The present study of the pressure fluctuations in the interaction region oif a two-dimensionals compression flow established that the frequency of the shock-wave unsteadiness is of the same order as the bursting frequency of the upstream boundary layer and that this frequency is independent of the downstream separated flow. The conditional-sampling technique developed herein is capable of separating phenomena due to shock-wave oscillations from those due to transport phenomena of turbulence. The results show that turbulence as inferred from wall-pressure fluctuations may be significantly amplified approaching the shock.

This paper is a continuation of the experimental study (Elder 1965), of free convection in a vertical slot, to unsteady and turbulent motion. The flow is specified by three dimensionless parameters: σ, the Prandtl number; h = H|L, the aspect ratio and $A = \gamma g \Delta TL^3|kv$, the Rayleigh number. The present experiments are generally for σ = 7 (water), h = 10–30 and A > 106.

For A above about 8 × 108S|h3, travelling, wave-like motions grow up the hot wall of the slot and also down the cold wall. These waves grow most readily mid-way between the two ends. At higher values of the Rayleigh number when the wave amplitude is finite, the phase of successive wave fronts becomes increasingly random till near A = 1·0 × 1010|h3 an intense entrainment and mixing process commences between the wall region and the interior. The middle portion of the interior is then turbulent, the extent of the region growing further toward the ends as A increases.

Measurements of the mean temperature and the probability distribution of temperature fluctuations of the turbulent flow are reported. Except within the thin wall layers and distant form the ends, the interior has a mean temperature, uniform to within 0·1%, superimposed on which is a nearly Gaussian fluctuation-field of variance of order 0·01ΔT. A comparison is made with recent theories of turbulent convection; moderate agreement is found with the similarity ideas of Priestley (1959). The wall layer is seen as a marginally unstable sublayer.

The purpose of this study is to generalize the experimental method for deciding when a fluid motion can be considered turbulent. The rationale advanced for processing a transducer signal, which indicates the intermittent nature of a turbulent field, is given a probabilistic outlook. In addition an improved detector function is introduced which uses information from longitudinal and lateral fluctuation components.

A significant amount of the fuel consumed by marine vehicles is expended to overcome skin-friction drag resulting from turbulent boundary layer flows. Hence, a substantial reduction in this frictional drag would notably reduce cost and environmental impact. Superhydrophobic surfaces (SHSs), which entrap a layer of air underwater, have shown promise in reducing drag in small-scale applications and/or in laminar flow conditions. Recently, the efficacy of these surfaces in reducing drag resulting from turbulent flows has been shown. In this work we examine four different, mechanically durable, large-scale SHSs. When evaluated in fully developed turbulent flow, in the height-based Reynolds number range of 10 000 to 30 000, significant drag reduction was observed on some of the surfaces, dependent on their exact morphology. We then discuss how neither the roughness of the SHSs, nor the conventional contact angle goniometry method of evaluating the non-wettability of SHSs at ambient pressure, can predict their drag reduction under turbulent flow conditions. Instead, we propose a new characterization parameter, based on the contact angle hysteresis at higher pressure, which aids in the rational design of randomly rough, friction-reducing SHSs. Overall, we find that both the contact angle hysteresis at higher pressure, and the non-dimensionalized surface roughness, must be minimized to achieve meaningful turbulent drag reduction. Further, we show that even SHSs that are considered hydrodynamically smooth can cause significant drag increase if these two parameters are not sufficiently minimized.

The low-frequency unsteadiness in the direct numerical simulation of a Mach 2.9 shock wave/turbulent boundary layer interaction with mean flow separation is analysed using dynamic mode decomposition (DMD). The analysis is applied both to three-dimensional and spanwise-averaged snapshots of the flow. The observed low-frequency DMD modes all share a common structure, characterized by perturbations along the shock, together with streamwise-elongated regions of low and high momentum that originate at the shock foot and extend into the downstream flow. A linear superposition of these modes, with dynamics governed by their corresponding DMD eigenvalues, accurately captures the unsteadiness of the shock. In addition, DMD analysis shows that the downstream regions of low and high momentum are unsteady and that their unsteadiness is linked to the unsteadiness of the shock. The observed flow structures in the downstream flow are reminiscent of Görtler-like vortices that are present in this type of flow due to an underlying centrifugal instability, suggesting a possible physical mechanism for the low-frequency unsteadiness in shock wave/turbulent boundary layer interactions.

The general incompressible flow uQ(x), quadratic in the space coordinates, and satisfying the condition uQ = · n = 0 on a sphere r = 1, is considered. It is shown that this flow may be decomposed into the sum of three ingredients – a poloidal flow of Hill's vortex structure, a quasi-rigid rotation, and a twist ingredient involving two parameters, the complete flow uQ(x) then involving essentially seven independent parameters. The flow, being quadratic, is a Stokes flow in the sphere.

The streamline structure of the general flow is investigated, and the results illustrated with reference to a particular sub-family of ‘stretch–twist–fold’ (STF) flows that arise naturally in dynamo theory. When the flow is a small perturbation of a flow u1(x) with closed streamlines, the particle paths are constrained near surfaces defined by an ‘adiabatic invariant’ associated with the perturbation field. When the flow u1 is dominated by its twist ingredient, the particles can migrate from one such surface to another, a phenomenon that is clearly evident in the computation of Poincaré sections for the STF flow, and that we describe as ‘trans-adiabatic drift’. The migration occurs when the particles pass a neighbourhood of saddle points of the flow on r = 1, and leads to chaos in the streamline pattern in much the same way as the chaos that occurs near heteroclinic orbits of low-order dynamical systems.

The flow is believed to be the first example ofa steady Stokes flow in a bounded region exhibiting chaotic streamlines.

Finite-amplitude, axially symmetric oscillations of small (0.2 mm) liquid droplets in a gaseous environment are studied, both experimentally and theoretically. When the amplitude of natural oscillations of the fundamental mode exceeds approximately 10% of the droplet radius, typical nonlinear effects like the dependence of the oscillation frequency on the amplitude, the asymmetry of the oscillation amplitude, and the interaction between modes are observed. As the amplitude decreases due to viscous damping, the oscillation frequency and the amplitude decay factor reach their asymptotical values predicted by linear theory. The initial behaviour of the droplet is described quite satisfactorily by a proposed nonlinear inviscid theoretical model.

It is well-known that sound generated by localized sources embedded in a jet undergoes refraction as the acoustic waves propagate through the jet mean flow. For isothermal or hot jets, the effect of refraction causes the deflection of the radiated sound waves away from the jet flow direction. This gives rise to a cone of silence around the jet axis where there is a significant reduction in the radiated sound intensity. In this work, the mean flow refraction problem is investigated through the use of the reciprocity principle. Instead of the direct source Green's function, the adjoint Green's function with the source and observation points interchanged is used to quantify the effect of mean flow on sound radiation. One advantage of the adjoint Green's function is that the Green's functions for all the source locations in the jet radiating to a given direction in the far field can be obtained in a single calculation. This provides great savings in computational effort. Another advantage of the adjoint Green's function is that there is no singularity in the jet flow so that the problem can be solved numerically with axial as well as radial mean flow gradients included in a fairly straightforward manner. Extensive numerical computations have been carried out for realistic jet flow profiles with and without exercising the locally parallel flow approximation. It is concluded that the locally parallel flow approximation is valid as long as the direction of radiation is outside the cone of silence.

The understanding and quantitative assessment of air flow fields and local micron-particle wall concentrations in tracheobronchial airways are very important for estimating the health risks of inhaled particulate pollutants, developing algebraic transfer functions of global lung deposition models used in dose-response analyses, and/or determining proper drug-aerosol delivery to target sites in the lung. In this paper (Part 1) the theory, model geometries, and air flow results are provided. In a companion paper (Part 2, Comer et al. 2001), the history of particle deposition patterns and comparisons with measured data sets are reported. Decoupling of the naturally dilute particle suspension makes it feasible to present the results in two parts.

Considering a Reynolds number range of 500 [les ] ReD [les ] 2000, it is assumed that the air flow is steady, incompressible and laminar and that the tubular double bifurcations, i.e. Weibel's generations G3–G5, are three-dimensional, rigid, and smooth with rounded as well as sharp carinal ridges for symmetric planar, and just rounded carinas for 90° non-planar configurations. The employed finite-volume code CFX (AEA Technology) and its user-enhanced FORTRAN programs were validated with experimental velocity data points for a single bifurcation. The resulting air flow structures are analysed for relatively low (ReD = 500) and high (ReD = 2000) Reynolds numbers. Sequential pressure drops due to viscous effects were calculated and compared, extending a method proposed by Pedley et al. (1977). Such detailed results for bifurcating lung airways are most useful in the development of global algebraic lung models.

In this paper we assess the importance as a noise source of the well-ordered large-scale structure of a jet. We propose two simple models of the structure: the first emphasizes those features in common with waves that initially grow on an unstable shear layer but eventually saturate and decay, while the second regards the abrupt pairing of eddies as the most significant event in the jet's development. Our models demonstrate the possibility that forcing at one frequency could increase the broad-band noise of a jet, though, for jets with supersonic eddy convection velocities, the sound propagating in the direction of the Mach angle retains the spectrum of the excitation field. These features are consistent with the available experimental data, and strongly support the view that the large-scale structure of jet turbulence provides the dominant contribution to jet noise.

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.

The evolution of the two- and three-dimensional structures in a temporally growing plane shear layer is numerically simulated with the discrete vortex dynamics method. We include two signs of vorticity and thus account for the effect of the weaker boundary layer leaving the splitter plate which is used to create a spatially developing mixing layer. The interaction between the two layers changes the symmetry properties seen in a single vorticity-layer calculation and results in closer agreement with experimental observations of the interface between the two streams. Our calculations show the formation of concentrated streamwise vortices in the braid region between the spanwise rollers, whereas the spanwise core instability is observed to grow only initially. Comparison with flow visualization experiments is given, and we find that the processes dominating the early stages of the mixing-layer development can be understood in terms of essentially inviscid vortex dynamics.

In this paper, the effects of adiabatic and isothermal conditions on the statistics in compressible turbulent channel flow are investigated using direct numerical simulation (DNS). DNS of two compressible turbulent channel flows (Cases 1 and 2) are performed using a mixed Fourier Galerkin and B-spline collocation method. Case 1 is compressible turbulent channel flow between isothermal walls, which corresponds to DNS performed by Coleman et al. (1995). Case 2 is the flow between adiabatic and isothermal walls. The flow of Case 2 can be a very useful framework for the present objective, since it is the simplest turbulent channel flow with an adiabatic wall and provides ideal information for modelling the compressible turbulent flow near the adiabatic wall. Note that compressible turbulent channel flow between adiabatic walls is not stationary if there is no sink of heat. In Cases 1 and 2, the Mach number based on the bulk velocity and sound speed at the isothermal wall is 1.5, and the Reynolds number based on the bulk density, bulk velocity, channel half-width, and viscosity at the isothermal wall is 3000.

To compare compressible and incompressible turbulent flows, DNS of two incompressible turbulent channel flows with passive scalar transport (Cases A and B) are performed using a mixed Fourier Galerkin and Chebyshev tau method. The wall boundary conditions of Cases A and B correspond to those of Cases 1 and 2, respectively. Case A corresponds to the DNS of Kim & Moin (1989). In Cases A and B, the Reynolds number based on the friction velocity, the channel half-width, and the kinematic viscosity is 150.

The mean velocity and temperature near adiabatic and isothermal walls for compressible turbulent channel flow can be explained using the non-dimensional heat flux and the friction Mach number. It is found that Morkovin's hypothesis is not applicable to the near-wall asymptotic behaviour of the wall-normal turbulence intensity even if the variable property effect is taken into account. The mechanism of the energy transfers among the internal energy, mean and turbulent kinetic energiesis investigated, and the difference between the energy transfers near isothermal and adiabatic walls is revealed. Morkovin's hypothesis is not applicable to the correlation coeffcient between velocity and temperature fluctuations near the adiabatic wall.

Numerical space-amplified solutions of the Orr-Sommerfeld equation for the case of a boundary layer on a flat plate have been calculated for a wide range of values of frequency and Reynolds number. The mean flow is assumed to be parallel and given by the appropriate component of the Blasius solution. The results are presented in a form suitable for comparison with experiment and are also compared with calculations of earlier authors.

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.

When two cylinders are counter-rotated at low Reynolds number about parallel horizontal axes below the free surface of a viscous fluid, the rotation being such as to induce convergence of the flow on the free surface, then above a certain critical angular velocity Ωc, the free surface dips downwards and a cusp forms. This paper provides an analysis of the flow in the neighbourhood of the cusp, via an idealized problem which is solved completely: the cylinders are represented by a vortex dipole and the solution is obtained by complex variable techniques. Surface tension effects are included, but gravity is neglected. The solution is analytic for finite capillary number [Cscr ], but the radius of curvature on the line of symmetry on the free surface is proportional to exp (−32π[Cscr ]) and is extremely small for [Cscr ] [gsim ] 0.25, implying (in a real fluid) the formation of a cusp. The equation of the free surface is cubic in (x, y) with coefficients depending on [Cscr ], and with a cusp singularity when [Cscr ] = ∞.

The influence of gravity is considered through a stability analysis of the free surface subjected to converging uniform strain, and a necessary condition for the development of a finite-amplitude disturbance of the free surface is obtained.

An experiment was carried out using the counter-rotating cylinders as described above, over a range of capillary numbers from zero to 60; the resulting photographs of a cross-section of the free surface are shown in figure 13. For Ω < Ωc, a rounded crest forms in the neighbourhood of the central line of symmetry; for Ω > Ωc, the downward-pointing cusp forms, and its structure shows good agreement with the foregoing theory.

New experiments with a gas-filled resonance tube have shown that not only heating, but also cooling of the tube wall is possible and that these phenomena are not restricted to oscillation amplitudes that generate shocks. The present paper concentrates on amplitudes outside the shock region. For this case, an extended acoustic theory is worked out. The results show cooling in the section of the tube with maximum velocity amplitude (and thus dissipation) and marked heating in the region of the velocity nodes. A strong dependence of these effects on the Prandtl number is noted. The results are in good agreement with experiments. Although the theory is not valid for proper resonance conditions, it nevertheless sheds some light on what happens when nonlinear effects dominate.

Closely related to the limit of validity of the thermoacoustic theory is the question of transition from laminar to turbulent flow in the viscous boundary layer (Stokes layer). This problem has also been investigated; the results are given in a separate paper (Merkli & Thomann 1975). In the present article laminar flow is assumed.

Direct numerical simulations of the motion of two- and three-dimensional finite Reynolds number buoyant bubbles in a periodic domain are presented. The full Navier–Stokes equations are solved by a finite difference/front tracking method that allows a fully deformable interface between the bubbles and the ambient fluid and the inclusion of surface tension. The rise Reynolds numbers are around 20–30 for the lowest volume fraction, but decrease as the volume fraction is increased. The rise of a regular array of bubbles, where the relative positions of the bubbles are fixed, is compared with the evolution of a freely evolving array. Generally, the freely evolving array rises slower than the regular one, in contrast to what has been found earlier for low Reynolds number arrays. The structure of the bubble distribution is examined and it is found that while the three-dimensional bubbles show a tendency to line up horizontally, the two-dimensional bubbles are nearly randomly distributed. The effect of the number of bubbles in each period is examined for the two-dimensional system and it is found that although the rise Reynolds number is nearly independent of the number of bubbles, the velocity fluctuations in the liquid (the Reynolds stresses) increase with the size of the system. While some aspects of the fully three-dimensional flows, such as the reduction in the rise velocity, are predicted by results for two-dimensional bubbles, the structure of the bubble distribution is not. The magnitude of the Reynolds stresses is also greatly over-predicted by the two-dimensional results.

Of particular importance to the development of models for isolated vortex ring dynamics in a real fluid is knowledge of ambient fluid entrainment by the ring. This time-dependent process dictates changes in the volume of fluid that must share impulse delivered by the vortex ring generator. Therefore fluid entrainment is also of immediate significance to the unsteady forces that arise due to the presence of vortex rings in starting flows. Applications ranging from industrial and transportation, to animal locomotion and cardiac flows, are currently being investigated to understand the dynamical role of the observed vortex ring structures. Despite this growing interest, fully empirical measurements of fluid entrainment by isolated vortex rings have remained elusive. The primary difficulties arise in defining the unsteady boundary of the ring, as well as an inability to maintain the vortex ring in the test section sufficiently long to facilitate measurements. We present a new technique for entrainment measurement that utilizes a coaxial counter-flow to retard translation of vortex rings generated from a piston–cylinder apparatus, so that their growth due to fluid entrainment can be observed. Instantaneous streamlines of the flow are used to determine the unsteady vortex ring boundary and compute ambient fluid entrainment. Measurements indicate that the entrainment process does not promote self-similar vortex ring growth, but instead consists of a rapid convection-based entrainment phase during ring formation, followed by a slower diffusive mechanism that entrains ambient fluid into the isolated vortex ring. Entrained fluid typically constitutes 30% to 40% of the total volume of fluid carried with the vortex ring. Various counter-flow protocols were used to substantially manipulate the diffusive entrainment process, producing rings with entrained fluid fractions up to 65%. Measurements of vortex ring growth rate and vorticity distribution during diffusive entrainment are used to explain those observed effects, and a model is developed to relate the governing parameters of isolated vortex ring evolution. Measurement results are compared with previous studies of the process, and implications for the dynamics of starting flows are suggested.

We present a new formulation of the motion of a flexible body with a vortex-sheet wake and use it to study propulsive forces generated by a flexible body pitched periodically at the leading edge in the small-amplitude regime. We find that the thrust power generated by the body has a series of resonant peaks with respect to rigidity, the highest of which corresponds to a body flexed upwards at the trailing edge in an approximately one-quarter-wavelength mode of deflection. The optimal efficiency approaches 1 as rigidity becomes small and decreases to 30–50% (depending on pitch frequency) as rigidity becomes large. The optimal rigidity for thrust power increases from approximately 60 for large pitching frequency to ∞ for pitching frequency 0.27. Subsequent peaks in response have power-law scalings with respect to rigidity and correspond to higher-wavenumber modes of the body. We derive the power-law scalings by analysing the fin as a damped resonant system. In the limit of small driving frequency, solutions are self-similar at the leading edge. In the limit of large driving frequency, we find that the distribution of resonant rigidities ~k−5, corresponding to fin shapes with wavenumber k. The input power and output power are proportional to rigidity (for small-to-moderate rigidity) and to pitching frequency (for moderate-to-large frequency). We compare these results with the range of rigidity and flapping frequency for the hawkmoth forewing and the bluegill sunfish pectoral fin.