bluuebunny/crossref_metadata_2025_split huggingface dataset:
Nonlinear wave interactions in shear flows. Part 1. A variational formulation
Authors: Usher J. R. , Craik A. D. D. 
Published: March 2006

A modified version of Bateman's variational formulation of the incompressible Navier-Stokes equations and boundary conditions (see Dryden, Murnaghan & Bateman 1956) is introduced. This is employed to examine a particular nonlinear problem of hydrodynamic stability which was treated previously, using a ‘direct’ approach, by Craik (1971). This problem concerns the resonant interaction at second order of a triad of wave modes in a parallel shear flow.The present method is conceptually attractive; it also has the major advantage over the ‘direct’ method of a substantial reduction in algebraic complexity, which allows results to be derived far more readily. Also, some further improvements are made upon Craik's previous analysis. Such a variational approach may often be simpler than present conventional methods of tackling nonlinear viscous-flow problems. The present paper shows how other problems of nonlinear stability and wave interactions may be tackled in this way.
Wave breaking in the presence of wind drift and swell
Authors: Phillips O. M. , Banner M. L. 
Published: March 2006

Wind, blowing over a water surface, induces a thin layer of high vorticity in which the wind stress is supported by molecular viscosity; the magnitude of the surface drift, the velocity difference across the layer, being of the order of 3% of the wind speed. When long waves move across the surface, there is a nonlinear augmentation of the surface drift near the long-wave crests, so that short waves, superimposed on the longer ones, experience an augmented drift in these regions. This is shown to reduce the maximum amplitude that the short waves can attain when they are at the point of incipient breaking.Theoretical estimates of the reduction are compared with measurements in wind-wave tanks by the authors and by Mitsuyasu (1966) in which long mechanically generated waves are superimposed on short wind-generated waves. The reductions measured in the energy density of the short waves by increasing the slope of the longer ones at constant wind speed are generally consistent with the predictions of the theory in a variety of cases.
The pressure field due to a large circular capped air bubble rising in water
Authors: Lazarek G. M. , Littman H. 
Published: March 2006

The pressure field due to a large circular capped air bubble rising in water has been determined experimentally. The results verify the Davies & Taylor cap boundary condition and the frontal pressure field is well approximated by that due to irrotational flow around an oval body.The pressure field extends axially as far as ten bubble half-widths below the bubble floor. Immediately below the floor the pressure is constant for about two-thirds of a bubble height. The wake is closed and contains symmetric pressure minima. For the bubbles studied, turbulence, as well as the diffusion of vorticity, probably controls the momentum distribution and energy dissipation in the wake.
Combined dye-streak and hydrogen-bubble visual observations of a turbulent boundary layer
Authors: Offen G. R. , Kline S. J. 
Published: March 2006

The turbulent boundary layer over a flat plate was observed visually using two dye injectors and a normal bubble wire. One dye injector was a standard wall slot; the other one was a small Pitot probe which could be placed anywhere in the flow. The purpose of these experiments was to improve understanding of the relationships between the bursting of low-speed streaks near the wall and the flow field farther away from the wall.On the basis of these observations, it seems that (i) each lift-up is associated with a disturbance which originates in the logarithmic region and is characterized by a mean motion towards the wall, and that (ii) such disturbances are generated by the interaction of an earlier burst from further upstream with the fluid motion in the logarithmic region.
Second-order effects in free convection
Authors: Walton I. C. 
Published: March 2006

The equations of conservation of momentum, energy and mass together with the equations of state are examined for free convection from a vertical paraboloid. A transformation due to Saville & Churchill is applied to the first- and second-order boundary-layer equations, which are then solved using series about the stagnation point, using asymptotic series far up the body and in between by a method due to Merk. The second-order outer inviscid flow is given in terms of infinite integrals as a solution of Laplace's equation in paraboloidal co-ordinates.Eight second-order effects are distinguished, depending on longitudinal and transverse curvatures, the displacement flow, heat flux into the boundary layer and the variation of density, viscosity, thermometric conductivity and the coefficient of expansion with temperature. Expressions for the skin friction, heat-transfer coefficient and various flux thicknesses are obtained and a comparison of the second-order effects is made.
Reynolds-shear-stress measurements in a compressible boundary layer within a shock-wave-induced adverse pressure gradient
Authors: Rose W. C. , Childs M. E. 
Published: March 2006

The results of an experimental investigation of the mean- and fluctuating-flow properties of a compressible turbulent boundary layer in a shock-wave-induced adverse pressure gradient are presented. The turbulent boundary layer developed on the wall of an axially symmetric nozzle and test section whose nominal free-stream Mach number and boundary-layer-thickness Reynolds number were 4 and 105, respectively. The adverse pressure gradient was induced by an externally generated, conical shock wave.Mean and time-averaged fluctuating-flow data, including the experimental Reynolds shear stresses and experimental turbulent heat-transfer rates, are presented for the boundary layer and external flow, upstream, within and downstream of the pressure gradient. The turbulent mixing properties of the flow were determined experimentally with a hot-wire anemometer. The calibration of the wires and the interpretation of the data are discussed.From the results of the investigation, it is concluded that the shock-wave/boundary-layer interaction significantly alters the shear-stress characteristics of the boundary layer.
The hypersonic laminar boundary layer near sharp compression and expansion corners
Authors: Bloy A. W. , Georgeff M. P. 
Published: March 2006

The momentum integral method of Klineberg is shown to provide a good description of the major characteristics of two-dimensional laminar viscous-inviscid interactions a t hypersonic speeds. Surface pressure and heat-transfer-rate measurements were made for sharp compression and expansion corners at Mach 12.2 and are compared with the theoretical predictions. The agreement is found to be good for attached, incipient and fully separated flows.Some theoretical comparisons between methods based on the Klineberg formulation are made which suggest that the full boundary-layer equations are well described using integral methods that incorporate the energy equation. It is further shown that the properties associated with the stability of the governing differential equations are mathematical properties of the analytical model and should not be associated with any physical characteristics of the boundary layer.A correlation of hypersonic, cold-wall, incipient separation data is also presented.
Upstream propagation of unsteady disturbances in supersonic boundary layers
Authors: Schneider Wilhelm 
Published: March 2006

It is shown that weak harmonic waves can propagate upstream in a supersonic stream along a plane wall over distances that are very large in comparison with the boundary-layer thickness. These waves are characterized by small reduced frequencies, large wavelengths and small phase velocities. Results are presented for the flow along a single plane wall and alsoforthe flow between two plane parallel plates (channel flow).The progressive-wave solutions are found by asymptotic expansions for small disturbances, large Reynolds numbers of the basic flow, and small reduced frequencies of the unsteady disturbances. It turns out that, as in the corresponding steady theory, four flow regions have to be distinguished: a middle layer which embraces most of the boundary layer; an inner layer near the wall; the outer flow field; and a transition layer between the middle layer and the outer layer. A quasi-steady treatment of the middle, transitional and outer layers is appropriate. Unsteady effects originate in the inner layer.The relative importance of viscosity and unsteady effects with regard to the waves is characterized by a dimensionless parameterNwhich is the product of certain powers of the reduced frequency and the Reynolds number. ForN→ ∞ and a single wall, Lighthill's steady theory of upstream influence in supersonic boundary layers is recovered as a limiting case of the present theory.
On the development of dunes in erodible channels
Authors: Fredsøe Jørgen 
Published: March 2006

A two-dimensional stability analysis of the flow in a straight alluvial channel has been carried out, using the vorticity transport equation. In the analysis an attempt has been made to account for the influence of gravity on bed-load transport, and this turned out to change the stability quite significantly.In the case of instability, the further growth of the dunes has been investigated using a second-order approximation, This nonlinear theory explains the experimental fact that the dunes very soon become asymmetric.
Experimental investigation of rarefied gas flow in different channels
Authors: Porodnov B. T. , Suetin P. E. , Borisov S. F. , Akinshin V. D. 
Published: March 2006

An experimental investigation of flows of a large number of inert and polyatomic gases in various channels, a non-ideal orifice, flat slits with different surface roughnesses and wall materials, capillary packets with molten walls and a capillary sieve, has been made.The unsteady flow method and a highly sensitive capacitance micromanometer were used (the sensitivity being ∼ 3 × 10−4N/m2Hz). Measurements were made in a range of Knudsen numbers 5 × 104–10−3at ∼ 293 °K, and some measurements for flow through a non-ideal orifice were carried out at 77.2°K.It was found that, both in the viscous slip-flow and free-molecule regimes for the channels with molten walls, the experimental conductivities were higher (by ∼ 15%) than theoretical ones calculated assuming diffuse molecular scattering by the walls. We have also observed that the channel conductivity essentially depends on the channel surface roughness and on the kind of gas. The larger the roughness height, the lower the conductivity. From the experimental data the tangential momentum accommodation coefficients were calculated.
Natural convection of viscoelastic fluids in a vertical slot
Authors: Gözüm Dogan , Arpaci V. S. 
Published: March 2006

Linear stability theory is applied to the natural convection of slightly, elastic, viscous fluids in an infinitely long vertical slot. Travelling, as well as stationary, disturbances are considered. It is found that the elasticity (i) slightly stabilizes the stationary disturbances while strongly destabilizing the travelling disturbances, (ii) strongly increases the wave speed while slightly decreasing the wavenumber and (iii) reduces the transition Prandtl number, which separates the stationary cells from the travelling waves, from its value of 12.7 for Newtonian fluids.Experiments are carried out with a viscoelastic fluid prepared by mixing Separan AP30 with water, giving a Prandtl number of about 30. This fluid is shown to produce wave instability at a Grashof number between 3900 and 4300. Under the same conditions, a Newtonian fluid is shown to remain stable to both stationary and travelling disturbances.
Wakes behind two-dimensional surface obstacles in turbulent boundary layers
Authors: Counihan J. , Hunt J. C. R. , Jackson P. S. 
Published: March 2006

By making simple assumptions, an analytical theory is deduced for the mean velocity behind a two-dimensional obstacle (of heighth) placed on a rigid plane over which flows a turbulent boundary layer (of thickness δ). It is assumed thath[Gt ] δ, and that the wake can be divided into three regions. The velocity deficit −uis greatest in the two regions in which the change in shear stress is important, a wall region (W) close to the wall and a mixing region (M) spreading from the top of the obstacle. Above these is the external region (E) in which the velocity field is an inviscid perturbation on the incident boundary-layer velocity, which is taken to have a power-law profileU(y) =U∞(y−y1)n/δn, wheren[Gt ] 1. In (M), assuming that an eddy viscosity (=KhU(h)) can be defined for the perturbed flow in terms of the incident boundary-layer flow and that the velocity is self-preserving, it is found thatu(x,y) has the form$\frac{u}{U(h)} = \frac{ C }{Kh^2U^2(h)} \frac{f(n)}{x/h},\;\;\;\; {\rm where}\;\;\;\; \eta = (y/h)/[Kx/h]^{1/(n+2)}$, and the constant which defines the strength of the wake is$C = \int^\infty_0 y^U(y)(u-u_E)dy$, whereu=uE(x, y) asy→ 0 in region (E).In region (W),u(y) is proportional to Iny.By considering a large control surface enclosing the obstacle it is shown that the constant of the wake flow is not simply related to the drag of the obstacle, but is equal to the sum of the couple on the obstacle and an integral of the pressure field on the surface near the body.New wind-tunnel measurements of mean and turbulent velocities and Reynolds stresses in the wake behind a two-dimensional rectangular block on a roughened surface are presented. The turbulent boundary layer is artificially developed by well-established methods (Counihan 1969) in such a way that δ = 8h. These measurements are compared with the theory, with other wind-tunnel measurements and also with full-scale measurements of the wind behind windbreaks.It is found that the theory describes the distribution of mean velocity reasonably well, in particular the (x/h)−1decay law is well confirmed. The theory gives the correct self-preserving form for the distribution of Reynolds stress and the maximum increase of the mean-square turbulent velocity is found to decay downstream approximately as$ (\frac{x}{h})^{- \frac{3}{2}} $in accordance with the theory. The theory also suggests that the velocity deficit is affected by the roughness of the terrain (as measured by the roughness lengthy0) in proportion to In (h/y0), and there seems to be some experimental support for this hypothesis.
Fine-structure turbulence in the wall region of a turbulent boundary layer
Authors: Ueda H. , Hinze J. O. 
Published: March 2006

Measurements have been made concerning the fine structure of the turbulence in the part adjacent to the wall of the wall region of a plane turbulent boundary layer. The objective was to gain further information concerning the larger-scale disturbance mechanism which is mainly responsible for the generation of turbulence. Hot-wire anemomet.ry was used and information on the fine structure was obtained by differentiating and filtering the hot-wire signal.The distributions of the Kolmogorov microscale and of the flatness and skewness factors of the axial fluctuating velocity u and its first and second derivative determined at two Reynolds numbers suggest the existence of Reynolds number similarity. In the region y+ < 15 the flatness and skewness factors of u increase with decreasing y+. At approximately y+ = 15 the flatness factor shows a minimum value, while the skewness factor becomes zero. This location agrees with that where the turbulence intensity u′ has a maximum value. In the outer part of the wall region (y+ > 100) the flatness and skewness factors approach values obtained in shear-free turbulence at the same turbulence Reynolds number.The fine structure of the turbulence is strongly associated with and dominated by the random, larger-scale, intermittent inrush-ejection cycle. In the viscous sublayer both the fine structure, and the large-scale mechanism of the turbulence are influenced mainly by the inrush phase, while further out in the wall region (y+ > 40) they are influenced by both inrush and ejection. As a result, in the viscous sublayer the average burst periods of the high frequency turbulence components and their flatness factors (of ∂u/∂t and of ∂2u/∂t2) attain values twice those in the outer part.The change in the mechanism of the fine structure with distance from the wall is clearly demonstrated by the spectra of non-negative variables, i.e. (∂u/∂t)2 and (∂2u/∂t2)2. The spectra agree with each other and decrease with increasing frequency, following a power law as predicted by Gurvich & Yaglom (1967). The power law applies to almost the whole frequency range, when the highest, viscous, frequency range is excluded. However, the exponent is different for the viscous sublayer and the outer part of the wall region. In the buffer layer the spectra have two distinct power-law regions. In the lower frequency range the exponent is the same as that for the viscous sublayer, while in the higher frequency range it is the same as that for the outer part of the wall region.
The vortex-street structure of ‘turbulent’ jets. Part 1
Authors: Lau J. C. , Fisher M. J. 
Published: March 2006

It was suggested by Lau, Fisher & Puchs (1972) that the basic structure of a ‘turbulent’ round jet might consist, essentially, of an axial array of fairly evenly spaced vortices moving downstream in the mixing region of the jet. The present experimental study is an attempt to establish this hypothesis on a sound footing. The problem which was posed was first to find proof of the existence of a fairly regular pattern in the mixing region, and second to extract detailed information on the component parts of this pattern to identify the nature of the structure.Hot-wire signals in the mixing layer are known to possess a predominance of spikes. In the region closer to the high velocity side of the layer, these spikes tend to be downward ones whilst in the opposite region, they are upward. These spikes have been attributed to the entrainment mechanism in the mixing layer and had been thought to be random. A closer study of time-history curves of these hotwire signals suggests that they might not be as random as would appear at first glance. A probability analysis was conducted of the time intervals between the successive downward spikes in the u′ signals, and it was found that indeed the highest probability occurred when the time interval corresponded to a frequency equal to the vortex passing frequency.A time-domain averaging (or eduction) technique was used to try to identify the nature of the flow structure using the spikes to trigger the eduction process. On the basis of these results it would seem that the suggestion of a vortex street is well founded. Furthermore, it appears that, as the individual vortices in the street move downstream, they are continuously transporting fluid masses across the mixing layer, and it is this effect which is producing the Reynolds stresses in the mixing layer, and causing the spikes in the u’ signals in this region.
Rectangular resonators on infinite and semi-infinite channels
Authors: Buchwald V. T. , Williams N. V. 
Published: March 2006

The surface elevations in a strip 0 <y<band in a rectangle -d<y< 0, |x| <aare expressed as a Fourier integral and Fourier series respectively. Using a Galerkin technique to match boundary conditions, the solution to the general problem of the response of a rectangular resonator to inviscid shallow-water waves in infinite and semi-infinite channels is obtained.Theoretical results are compared with laboratory experiments of James (1970, 1971a, b). Agreement is generally very good, except that the inviscid and linear theory does not predict the observed large energy losses in the resonator at resonance.The theory is also applied to a geometry corresponding to the Gulf of Carpentaria, and the calculated response of the Gulf to semi-diurnal tides gives a zero response at Kuramba, in agreement with observations. The full response of the Gulf is calculated in subsequent work (Williams 1974) which takes the effects of the earth's rotation into account.
A method for determination and control of the frequency response of the constant-temperature hot-wire anemometer
Authors: Wood N. B. 
Published: March 2006

The theory of the constant-temperature anemometer has been extended in order to obtain quantitative results for the frequency response. A simple electrical test against which to check the theory has been devised, and the validity of the anemometer equations is demonstrated. Important differences in design philo-sophies and modes of operation are indicated, and results are presented for a design in which high d.c. gain is employed in the servo amplifier. The square-wave response is briefly investigated, and it is concluded that commonly used criteria for determining the frequency response from it should be treated with caution.To measure fluctuations with a hot-wire anemometer in flows containing both velocity and temperature perturbations, the hot wire must be operated at more than one temperature. Variation of the mean wire temperature causes, in general, a variation in the frequency response, as does variation of the mean flow conditions. It is shown that, by simultaneous variation of the gain of the servo amplifier in the anemometer, the frequency response may be held nearly constant over a useful range of both overheat and flow conditions.
The ‘sliced-cylinder’ laboratory model of the wind-driven ocean circulation. Part 1. Steady forcing and topographic Rossby wave instability
Authors: Beardsley R. C. , Robbins K. 
Published: March 2006

The nonlinear response of the ‘sliced-cylinder’ laboratory model for the wind-driven ocean circulation is re-examined here in part 1 for the case of strong steady forcing. Introduced by Pedlosky & Greenspan (1967), the model consists of a rapidly rotating right cylinder with a planar sloping bottom. The homogeneous contained fluid is driven by the slow rotation of the flat upper lid relative to the rest of the basin. Except in thin Ekman and Stewartson boundary layers on the solid surfaces of the basin, the horizontal flow in the interior and western boundary layer is constrained by the rapid rotation of the basin to be independent of depth. The model thus effectively simulates geophysical flows through the physical analogy between topographic vortex stretching in the laboratory model and the creation of relative vorticity in planetary flows by the β effect.As the forcing is increased, the flow in both the sliced-cylinder laboratory and numerical models first exhibits downstream intensification in the western boundary layer. At greater forcing, separation of the western boundary current occurs with the development of stationary topographic Rossby waves in the western boundary-layer transition regions. The observed flow ultimately becomes unstable when a critical Ekman-layer Reynolds number is exceeded. We first review and compare the experimental and numerical descriptions of this low-frequency instability, then present a simple theoretical model which successfully explains this observed instability in terms of thelocalbreakdown of the finite-amplitude topographic Rossby waves embedded in the western boundary current transition region. The inviscid stability analysis of Lorenz (1972) is extended to include viscous effects, with the consequence that dissipative processes in the sliced-cylinder problem (i.e. lateral and bottom friction) are shown to inhibit the onset of the instability until the topographic Rossby wave slope exceeds a finite critical value.