A laboratory experiment was conducted to investigate the characteristics of turbulencegenerated by an internal wave ray breaking on a sloping bed. The width of the incident waveray was small compared to the bed length, so that an isolated turbulent patch was generatedby the breaking process, a configuration unique to the present study. The parameter rangecovered subcritical, critical and supercritical frequencies. Flow visualization and velocitymeasurements revealed that near critical conditions the flow was confined to a narrow regionabove the bed and, contrary to expectations, critical waves showed a weak turbulence field.Subcritical and supercritical reflection resembled wave–wave interaction between theincident and the reflected waves and showed comparable centred displacement lengthscales. Asthe incident waves became progressively supercritical instabilities were first initiatedaway from the bed. For supercritical waves the centred displacement lengthscale and theturbulent Reynolds number both increased steadily up to about γ≈2, after which they startedto decrease (γ=ω/ωc, where ω is the frequency of the incidentwave and ωc=Nsinβ is the critical frequency foran ambient uniform stratification of magnitude N and a bed angle of β). Forsubcritical waves an increase in the centred displacement lengthscale and the turbulentReynolds number was also observed. The mixed fluid generated at the boundary collapsed intothe fluid interior in the form of a horizontal two-dimensional viscous–buoyancy intrusion:the efficiency of mixing was, however, very small and no measurable change in the meandensity gradient was observed over the duration of the experiments.

Experimental results are presented that reveal the structure of a two-dimensionalturbulent boundary layer which has been investigated by measuring the time-dependentvorticity flux at the wall, vorticity vector, strain-rate tensor and dissipation-rate tensorin the near-wall region with spatial resolution of the order of 7 Kolmogorov viscous lengthscales. Considerations of the structure function of velocity and pressure, which constitutevorticity flux and vorticity, indicated that, in the limit of vanishing distance, themaximum attainable content of these quantities which corresponds to unrestricted resolution,is determined by Taylor's microscale. They also indicated that most of the contributions tovorticity or vorticity flux come from the uncorrelated part of the two signals involved. Themeasurements allowed the computation of all components of the vorticity stretching vector,which indicates the rate of change of vorticity on a Lagrangian reference frame if viscouseffects are negligible, and several matrix invariants of the velocity gradient orstrain-rate tensor and terms appearing in the transport equations of vorticity, strain rateand their squared fluctuations. The orientation of vorticity revealed several preferentialdirections. During bursts or sweeps vorticity is inclined at 35° to the longitudinaldirection. It was also found that there is high probability of the vorticity vector aligningwith the direction of the intermediate extensive strain corresponding to the middleeigenvector of the strain-rate matrix. The results of the joint probability distributions ofthe vorticity vector orientation angles showed that these angles may be related to those ofhairpin vortex structures. All invariants considered exhibit a very strong intermittentbehaviour which is characterized by large-amplitude bursts which may be of the order of 10r.m.s. values. Small-scale motions dominated by high rates of turbulent kinetic energydissipation and high enstrophy density are of particular interest. It appears that thefluctuating strain field dominates the fluctuations of pressure more than enstrophy. Localhigh values of the invariants are also often associated with peaks in the shear stress.

Laboratory experiments dealing with Reynolds stress gradients in shear-free turbulence inhomogeneous rotating fluids were conducted to better understand associated physicalphenomena. The study was motivated by possible applications to the oceanic environment wheresuch Reynolds stress gradients are ubiquitous (e.g. in the vicinity of the continental shelfbreak, where turbulence decays away from the boundary). The turbulence was generated byvertical oscillations of a circular shaft with O-ring surface roughness elements; the oscillation axis coincided with theaxis of symmetry of the cylindrical test cell.

In the absence of background rotation, the turbulence is strong in the immediate vicinityof the shaft surface and decays with the radial distance, r. The turbulencein the boundary layer is such that ur∼uθ∼w,where ur, uθ, w are the radial, azimuthal and vertical r.m.s. velocity components,respectively. These velocity components are found to be proportional to Sω,where S and ω are the stroke and frequency of the shaft oscillations,respectively, i.e. much the same as for the case of oscillating-grid turbulence, which hasbeen studied extensively.

When background rotation is present, the steady-state turbulent intensity close to theshaft is similar to that of the non-rotating experiments. Away from the shaft, in thecentral portion of the test cell, large-scale motions containing randomly distributedcyclonic and anticyclonic vortices are developed owing to small local Rossby numbers. In thevicinity of the shaft, a rectified anticyclonic flow Uθ isobserved. The magnitude of Uθ is found to be proportional to thecharacteristic r.m.s. turbulence velocity u, but independent of the rate ofbackground rotation.

Consideration of the equations of motion shows that mean flows should not be expected ifbackground rotation is absent. With rotation, however, the equations indicate that theturbulent stresses can initiate, further develop and then maintain a mean anticyclonic(rectified) flow around the cylinder; the azimuthal momentum equation is shown to play acritical role in the generation of the mean anticyclonic flow.

This paper analyses the results of two series of experiments concerned with the responseof a single vertical cylinder in the inertia regime in steep non-breaking waves. We recordedfirst the loading on a cylinder when it was held stationary, and secondly, its response inthe same waves when it was pivoted just above the floor of the wave flume, and supported atthe top by springs in the horizontal plane. Spring stiffnesses were set to achieve naturalfrequencies (measured in still water) in the range between 3 and 11 times the dominant wavefrequency. The experiments were repeated with cylinders of three different diameters.

Peak loading on stationary cylinders was found to exceed the predictions of a Morisonmodel (based on kinematics computed from a numerical model of the measured waves), thoughimprovements were achieved through the inclusion of slender-body terms. Measured ringingresponses are generally in good agreement with those computed on a quasi-static basis fromthe measured loading history, but in some conditions, particularly at low frequency ratios,there is clearly some feedback from the motion to the excitation. Peak accelerations in thesteepest waves are found to be limited approximately to those that would occur if themaximum loading were applied as a step change. Particular attention is given to a rapidcycle of loading that occurs after the crest has passed the cylinder's axis, and to imagesof the flow around the cylinder at the water surface.

Two-dimensional surface-tension-driven Bénard convection in a layer with a free-slipbottom is investigated in the limit of small Prandtl number using accurate numericalsimulations with a pseudospectral method complemented by linear stability analysis and aperturbation method. It is found that the system attains a steady state consisting ofcounter-rotating convection rolls. Upon increasing the Marangoni number Mathe system experiences a transition between two typical convective regimes. The first one isthe regime of weak convection characterized by only slight deviations of the isotherms fromthe linear conductive temperature profile. In contrast, the second regime, called inertialconvection, shows significantly deformed isotherms. The transition between the two regimesbecomes increasingly sharp as the Prandtl number is reduced. For sufficiently small Prandtlnumber the transition from weak to inertial convection proceeds via a subcriticalbifurcation involving weak hysteresis. In the viscous zero-Prandtl-number limit thetransition manifests itself in an unbounded growth of the flow amplitude for Marangoninumbers beyond a critical value Mai. For Ma<Mai thezero-Prandtl-number equations provide a reasonable approximation for weak convection atsmall but finite Prandtl number. The possibility of experimental verification of inertialBénard–Marangoni convection is briefly discussed.

In this paper, an experimental investigation is described for a concentric annular flowover an axisymmetric sudden expansion by using both flow visualization and laser-Doppleranemometry (LDA) techniques. Depending upon the value of the Reynolds number and whether theReynolds number was increased or decreased, four typical flow patterns were classifiedaccording to the characteristics of the central and corner recirculation zones. The flowpatterns are open annular flow, closed annular flow, vortex shedding, and stable centralflow. Bifurcation for this flow occurred when 230 < Re < 440, whichwas verified by observing the variation of the reattachment length. The spatial growth ofvelocity fluctuations from the measurements demonstrated a tendency that shedding vorticesbehind the centrebody more strongly affect the reattachment length than flows without acentrebody.

An experiment was performed to measure near-wall velocity and Reynolds stress profiles ina pressure-driven three-dimensional turbulent boundary layer. An initially two-dimensionalboundary layer (Reθ≈4000) was exposed to a strong spanwisepressure gradient. At the furthest downstream measurement locations there was also a fairlystrong favourable streamwise pressure gradient.

Measurements were made using a specially designed near-wall laser-Doppler anemometer(LDA), in addition to conventional methods. The LDA used short focal length optics, a mirrorprobe suspended in the flow, and side-scatter collection to achieve a measuring volume 35 μmin diameter and approximately 65 μm long.

The data presented include mean velocity measurements and Reynolds stresses, all extendingwell below y+=10, at several profile locations. Terms of theturbulent kinetic energy transport equation are presented at two profile locations. The meanflow is nearly collateral (i.e. W is proportional to U) atthe wall. Turbulent kinetic energy is mildly suppressed in the near-wall region and theshear stress components are strongly affected by three-dimensionality. As a result, theratio of shear stress to turbulent kinetic energy is suppressed throughout most of theboundary layer. The angles of stress and strain are misaligned, except very near the wall(around y+=10) where the angles nearly coincide with the meanflow angle. Three-dimensionality appears to mildly reduce the production of turbulentkinetic energy.

Thermal Rossby waves driven by centrifugal buoyancy in a rotating cylindrical fluid gapbecome unstable right at the onset of convection when the Prandtl number is small. TheBenjamin–Feir–Newell instability leads to modulated thermal Rossby waves which can also bedescribed by a generalized Ginzburg–Landau equation. A resonance instability occurs at afinite distance in Rayleigh number from the neutral curve. It leads to two independent wavepatterns propagating past each other and finally gives rise to vacillations of the amplitudeof convection. Most of these features can be described to a good approximation by a systemof three coupled amplitude equations. Time integrations based on a Galerkin expansion showtransitions to chaotic convection at higher Rayleigh numbers.

A theoretical study into the effects of wall compliance on the stability of therotating-disc boundary layer is described. A single-layer viscoelastic wall model is coupledto a sixth-order system of fluid stability equations which take into account the effects ofviscosity, Coriolis acceleration, and streamline curvature. The coupled system of equationsis integrated numerically by a spectral Chebyshev-tau technique.

Travelling and stationary modes are studied and wall compliance is found to greatlyincrease the complexity of the eigenmode spectrum. It is effective in stabilizing theinviscid Type I (or cross-flow) instability. The effect on the viscous (Type II) eigenmodeis more complex and can be strongly destabilizing. An analysis of the energy flux indicatesthat this destabilization arises as a result of a large degree of energy production byviscous stresses at the wall/flow interface.

The Type I and II instabilities are shown to be negative and positive energy wavesrespectively. The co-existence of eigenmodes of opposite energy type indicates thepossibility of modal interaction and coalescence. It is found that, compared with the rigiddisc, wall compliance promotes the interaction and coalescence of the Type I and IIeigenmodes. There is an associated strong instability which appears to be characterized bymarked horizontal motion of the compliant surface. Modal coalescence is interpretedphysically as producing local algebraic growth which could advance the onset of nonlineareffects.

A numerical study has been undertaken of the influence of a compliant boundary on absoluteinstability. In a certain parameter range absolute instability occurs in the boundary layeron a rotating disc, thereby instigating rapid transition to turbulence. The conventional useof wall compliance as a laminar-flow control technique has been to lower growth rates ofconvective instabilities. This has the effect of reducing amplification of disturbances asthey propagate downstream. For absolute instability, however, only the suppression of itsonset would be a significant gain. This paper addresses the question of whether passive wallcompliance can be advantageous when absolute instability exists in a boundary layer.

A theoretical model of a single-layer viscoelastic compliant wall was used in conjunctionwith the sixth-order system of differential equations which govern the stability of theboundary-layer flow over a rotating disc. The absolute/convective nature of the flow wasascertained by using a spatio-temporal analysis. Pinch-point singularities of the dispersionrelation and a point of zero group velocity identify the presence of absolute instability.It was found that only a low level of wall compliance was enough to delay the appearance ofabsolute instability to higher Reynolds numbers. Beyond a critical level of wall complianceresults suggest that complete suppression of absolute instability is possible. This wouldthen remove a major route to transition in the rotating-disc boundary layer.

In many geophysical and astrophysical contexts, thermal convection is influenced by bothrotation and an underlying shear flow. The linear theory for thermal convection ispresented, with attention restricted to a layer of fluid rotating about a horizontal axis,and plane Couette flow driven by differential motion of the horizontal boundaries.

The eigenvalue problem to determine the critical Rayleigh number is solved numericallyassuming rigid, fixed-temperature boundaries. The preferred orientation of the convectionrolls is found, for different orientations of the rotation vector with respect to the shearflow. For moderate rates of shear and rotation, the preferred roll orientation depends onlyon their ratio, the Rossby number.

It is well known that rotation alone acts to favour rolls aligned with the rotationvector, and to suppress rolls of other orientations. Similarly, in a shear flow, rollsparallel to the shear flow are preferred. However, it is found that when the rotation vectorand shear flow are parallel, the two effects lead counter-intuitively (as in other,analogous convection problems) to a preference for oblique rolls, and a critical Rayleighnumber below that for Rayleigh–Bénard convection.

When the boundaries are poorly conducting, the eigenvalue problem is solved analyticallyby means of an asymptotic expansion in the aspect ratio of the rolls. The behaviour of thestability problem is found to be qualitatively similar to that for fixed-temperatureboundaries.

Fully nonlinear numerical simulations of the convection are also carried out. These aregenerally consistent with the linear stability theory, showing convection in the form ofrolls near the onset of motion, with the appropriate orientation. More complicated statesare found further from critical.

A conical flame, in the presence of high-frequency (≈1000 Hz) and high-amplitude acousticmodulation of the cold gases, deforms to a shape which is approximately hemispherical. It isshown that the acoustic level required to produce a hemispherical flame is such that theratio of acoustic velocity to laminar combustion velocity is about 3. This flame flatteningis equivalent to the phenomenon of acoustic restabilization observed for cellular flamespropagating in tubes. The transition between the conical flame and a hemispherical flame isdescribed. The surface area of the reaction zone of the flame is found to be unmodified whenthe flame flattens. The velocity field at the burner outlet is examined with and without aflame. The mean flow lines are strongly deflected when the hemispherical flame is present.We show that the presence of the flame creates an unusual situation where the oscillatingflow controls the geometry of the mean flow.

The stability of two vortex pairs is analysed as a model for the vortex system generatedby an aircraft in flaps-down configuration. The co-rotating vortices on the starboard andport sides tumble about one another as they propagate downward. This results in atime-periodic basic state for the stability analysis. The dynamics and instability of thetrailing vortices are modelled using thin vortex filaments. Stability equations are derivedby matching the induced velocities from Biot–Savart integrals with kinematic equationsobtained by temporal differentiation of the vortex position vectors. The stability equationsare solved analytically as an eigenvalue problem, using Floquet theory, and numerically asan initial value problem. The instabilities are periodic along the axes of the vortices withwavelengths that are large compared to the size of the vortex cores. The results showsymmetric instabilities that are linked to the long-wavelength Crow instability. Inaddition, new symmetric and antisymmetric instabilities are observed at shorter wavelengths.These instabilities have growth rates 60–100% greater than the Crow instability. The systemof two vortex pairs also exhibits transient growth which can lead to growth factors of 10 or15 in one-fifth of the time required for the same growth due to instability.

Two parallel circular jets, in inviscid incompressible flow, with uniform axial velocityof the same magnitude and direction are placed near to one another, resulting in a stronglycoupled field. A given (small) wavenumber in the axial direction is taken and a dispersionrelation is found relating the frequency and wavenumber for a given disturbance mode, alongwith the velocity potentials within and exterior to the jets. The problem is tackledanalytically using bipolar coordinates and asymptotic forms for the dispersion relation arefound in the small-separation and large-separation limits. Results are then compared withthe corresponding two-dimensional problem for plane jets. It is concluded thatclose-proximity interactions greatly destabilize the varicose mode of the coupled jet, andgreatly stabilize the sinuous mode.

On the basis of the two-point velocity correlation equation a new tensor length-scaleequation and in turn a dissipation rate tensor equation and the pressure–strain correlationare derived by means of asymptotic analysis and frame-invariance considerations. The newdissipation rate tensor equation can account for non-isotropy effects of the dissipationrate and streamline curvature. The entire analysis is valid for incompressible as well asfor compressible turbulence in the limit of small Mach numbers. The pressure–straincorrelation is expressed as a functional of the two-point correlation, leading to anextended compressible version of the linear formulation of the pressure–strain correlation.In this turbulence modelling approach the only terms which still need ad hoc closure assumptions are the triple correlation of the fluctuating velocitiesand a tensor relation between the length scale and the dissipation rate tensor. Hence, aconsistent formulation of the return term in the pressure–strain correlation and thedissipation tensor equation is achieved. The model has been integrated numerically forseveral different homogeneous and inhomogeneous test cases and results are compared withDNS, LES and experimental data.