Flow visualization and laser-Doppler anemometry have been used to provide a detailed description of the velocity characteristics of the asymmetric flows which form in symmetric, two-dimensional, plane, sudden-expansion geometries. The flow and geometry boundary conditions which give rise to asymmetric flow are indicated, and the reason for the phenomenon is shown to lie in disturbances generated at the edge of the expansion and amplified in the shear layers. The spectral distributions of the fluctuations in velocity are quantitatively related to the dimensions of the two unequal regions of flow recirculation. It is also shown that the intensity of fluctuating energy in these low Reynolds number flows can be larger than that in corresponding turbulent flows.

A solution of decaying two-dimensional turbulence at large Reynolds number is analysed by means of an automated vortex census. The census identifies the flow structures which approximately conform to the idealized shape of an isolated, coherent vortex. It also determines vortex characteristics, such as amplitude, size, radial profile, and deformation from the ideal axisymmetric shape. The distributions of these characteristics within the vortex population are examined, as are their time evolutions. Interpretation of these distributions is made with reference to both the random initial conditions for the solution and the dynamical processes of vortex emergence, survival, and interaction.

Experiments were carried out using models having L/D [les ] 2 and the resulting pressure distributions and vortex shedding characteristics are presented. A simple visualization technique which provides explanations of some of the measured results is described. It is concluded that splitter planes reduce the drag markedly by stabilizing the separation points and produce a wake narrower than that for a plain cylinder, raise the base pressure by as much as 50% and affect the Strouhal number to a lesser degree. Careful measurement techniques have enabled these effects to be presented accurately.

Rotationally coherent Lagrangian vortices are formed by tubes of deforming fluid elements that complete equal bulk material rotation relative to the mean rotation of the deforming fluid volume. We show that the initial positions of such tubes coincide with tubular level surfaces of the Lagrangian-averaged vorticity deviation (LAVD), the trajectory integral of the normed difference of the vorticity from its spatial mean. The LAVD-based vortices are objective, i.e. remain unchanged under time-dependent rotations and translations of the coordinate frame. In the limit of vanishing Rossby numbers in geostrophic flows, cyclonic LAVD vortex centres are precisely the observed attractors for light particles. A similar result holds for heavy particles in anticyclonic LAVD vortices. We also establish a relationship between rotationally coherent Lagrangian vortices and their instantaneous Eulerian counterparts. The latter are formed by tubular surfaces of equal material rotation rate, objectively measured by the instantaneous vorticity deviation (IVD). We illustrate the use of the LAVD and the IVD to detect rotationally coherent Lagrangian and Eulerian vortices objectively in several two- and three-dimensional flows.

The effects of vortex generators and periodic excitation on vorticity dynamics and the phenomenon of axis switching in a free asymmetric jet are studied experimentally. Most of the data reported are for a 3:1 rectangular jet at a Reynolds number of 450 000 and a Mach number of 0.31. The vortex generators are in the form of ‘delta tabs’, triangular-shaped protrusions into the flow, placed at the nozzle exit. With suitable placement of the tabs, axis switching could be either stopped or augmented. Two mechanisms are identified governing the phenomenon. One, as described by previous researchers, is due to the difference in induced velocities for different segments of a rolled-up azimuthal vortical structure. The other is due to the induced velocities of streamwise vortex pairs in the flow. While the former mechanism, referred to here as the ωθ-dynamics, is responsible for a rapid axis switching in periodically forced jets, e.g. screeching supersonic jets, the effect of the tabs is governed mainly by the latter mechanism, referred to as the ωx-dynamics. Both dynamics can be active in a natural asymmetric jet; the tendency for axis switching caused by the ωθ-dynamics may be, depending on the streamwise vorticity distribution, either resisted or enhanced by the ωx-dynamics. While this simple framework qualitatively explains the various observations made on axis switching, mechanisms actually in play may be much more complex. The two dynamics are not independent as the flow field is replete with both azimuthal and streamwise vortical structures which continually interact. Phase-averaged measurements for a periodically forced case, over a volume of the flow field, are carried out in an effort to gain insight into the dynamics of these vortical structures. The results are used to examine such processes as the reorientation of the azimuthal vortices, the resultant evolution of streamwise vortex pairs, as well as the redistribution of streamwise vortices originating from secondary flow within the nozzle.

The ‘plug’ flow emerging from a long rotating tube into a large stationary reservoir has been used in an experimental investigation of centrifugally unstable swirling jets. A moderate Reynolds number, $\hbox{\it Re}\,{=}\,1000$, was studied extensively, and swirl numbers, $S$, the ratio of nozzle exit rotating speed to the mean mass axial velocity, were in the range 0–1.1. Four regimes were covered: non-swirling jets with $S\,{=}\,0$, weakly swirling jets in the range $0\,{<}\,S\,{<}\,S_{c1}$, strongly swirling jets before vortex breakdown with $S_{c1}\,{<}\,S\,{<}\,S_{c2}$, and stable vortex breakdown for $S\,{>}\,S_{c2}$, where $S_{c1}\,{=}\,0.6$ and $S_{c2}\,{=}\,0.88$.

The linearized stability problem for steady, cellular convection resulting from gradients in surface tension is examined in some detail. Earlier work by Pearson (1958) and Sternling & Scriven (1959, 1964) has been extended by considering the effect of gravity waves. In order to avoid the use of an assumed coupling mechanism at the interface, the relevant dynamical equations were retained for both phases. It is shown that the existence of a critical Marangoni number is assured, and that for many situations this critical value is essentially that which is appropriate to the case of a non-deformable interface. Usually, surface waves are important only at very small wave-numbers, but they are dominant for unusually thin layers of very viscous liquids.

The flow produced by an infinite rotating disk when the fluid at infinity is in a state of solid rotation is investigated numerically. When the fluid at infinity is rotating in the same sense as the disk, physically acceptable solutions exist in all cases. When the fluid at infinity is rotating in the opposite sense to that of the disk, the only physically acceptable solutions appear to be those in which there is a uniform suction present acting through the disk.

We present novel measurements of the primary instabilities of thin liquid films flowing down an incline. A fluorescence imaging method allows accurate measurements of film thickness h(x, y, t) in real time with a sensitivity of several microns, and laser beam deflection yields local measurements with a sensitivity of less than one micron. We locate the instability with good accuracy despite the fact that it occurs (asymptotically) at zero wavenumber, and determine the critical Reynolds number Rc for the onset of waves as a function of angle β. The measurements of Rc(β) are found to be in good agreement with calculations, as are the growth rates and wave velocities. We show experimentally that the initial instability is convective and that the waves are noisesustained. This means that the waveform and its amplitude are strongly affected by external noise at the source. We investigate the role of noise by varying the level of periodic external forcing. The nonlinear evolution of the waves depends strongly on the initial wavenumber (or the frequency f). A new phase boundary f*s(R) is measured, which separates the regimes of saturated finite amplitude waves (at high f) from multipeaked solitary waves (at low f). This boundary probably corresponds approximately to the sign reversal of the third Landau coefficient in weakly nonlinear theory. Finally, we show that periodic waves are unstable over a wide frequency band with respect to a convective subharmonic instability. This instability leads to disordered two-dimensional waves.

We investigate numerically vortex-induced vibrations (VIV) of two identical two-dimensional elastically mounted cylinders in tandem in the proximity–wake interference regime at Reynolds number Re = 200 for systems having both one (transverse vibrations) and two (transverse and in-line) degrees of freedom (1-DOF and 2-DOF, respectively). For the 1-DOF system the computed results are in good qualitative agreement with available experiments at higher Reynolds numbers. Similar to these experiments our simulations reveal: (1) larger amplitudes of motion and a wider lock-in region for the tandem arrangement when compared with an isolated cylinder; (2) that at low reduced velocities the vibration amplitude of the front cylinder exceeds that of the rear cylinder; and (3) that above a threshold reduced velocity, large-amplitude VIV are excited for the rear cylinder with amplitudes significantly larger than those of the front cylinder. By analysing the simulated flow patterns we identify the VIV excitation mechanisms that lead to such complex responses and elucidate the near-wake vorticity dynamics and vortex-shedding modes excited in each case. We show that at low reduced velocities vortex shedding provides the initial excitation mechanism, which gives rise to a vertical separation between the two cylinders. When this vertical separation exceeds one cylinder diameter, however, a significant portion of the incoming flow is able to pass through the gap between the two cylinders and the gap-flow mechanism starts to dominate the VIV dynamics. The gap flow is able to periodically force either the top or the bottom shear layer of the front cylinder into the gap region, setting off a series of very complex vortex-to-vortex and vortex-to-cylinder interactions, which induces pressure gradients that result in a large oscillatory force in phase with the vortex shedding and lead to the experimentally observed larger vibration amplitudes. When the vortex shedding is the dominant mechanism the front cylinder vibration amplitude is larger than that of the rear cylinder. The reversing of this trend above a threshold reduced velocity is associated with the onset of the gap flow. The important role of the gap flow is further illustrated via a series of simulations for the 2-DOF system. We show that when the gap-flow mechanism is triggered, the 2-DOF system can develop and sustain large VIV amplitudes comparable to those observed in the corresponding (same reduced velocity) 1-DOF system. For sufficiently high reduced velocities, however, the two cylinders in the 2-DOF system approach each other, thus significantly reducing the size of the gap region. In such cases the gap flow is entirely eliminated, and the two cylinders vibrate together as a single body with vibration amplitudes up to 50% lower than the amplitudes of the corresponding 1-DOF in which the gap flow is active. Three-dimensional simulations are also carried out to examine the adequacy of two-dimensional simulations for describing the dynamic response of the tandem system at Re = 200. It is shown that even though the wake transitions to a weakly three-dimensional state when the gap flow is active, the three-dimensional modes are too weak to affect the dynamic response of the system, which is found to be identical to that obtained from the two-dimensional computations.

The linear theory for water waves impinging obliquely on a vertically sided porous structure is examined. For normal wave incidence, the reflection and transmission from a porous breakwater has been studied many times using eigenfunction expansions in the water region in front of the structure, within the porous medium, and behind the structure in the down-wave water region. For oblique wave incidence, the reflection and transmission coefficients are significantly altered and they are calculated here.

Using a plane-wave assumption, which involves neglecting the evanescent eigenmodes that exist near the structure boundaries (to satisfy matching conditions), the problem can be reduced from a matrix problem to one which is analytic. The plane-wave approximation provides an adequate solution for the case where the damping within the structure is not too great.

An important parameter in this problem is Γ2 = ω2h(s - if)/g, where ω is the wave angular frequency, h the constant water depth, g the acceleration due to gravity, and s and f are parameters describing the porous medium. As the friction in the porous medium, f, becomes non-zero, the eigenfunctions differ from those in the fluid regions, largely owing to the change in the modal wavenumbers, which depend on Γ2.

For an infinite number of values of ΓF2, there are no eigenfunction expansions in the porous medium, owing to the coalescence of two of the wavenumbers. These cases are shown to result in a non-separable mathematical problem and the appropriate wave modes are determined. As the two wavenumbers approach the critical value of Γ2, it is shown that the wave modes can swap their identity.

This paper reports on an experimental investigation to determine the structure and mean flow quantities of round zero-net-mass-flux (ZNMF) jets. These jets are generated by a piston oscillating in a cavity behind a circular orifice. Several different flow patterns were observed with dye flow visualization and a parameter map of these was generated. Cross-correlation digital particle image velocimetry was used to measure instantaneous two-dimensional in-plane velocity fields in a plane containing the orifice axis. These velocity fields are used to investigate the existence of a self-preserving velocity profile in the far field of the ZNMF jet. The mean flow quantities and turbulent statistics of the ZNMF jets were compared with measurements for ‘equivalent’ continuous jets in the same apparatus. Phase-averaged velocity measurements were obtained in the near field of the ZNMF jets and were used to determine the radial entrainment. The out-of-plane vorticity fields were also investigated to gain an understanding of the mechanisms responsible for the difference in spreading rate of ZNMF jets compared to conventional continuous jets. A conceptual model of the ZNMF jet structure in the near field for Strouhal numbers much less than one is proposed that explains the observed behaviour of these ZNMF jets.

The most effective movements of swimming aquatic animals of almost all sizes appear to have the form of a transverse wave progressing along the body from head to tail. The main features of this undulatory mode of propulsion are discussed for the case of large Reynolds number, based on the principle of energy conservation. The general problem of a two-dimensional flexible plate, swimming at arbitrary, unsteady forward speeds, is solved by applying the linearized in viscid flow theory. The large-time asymptotic behaviour of an initial-value harmonic motion shows the decay of the transient terms. For a flexible plate starting with a constant acceleration from at rest, the small-time solution is evaluated and the initial optimum shape is determined for the maximum thrust under conditions of fixed power and negligible body recoil.

In a horizontal convecting layer several distinct transitions occur before the flow becomes turbulent. These are studied experimentally for several Prandtl numbers from 1 to 104. Cell size plan form, transitions in plan form, transition to time-dependence, as well as the heat flux, are measured for Rayleigh numbers from 103 to 105. The second transition, occurring at around 12 times the critical Rayleigh number, is one from steady two-dimensional rolls to a steady regular cellular pattern. There is associated with this a discrete change of slope of the heat flux curve, coinciding with the second transition observed by Malkus. Transitions to time-dependence will be discussed in part 2.

The impact of a drop on the plane surface of the same liquid is studied numerically. The accuracy of the calculation is substantiated by its good agreement with available experimental data. An attempt is made to explain the recent observation that, in a restricted range of drop radii and impact velocities, small air bubbles remain entrained in the liquid. The implications of this process for the underwater sound due to rain are considered. The numerical approach consists of a new formulation of the boundary-element method which is explained in detail. Techniques to stabilize the calculation in the presence of strong surface-tension effects are also described.

This work examines the sudden erosional flow initiated by the release of a dam-break wave over a loose sediment bed. Extended shallow-water equations are formulated to describe the development of the surge. Accounting for bed material inertia, a transport layer of finite thickness is introduced, and a sharp interface view of the morphodynamic boundary is adopted. Approximations are sought for an intermediate range of wave evolution, in which equilibration of the sediment load can be assumed instantaneous but momentum loss due to bed friction has not yet been felt. The resulting homogeneous hyperbolic equations are mathematically tractable using the Riemann techniques of gas dynamics. Dam-break initial conditions give rise to self-similar flow profiles. The wave structure features piecewise constant states, two smoothly varied simple waves, and a special type of shock: an erosional bore forming at the forefront of the wave. Profiles are constructed through a semi-analytical procedure, yielding a geomorphic generalization of the Stoker solution for dam-break waves over rigid bed. For most flow properties, the predictions of the theoretical treatment compare favourably with experimental tests visualized using particle imaging techniques.

A number of mechanisms which transport dissolved constituents and maintain the salt balance in estuaries are described. Although some of these have already been analysed, two which appear to be the most important in many real estuaries have received little previous attention. The Mersey Estuary is used as an example in which to estimate the amount of mass transported by each mechanism. The computations show in part how little is known and how much hypothesis is still required in spit?e of the number of previous estuarine studies; one may conclude, however, that in many real estuaries the most important mass transport mechanism is the net (non-tidal) transverse circulation, which is induced in part by the boundary geometry and in part by the longitudinal density gradient.

Water tunnel experiments were conducted to examine the effect of hole exit geometry on the near-field characteristics of crossflow jets. Hole shapes investigated were round, elliptical, square, and rectangular, all having the same cross-sectional area. Laser-induced fluorescence (LIF) and particle image velocimetry (PIV) were used.

The vorticity around the circumference of the jet was tracked to identify its relative contributions to the nascent streamwise vortices, which evolve eventually into kidney vortices downstream. The distinction between sidewall vorticity and that from the leading and trailing edges, though blurred for a round hole, became clear for a square or a rectangular hole. The choice of non-circular holes also made it possible to reveal the unexpected double-decked structures of streamwise vortices and link them to the vorticity generated along the wall of the hole.

The lowermost vortex pair of the double-decked structures, located beneath the jet, is what we call a ‘steady’ vortex pair. This pair is always present and has the same sense of rotation as the kidney vortices. The origin of these lower-deck vortices is the hole sidewall boundary layer: as the jet emanates from the hole, the crossflow forces the sidewall boundary layer to roll up into nascent kidney vortices. Here, hole width sets the lateral separation of these steady sidewall vortices.

The vortices comprising the upper deck ride intermittently over the top of the ‘steady’ lower pair. The sense of rotation of these upper-deck vortices depends on hole geometry and can be the same as, or opposite to, the lower pair. The origin of the upper deck is the hole leading-edge boundary layer. This vorticity, initially aligned transverse to the crossflow direction, is realigned by the entrainment of crossflow momentum and thus induces a streamwise component of vorticity. Depending on hole geometry, this induced streamwise vorticity can be opposite to the lower-deck vortex pair. The opposing pair, called the ‘anti-kidney’ pair, competes with the nascent kidney-vortices and affects the jet lift-off. The hole trailing-edge boundary layer can likewise be turned toward the streamwise direction. In this case, the turning is caused by the strong reverse flow just downstream of the jet.

In the present range of parameters, all hole boundary layer vorticity, regardless of its origin along the hole circumference, is found to influence the kidney vortices downstream.

A two-dimensional acoustic waveguide of infinite extent described by two parallel lines contains an obstruction of fairly general shape which is symmetric about the centreline of the waveguide. It is proved that there exists at least one mode of oscillation, antisymmetric about the centreline, that corresponds to a local oscillation at a particular frequency, in the absence of excitation, which decays with distance down the waveguide away from the obstruction. Mathematically, this trapped mode is related to an eigenvalue of the Laplace operator in the waveguide. The proof makes use of an extension of the idea of the Rayleight quotient to characterize the lowest eigenvalue of a differential operator on an infinite domain.

In this paper, we investigate the three-dimensional instability of a counter-rotating vortex pair to short waves, which are of the order of the vortex core size, and less than the inter-vortex spacing. Our experiments involve detailed visualizations and velocimetry to reveal the spatial structure of the instability for a vortex pair, which is generated underwater by two rotating plates. We discover, in this work, a symmetry-breaking phase relationship between the two vortices, which we show to be consistent with a kinematic matching condition for the disturbances evolving on each vortex. In this sense, the instabilities in each vortex evolve in a coupled, or ‘cooperative’, manner. Further results demonstrate that this instability is a manifestation of an elliptic instability of the vortex cores, which is here identified clearly for the first time in a real open flow. We establish a relationship between elliptic instability and other theoretical instability studies involving Kelvin modes. In particular, we note that the perturbation shape near the vortex centres is unaffected by the finite size of the cores. We find that the long-term evolution of the flow involves the inception of secondary transverse vortex pairs, which develop near the leading stagnation point of the pair. The interaction of these short-wavelength structures with the long-wavelength Crow instability is studied, and we observe significant modifications in the longevity of large vortical structures.