axial velocity fluctuations followed by a peak in the cross-stream spatial derivative. A second peak always occurred midway through the burst. The sequence of events is somewhat similar to that in the last stage of laminar-to-turbulent transition.
Growth and equilibrium of short gravity waves in a wind-wave tank
Authors: Plant W. J. , Wright J. W. 
Published: April 2006

Temporal and spatial development of short gravity waves in a linear wind-wave tank has been measured for wind speeds up to 15 m/s using microwave Doppler spectrometry. Surface waves of wavelength 4·1 cm, 9·8 cm, 16·5 cm and 36 cm were observed as a function of fetch, wind speed and wind duration. The waves grew exponentially from inception until they were about 10 dB smaller than their maximum height, and the temporal growth and spectral transport (spatial growth) rates were about equal when the wave amplitude was sufficiently small. The amplitude of a short gravity wave of fixed wavelength was found to decrease substantially at winds, fetches or durations greater than those at which the short gravity wave was approximately the dominant wave; such phenomena are sometimes referred to as overshoot. The dominant short gravity wave was observed to reach a maximum amplitude which depended only on wavelength, showing that wave breaking induced by an augmented wind drift cannot be the primary limitation to the wave height. Waves travelling against the wind were observed for wavelengths of 9·8 cm, 16·5 cm and 36 cm and were shown to be generated by the air flow at low wind speeds.Measured initial growth rates for 16·5 cm and 36 cm waves were greater than expected, suggesting the existence of a growth mechanism in addition to direct transfer from the wind via linear instability of the boundary-layer flow. Initial temporal growth rates and spectral transport rates were compared to yield an experimental determination of the magnitude of the sum of nonlinear interactions and dissipation in short gravity waves. If the steady-state energy input in the neighbourhood of the dominant wave occurs at the measured initial temporal growth rates, then most of the energy input is locally dissipated; relatively little is advected away. Calculated gravitycapillary nonlinear energy transfer rates match those determined from initial growth rates for 9·8 cm waves and the gravity–capillary wave interaction continues to be significant for waves as long as 16·5 cm. For longer waves the gravity–capillary interaction is too small to bring the short gravity wave to a steady state when it is the dominant wave of the wind-wave system.
Stability of time-dependent double-diffusive convection in an inclined slot
Authors: Chen C. F. , Sandford R. D. 
Published: April 2006

The two-dimensional motion of a stably stratified fluid containing two solutes with different molecular diffusivities in an inclined slot has recently been examined by Chen (1975, hereafter referred to as I). The two solutes have continuous opposing gradients with the slower-diffusing one more dense at the bottom. It is found that, in the steady state, there exists a slow upward flow along the slope driven by the slight buoyancy difference near the wall, not unlike the solution found by Wunsch (1970) and Phillips (1970) for a single solute. For the time-dependent flow resulting from switching on the diffusivities at t = 0, there may be a flow reversal near the wall depending on the relative magnitude of λ and τ (where λ is the ratio of the density gradient and τ−1 is the ratio of the diffusivity of the faster-diffusing solute T to that of the slower-diffusing one S). By examining the distributions of S and T across the slot, it becomes apparent that in cases with flow reversal double-diffusive instability is likely to occur.In this paper, we examine the stability of time-dependent double-diffusive convection in an inclined slot both analytically and experimentally. The time-dependent perturbation equations are numerically integrated starting with an initial distribution of small random disturbances in the vorticity. The growth or decay of the kinetic energy of the perturbations serves to indicate whether the flow is unstable or stable. The results show that the flow becomes more unstable (a) with increasing λ at a given angle of inclination with respect to the vertical and (b) with increasing angle of inclination at a given value of λ. Experiments were carried out in a 2[sdot ]54 cm wide slot using sugar and salt solutions at angles of inclination of 30°, 45° and 60°. Results obtained confirm the trends predicted by the analysis. Good agreement was obtained between the predicted and the experimental values of the critical wavelength for the case λ = 0[sdot ]7.
Differential equations for long-period gravity waves on fluid of rapidly varying depth
Authors: Hamilton James 
Published: April 2006

The conventional long-wave equations for waves propagating over fluid of variable depth depend for their formal derivation on a Taylor series expansion of the velocity potential about the bottom. The expansion, however, is not possible if the depth is not an analytic function of the horizontal co-ordinates and it is a necessary condition for its rapid convergence that the depth is also slowly varying. We show that if in the case of two-dimensional motions the undisturbed fluid is first mapped conformally onto a uniform strip, before the Taylor expansion is made, the analytic condition is removed and the approximations implied in the lowest-order equations are much improved.In the limit of infinitesimal waves of very long period, consideration of the form of the error suggests that by modifying the coefficients of the reformulated equation we may find an equation exact for arbitrary depth profiles. We are thus able to calculate the reflexion coefficients for long-period waves incident on a step change in depth and a half-depth barrier. The forms of the coefficients of the exact equation are not simple; however, for these particular cases, comparison with the coefficients of the reformulated long-wave equation suggests that in most cases the latter may be adequate. This opens up the possibility of beginning to study finite amplitude and frequency effects on regions of rapidly varying depth.
Heat thermal structure in the interfacial boundary layer measured in an open tank of water in turbulent free convection
Authors: Katsaros Kristina B. , Liu W. Timothy , Businger Joost A. , Tillman James E. 
Published: April 2006

The thermal structure in the boundary layer and its relation to the heat flux from the cooling and evaporating surface of a deep tank of water are investigated. When a deep layer of water in contact with still air above loses heat to the air, the cooled water in a region just under the surface converges along lines and then plunges down in sheets. These sheets of falling water dissipate as they move into the body of the water, which is in turbulent motion. The vertical profiles of the horizontally averaged temperature and its standard deviation agree fairly closely with theoretical profiles based on time averages of the solution to the heat diffusion equation. The differences between observed and thus predicted profile shapes are consistent with the expected effects of the falling cold thermals and the warm return flow, which are neglected in the theories. The profiles of the standard deviation have large values up to the interface and lie between predictions based on boundary conditions of constant surface temperature and constant heat flux, in keeping with the experimental conditions.The relation between the net heat flux and the temperature difference across the boundary layer is given in non-dimensional form by N = 0[sdot ]156R0[sdot ]33, which is in good agreement with the asymptotic similarity prediction N [vprop ] R1/3 but lower than theoretical calculations of the upper bound of N vs. R.
Laminar flow in a square duct of strong curvature
Authors: Humphrey J. A. C. , Taylor A. M. K. , Whitelaw J. H. 
Published: April 2006

Calculated values of the three velocity components and measured values of the longitudinal component are reported for the flow of water in a 90° bend of 40 x 40mm cross-section; the bend had a mean radius of 92mm and was located downstream of a 1[sdot ]8m and upstream of a 1[sdot ]2m straight section. The experiments were carried out at a Reynolds number, based on the hydraulic diameter and bulk velocity, of 790 (corresponding to a Dean number of 368). Flow visualization was used to identify qualitatively the characteristics of the flow and laser-Doppler anemometry to quantify the velocity field. The results confirm and quantify that the location of maximum velocity moves from the centre of the duct towards the outer wall and, in the 90° plane, is located around 85% of the duct width from the inner wall. Secondary velocities up to 65% of the bulk longitudinal velocity were calculated and small regions of recirculation, close to the outer corners of the duct and in the upstream region, were also observed.The calculated results were obtained by solving the Navier–Stokes equations in cylindrical co-ordinates. They are shown to exhibit the same trends as the experiments and to be in reasonable quantitative agreement even though the number of node points used to discretize the flow for the finite-difference solution of the differential equations was limited by available computer time and storage. The region of recirculation observed experimentally is confirmed by the calculations. The magnitude of the various terms in the equations is examined to determine the extent to which the details of the flow can be represented by reduced forms of the Navier–Stokes equations. The implications of the use of so-called ‘partially parabolic’ equations and of potential- and rotational-flow analysis of an ideal fluid are quantified.