Experiments have been made to investigate the motion generated by a body moving along the axis of a uniformly rotating fluid.

Part of the investigation concerns the motion generated in a cylinder whose radial dimensions are much greater than those of the body. Measurements have been made of the velocities of particles on the axis of rotation both ahead of and behind the body, and the results indicate that there is a significant axial motion generated by the body over a wide range of Rossby numbers. A measurement of the instantaneous velocity profile ahead of the body, determined as a function of the radius, agrees fairly well with a low Rossby number calculation of the flow due to a circular disk (Morgan 1951). In addition, the forward influence of the body has been measured as a function of the Rossby number and from these results it is suggested that the body has a finite influence far upstream at all Rossby numbers and that the blocking phenomenon first reported by Taylor (1922) probably occurs for all values of the Rossby number (UΩa) less than a critical value which is about 0·7.

Experiments have also been made in a long cylindrical tube which acts as a wave guide. At large distances from the body the separate effects of the various modes can be observed and hence it is possible to measure the flow corresponding to an individual wave-number: these measurements show that, as a result of the Doppler effect, the motion a large distance ahead of the body is different from that far behind (see Lighthill 1967). Moreover, the experiments indicate that no disturbances propagate ahead of the body when its velocity exceeds the maximum group velocity in the fluid, but that disturbances trail behind the body when its velocity is far in excess of the maximum group velocity. Measurements of the maximum group velocity are in good agreement with the theoretical value.

The redistribution of mean momentum and vorticity, along with the mechanisms underlying these redistribution processes, is explored for post-laminar flow in fully developed, pressure driven, channel flow. These flows, generically referred to as transitional, include an instability stage and a nonlinear development stage. The central focus is on the nonlinear development stage. The present analyses use existing direct numerical simulation data sets, as well as recently reported high-resolution molecular tagging velocimetry measurements. Primary considerations stem from the emergence of the effects of turbulent inertia as represented by the Reynolds stress gradient in the mean differential statement of dynamics. The results describe the flow evolution following the formation of a non-zero Reynolds stress peak that is known to first arise near the critical layer of the most unstable disturbance. The positive and negative peaks in the Reynolds stress gradient profile are observed to undergo a relative movement toward both the wall and centreline for subsequent increases in Reynolds number. The Reynolds stress profiles are shown to almost immediately exhibit the same sequence of curvatures that exists in the fully turbulent regime. In the transitional regime, the outer inflection point in this profile physically indicates a localized zone within which the mean dynamics are dominated by inertia. These observations connect to recent theoretical findings for the fully turbulent regime, e.g. as described by Fife, Klewicki & Wei (J. Discrete Continuous Dyn. Syst., vol. 24, 2009, p. 781) and Klewicki, Fife & Wei (J. Fluid Mech., vol. 638, 2009, p. 73). In accord with momentum equation analyses at higher Reynolds number, the present observations provide evidence that a logarithmic mean velocity profile is most rapidly approximated on a sub-domain located between the zero in the Reynolds stress gradient (maximum in the Reynolds stress) and the outer region location of the maximal Reynolds stress gradient (inflection point in the Reynolds stress profile). Overall, the present findings provide evidence that the dynamical processes during the post-laminar regime and those operative in the high Reynolds number regime are connected and describable within a single theoretical framework.

We consider near-inertial waves continuously excited by a localized source and their subsequent radiation and evolution on a two-dimensional -plane. Numerical simulations are used to quantify the wave propagation and the energy flux in a realistically stratified ocean basin. We focus on the dynamics near and poleward of the inertial latitude where the local value of the Coriolis parameter matches the forcing frequency , contrasting the behaviour of waves under the traditional approximation (TA), where only the component of the Earth’s rotation aligned with gravity is retained in the dynamics, with that obtained under the non-traditional approach (non-TA) in which the horizontal component of rotation is retained. Under the TA, assuming inviscid linear wave propagation in the WKB limit, all energy radiated from the source eventually propagates toward the equator, with the initially poleward propagation being internally reflected at the inertial latitude. Under the non-TA however, these waves propagate sub-inertially beyond their inertial latitude, exhibiting multiple reflections between internal turning points that lie poleward of the inertial latitude and the bottom. The numerical experiments complement and extend existing theory by relaxing the linearity and WKB approximations, and by illustrating the time development of the steadily forced flow and the spatial patterns of energy flux and flux divergence. The flux divergence of the flow at both the forcing frequency and its first harmonic reveal the spatial patterns of nonlinear energy transfer and highlight the importance of nonlinearity in the vicinity of near-critical bottom reflection at the inertial latitude of the forced waves.

In the laboratory experiments by Fultz & Riehl (1957) and by Hide (1958) on heated rotating liquids contained in the annulus between two cylinders, it has been observed that a strongly marked jet stream appears on the free surface of the liquid under certain conditions of rotating and heating. This jet stream meanders around the annulus in a regular wave-like pattern alternately approaching the outer and inner cylindrical boundaries. The present paper puts forward an analytical theory for this jet, or Rossby regime, in the course of which exact solutions are presented of certain fundamental non-linear partial differential equations. The assumption is made that the flow is geostrophic at the first approximation and that the heat transfer across the stream lines of geostrophic flow (that is, the isobars) is due to molecular conduction. From a calculation of the heat flow it appears that this leads to values of the heat transfer which are too small, so that the ageostrophic terms must be of importance in the actual heat transfer; never-theless, the exact solution obtained here probably reveals the mechanism of the change from one wave pattern to another and certainly provides an explanation for the observed upper limit to the number of waves in a given geometrical configuration, as discussed by Hide. It has been established that the mean zonal flow and mean zonal temperature field are dependent upon the amplitude function of a finite amplitude wave solution. In this exact solution it is found that the amplitude and phase functions of the wave patterns are themselves interdependent and that the shape of the wave depends on the quantity of heat and angular momentum being transferred. It is shown that the wave pattern consisting of an integral number m lobes or petals can exist only in a restricted range of the Rossby number S—this is well-known from the experimental work of Fultz and Hide.

Using the method of matched asymptotic expansions, the interaction between axisymmetric laminar boundary layers and supersonic external flows is investigated in the limit of large Reynolds numbers. Numerical solutions to the interaction equations are presented for flare angles α that are moderately large. If α > 0 the boundary layer separates upstream of the corner and the formation of a plateau structure similar to the two-dimensional case is observed. In contrast to the case of planar flow, however, separation can occur also if α < 0, owing to the axisymmetric effect of overexpansion and recompression. The separation point then is located downstream of the corner and, most remarkable, a hysteresis phenomenon is observed.

In this paper we consider the flow field generated by a uniform electrostatic field in and about a pair of identical liquid drops immersed in a conducting fluid. It is assumed that the undisturbed electric field is parallel to the line joining the centres of the two drops. The flow field is due to the tangential electric stress over the surfaces of the drops and here this stress and the flow field are expressed in terms of bispherical harmonics. When the distance between the centres of the drops is many drop diameters the tangential electric stress and the flow field in and about one drop are unaffected by the presence of the other drop, as expected. When the distance between the centres of the drops is of the order of two drop diameters there is a substantial modification in the tangential electric stress at the surfaces of the drops and in the induced flow field, especially in the region between the planes through the drop centres perpendicular to the undisturbed electric field.

The surfactant concentration distribution on a planar uniform flow with a surface-piercing barrier was measured via the nonlinear optical technique of second-harmonic generation. The measurements were performed for an insoluble surfactant monolayer on the air/water interface. A theoretical model balancing surface elasticity and bulk shear at the interface was developed to predict the concentration profile for any insoluble monolayer. Measured equations of state, relating the surface tension to the surfactant concentration, were used in the model along with velocity data obtained using boundary-fitted digital particle image velocimetry. Theoretical concentration profiles were in agreement with experimental results. Additionally, global predictions from the model for four different insoluble surfactant systems also showed agreement with experimental measurements.

The subject of the present study is the question of how the sound power of a jet of constant exit velocity would vary if the jet exit density were varied. Changes in jet exit density would inevitably be accompanied in a real experiment by changes in the speed of sound (temperature) in the jet, so that both effects must be considered simultaneously. The point of view advanced at the end of the study is that experimentally observed results in this area seem to admit an explanation based on how the radiative efficiency of moving acoustic sources is affected by the shrouding effect of a jet flow whose velocity, temperature and density differ from those of the ambient fluid. This change in efficiency is calculated with the aid of a simple model as follows. We determine the acoustic power output of a convected monopole source, simple harmonic in its own frame of reference, moving along the axis of a plug-flow round jet whose velocity is the same as that of the source. The jet is doubly infinite and the source is assumed to have an infinite lifetime. The density and temperature of the jet are allowed to differ from those of the ambient fluid though the specific-heat ratio of the jet fluid is assumed to be the same as that of the ambient. The requirement of equality of the static pressure inside and outside the jet then calls for a certain restraint on how the jet density and temperature vary. For a specific value of the jet exit velocity, the variation of acoustic power with the ratio of jet to ambient density along with a simple assumption on how the source strength varies with jet density are employed to deduce theoretically the ‘jet density exponent for jets which are subsonic with respect to the ambient speed of sound. The jet density exponent is found to depend both on the jet Mach number and even more strongly on a source frequency parameter. The theoretical results are compared with some experimental studies of this problem. Encouraging agreement is obtained both for the detailed observed effects on the power spectrum and the exponent for the overall power.

The reorientation phenomenon of a single red blood cell during sedimentation is simulated using the boundary element method. The cell settles downwards due to a density difference between the internal and external fluids, and it changes orientation toward a vertical orientation regardless of Bond number or viscosity ratio. The reorientation phenomenon is explained by a shape asymmetry caused by the gravitational driving force, and the shape asymmetry increases almost linearly with the Bond number. When velocities are normalised by the driving force, settling/drifting velocities are weak functions of the Bond number and the viscosity ratio, while the angular velocity of the reorientation drastically changes with these parameters: the angular velocity is smaller for lower Bond number or higher viscosity ratio. As a consequence, trajectories of the sedimentation are also affected by the angular velocity, and blood cells with slower reorientation travel longer distances in the drifting direction. We also explain the mechanism of the reorientation using an asymmetric dumbbell. From the analysis, we show that the magnitude of the angular velocity is explained by two main factors: the shape asymmetry and the instantaneous orientation angle.

Oceanic internal solitary waves are typically generated by barotropic tidal flow over localised topography. Wave generation can be characterised by the Froude number $F=U/c_{0}$, where $U$ is the tidal flow amplitude and $c_{0}$ is the intrinsic linear long wave phase speed, that is the speed in the absence of the tidal current. For steady tidal flow in the resonant regime, $\unicode[STIX]{x1D6E5}_{m}<F-1<\unicode[STIX]{x1D6E5}_{M}$, a theory based on the forced Korteweg–de Vries equation shows that upstream and downstream propagating undular bores are produced. The bandwidth limits $\unicode[STIX]{x1D6E5}_{m,M}$ depend on the height (or depth) of the topographic forcing term, which can be either positive or negative depending on whether the topography is equivalent to a hole or a sill. Here the wave generation process is studied numerically using a forced Korteweg–de Vries equation model with time-dependent Froude number, $F(t)$, representative of realistic tidal flow. The response depends on $\unicode[STIX]{x1D6E5}_{max}=F_{max}-1$, where $F_{max}$ is the maximum of $F(t)$ over half of a tidal cycle. When $\unicode[STIX]{x1D6E5}_{max}<\unicode[STIX]{x1D6E5}_{m}$ the flow is always subcritical and internal solitary waves appear after release of the downstream disturbance. When $\unicode[STIX]{x1D6E5}_{m}<\unicode[STIX]{x1D6E5}_{max}<\unicode[STIX]{x1D6E5}_{M}$ the flow reaches criticality at its peak, producing upstream and downstream undular bores that are released as the tide slackens. When $\unicode[STIX]{x1D6E5}_{max}>\unicode[STIX]{x1D6E5}_{M}$ the tidal flow goes through the resonant regime twice, producing undular bores with each passage. The numerical simulations are for both symmetrical topography, and for asymmetric topography representative of Stellwagen Bank and Knight Inlet.

This paper contains the details of an experimental study of the vortex formed in front of a piston as it moves through a cylinder. The mechanism for the formation of this vortex is the removal of the boundary layer forming on the cylinder wall in front of the advancing piston. The trajectory of the vortex core and the vorticity distribution on the developing vortex have been measured for a range of piston velocities. Velocity field measurements indicate that the vortex is essentially an inviscid structure at the Reynolds numbers considered, with viscous effects limited to the immediate corner region. Inviscid flow is defined in this paper as being a region of the flow where inertial forces are significantly larger than viscous forces. Flow visualization and vorticity measurements show that the vortex is composed mainly of material from the boundary layer forming over the cylinder wall. The characteristic dimension of the vortex appears to scale in a self-similar fashion, while it is small in relation to the apparatus length scale. This scaling rate of t0.85+0.7m, where the piston speed is described as a power law Atm, is somewhat faster than the t3/4 scaling predicted by Tabaczynski et al. (1970) and considerably faster than a viscous scaling rate of t1/2. The reason for the structure scaling more rapidly than predicted is the self-induced effect of the secondary vorticity that is generated on the piston face. The vorticity distribution shows a distinct spiral structure that is smoothed by the action of viscosity. The strength of the separated vortex also appears to scale in a self-similar fashion as t2m+1. This rate is the same as suggested from a simple model of the flow that approximates the vorticity being ejected from the corner as being equivalent to the flux of vorticity over a flat plate started from rest. However, the strength of the vorticity on the separated structure is 25% of that suggested by this model, sometimes referred to as the ‘slug’ model. Results show that significant secondary vorticity is generated on the piston face, forming in response to the separating primary vortex. This secondary vorticity grows at the same rate as the primary vorticity and is wrapped around the outside of the primary structure and causes it to advect away from the piston surface.

TriGlobal linear instability analysis and direct numerical simulations have been performed to unravel the mechanisms ultimately responsible for transition of steady laminar flow over a long rectangular finite-span open cavity with dimensions $L$ : $D$ : $W$$=$ 6 : 1 : 2 to unsteadiness. The steady laminar three-dimensional flow loses stability at $\mathit{Re}_{D,cr}\approx 1080$ as a consequence of linear amplification of a travelling eigenmode that is qualitatively analogous to the shear-layer mode known from analyses of flow in spanwise-periodic cavities, but has a three-dimensional structure which is strongly influenced by the cavity lateral walls. Differences in the eigenspectrum of the present and the spanwise homogeneous flow configuration are documented. Topological changes exerted on the steady laminar flow by linear amplification of the unstable shear-layer mode are reminiscent of observations in experiments at an order of magnitude higher Reynolds number.

A simultaneous technique employing particle image velocimetry (PIV) and shadowgraphy was used to study vertical slug flow in non-Newtonian fluids. Two aqueous solutions of 0.8 and 1.0 wt% carboxymethylcellulose (CMC) were studied and the flow field around individual Taylor bubbles fully characterized. The rheological fluid properties and pipe dimension yielded Reynolds numbers of 8 and 4 and Deborah numbers of 0.2 and 0.4. A negative wake was found downstream of the Taylor bubbles in both fluids. Below the bubble trailing edge, along the axis region, the fluid flows in the opposite direction to the bubble (negative wake), originating rotational liquid movements in adjacent regions. Even far downward from the bubble, rotational liquid movements are clearly seen and measured. In the 1.0 wt% CMC solution, the bubble trailing edge has the shape of a two-dimensional cusp. This two-dimensional cusp, of small dimensions, is seen in different orientations during the bubble rise-indicating a fast rotational movement. The asymmetrical shape of the trailing edge is responsible for small asymmetries in the flow in the wake region (three-dimensional flow). The asymmetrical shape associated with the rotational movement is responsible for an unsteady flow of small amplitude. In the 0.8 wt% CMC solution, the shape of the trailing edge changes during the bubble rise. An axisymmetric axial oscillation a continuous expansion and contraction of the trailing edge, is the origin of this behaviour. This oscillatory movement is responsible for an unsteady flow of small amplitude in the wake region.

The viscometer investigations of Donnelly & Ozima (1962) on the stability of flow between rotating cylinders in the presence of a magnetic field have been extended by making careful torque measurements in the subcritical range using improved mercury. The results show that a small difference in stability can be observed with conducting cylinders as compared with insulating cylinders. The results also suggest that a heretofore unnoticed instability begins well before the instability studied earlier. This relatively weak instability accounts for some of the anomalous effective viscosity observed by Donnelly & Ozima.

The linear stability of the developing flow of an incompressible fluid in the entrance region of a circular tube is investigated. The case of non-axisymmetric small disturbances is considered in the analysis. The main-flow velocity distribution used in the stability calculations is that from the solution of the linearized momentum equation. The eigenvalue problem consisting of the disturbance equations and the boundary conditions is solved by a direct numerical integration scheme along with an iteration procedure. An orthonormalization method is employed to remove the ‘parasitic errors’ inherent in the numerical integration of the coupled disturbance equations. The flow is found to be unstable to non-axisymmetric disturbances with an azimuthal wavenumber of one. Neutral-stability curves and critical Reynolds numbers at various axial locations are presented. A comparison of these results is made with those for axisymmetric disturbances reported by Huang & Chen. It is found that the first instability of the flow is due to non-axisymmetric disturbances and occurs in the entrance region of the pipe with a minimum critical Reynolds number of 19 780.

We examine the statistical properties of extreme and rogue wave activity in crossing directional seas, to constrain the probabilistic distributions of wave heights and wave crests in complex sea states; such crossing seas alter the statistical structure of surface waves and are known to have been involved in several marine accidents. Further, we examine the relationship between the kurtosis as an indicator of nonlinearity in the spectrum and the directionality and crossing angles of the sea-state components. Experimental tests of two-component directionally spread irregular waves with varying frequency, directional spreading and component crossing angles were carried out at the Ocean Basin Laboratory in Trondheim, Norway. The results from the experiments show that wave heights are well described by a first-order (linear) statistical distribution, while for the wave crest heights several cases exceed a second-order distribution. The number of rogue waves is relatively low overall, which agrees with previous findings in directionally spread seas. The kurtosis and wave and crest height exceedance probabilities were more affected by varying the directional spreading of the components than by varying the crossing angles between components; reducing the component directional spreading increases the kurtosis and increases the exceedance probabilities. The kurtosis can be estimated quite well for two-component seas from the directional spreading using an empirical relationship based on the two-dimensional Benjamin–Feir index when the effects of bound modes are included. This result may allow forecasting of the probability of extreme waves from the directional spreading in complex sea states.

We investigate the convection and density stratification that form when buoyancy fluxes are simultaneously applied to a finite volume in both a turbulent buoyant plume from a small source and as a uniform heat flux from a horizontal boundary. The turbulent plume tends to produce a stable density stratification, whereas the distributed flux from a boundary tends to force vigorous overturning and vertical mixing. Experiments show that steady, partially mixed and partially stratified states can exist when the plume buoyancy flux is greater than the distributed flux.

When the two fluxes originate from the same boundary, the steady state involves a balance between the rate at which the mixed layer deepens due to encroachment and vertical advection of the stratified water far from the plume due to the plume volume flux acquired by entrainment. There is a monotonic relationship between the normalized mixed layer depth and flux ratio R (boundary flux/plume flux) for 0<R<1, and the whole tank overturns for R>1. The stable density gradient in the stratified region is primarily due to the buoyancy from the plume but is strengthened by a stabilizing temperature gradient resulting from entrainment of heat into the plume from the mixed layer. This result may be relevant to the upper oceans of high latitude where there is commonly a destabilizing heat flux from the sea surface as well as more localized and intense deep convection from the surface.

For the case of fluxes from a plume on one boundary and a uniform heat flux from the opposite boundary the shape of the density profile is that given by the Baines & Turner (1969) ‘filling-box’ mechanism, with the gradient reduced by a factor (1 + R) due to the heating. Thus, when R<−1 there is no stratified region and the whole water column overturns. When 0>R>−1, the constant depth of the convecting layer is determined by a balance between buoyancy and turbulent kinetic energy in the outflow layer from the plume.

A theoretical study is carried out for bubble oscillation in a compressible liquid with significant acoustic radiation based on the Keller–Miksis equation using a multi-scaled perturbation method. The leading-order analytical solution of the bubble radius history is obtained to the Keller–Miksis equation in a closed form including both compressible and surface tension effects. Some important formulae are derived including: the average energy loss rate of the bubble system for each cycle of oscillation, an explicit formula for the dependence of the oscillation frequency on the energy, and an implicit formula for the amplitude envelope of the bubble radius as a function of the energy. Our theory shows that the frequency of oscillation does not change on the inertial time scale at leading order, the energy loss rate on the long compressible time scale being proportional to the Mach number. These asymptotic predictions have excellent agreement with experimental results and the numerical solutions of the Keller–Miksis equation over very long times. A parametric analysis is undertaken using the above formula for the energy of the bubble system, frequency of oscillation and minimum/maximum bubble radii in terms of the dimensionless initial pressure of the bubble gases (or, equivalently, the dimensionless equilibrium radius), Weber number and polytropic index of the bubble gas.

The inviscid and viscous stability problems are addressed for a boundary layer which can support both Görtler and crossflow vortices. The change in structure of Görtler vortices is found when the parameter representing the degree of three-dimensionality of the basic boundary-layer flow under consideration is increased. It is shown that crossflow vortices emerge naturally as this parameter is increased and ultimately become the only possible vortex instability of the flow. It is shown conclusively that at sufficiently large values of the crossflow there are no unstable Görtler vortices present in a boundary layer which, in the zero-crossflow case, is centrifugally unstable. The results suggest that in many practical applications Görtler vortices cannot be a cause of transition because they are destroyed by the three-dimensional nature of the basic state. In swept-wing flows the Görtler mechanism is probably not present for typical angles of sweep of about 20°.

Some discussion of the receptivity problem for vortex instabilities in weakly three-dimensional boundary layers is given; it is shown that inviscid modes have a coupling coefficient marginally smaller than those of the fastest growing viscous modes discussed recently by Denier, Hall & Seddougui (1991). However, the fact that the growth rates of the inviscid modes are the larger in most situations means that they are probably the more likely source of transition.

The wake structure and transition process of an incompressible viscous fluid flow past a sphere affected by an imposed streamwise magnetic field are investigated numerically over flow regimes that include steady and unsteady laminar flows at Reynolds numbers up to 300. For cases without a magnetic field, a subregion with the existence of a limit cycle is found in the range $210<Re<270$. The point of division is between $Re=220$ and $Re=230$. For cases with a streamwise magnetic field, five wake patterns are the steady axisymmetric wake with an attached separation bubble, the steady plane symmetric wake with a small spiral dismissed, the steady plane symmetric wake with a limit cycle, the steady plane symmetric wake with a small spiral fed by the upstream fluid and the unsteady plane symmetric wake with a wave-like oscillation or vortex shedding. Under the influence of an imposed streamwise magnetic field, the wake will be transitioned to various patterns. An interesting ‘reversion phenomenon’, which describes the topological structure behind a sphere with a higher Reynolds number and a certain interaction parameter which corresponds to a lower Reynolds number case with a certain interaction parameter or a much lower Reynolds number case without a magnetic field, is also found. The principal results of the present work are summarized in a map of regimes in the $\{N,Re\}$ plane.