Computational fluid dynamics has been used to study inviscid shock interactions on double-wedge geometries with the purpose of understanding the fundamental gas dynamics of these interactions. The parameter space of the interactions has been explored and the different types of interactions that occur have been identified. Although the interactions are produced by a different geometry, all but one of them may be identified as an Edney Type I, IV, V, or VI interaction. The previously unidentified interaction occurs because of the geometrical constraints imposed by the double wedge. The physical mechanisms for transition have been studied, and the transition criteria have been identified. An important result is that there are two different regimes of the parameter space in which the state of the flow downstream of the interaction point is fundamentally different. At high Mach numbers this flow is characterized by an underexpanded jet which impinges on the wedge and produces large-amplitude surface pressure variations. At low Mach numbers, the jet becomes a shear layer which no longer impinges on the wedge surface.

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.

Results are reported on direct numerical simulations of transition from two-dimensional to three-dimensional states due to secondary instability in the wake of a circular cylinder. These calculations quantify the nonlinear response of the system to three-dimensional perturbations near threshold for the two separate linear instabilities of the wake: mode A and mode B. The objectives are to classify the nonlinear form of the bifurcation to mode A and mode B and to identify the conditions under which the wake evolves to periodic, quasi-periodic, or chaotic states with respect to changes in spanwise dimension and Reynolds number. The onset of mode A is shown to occur through a subcritical bifurcation that causes a reduction in the primary oscillation frequency of the wake at saturation. In contrast, the onset of mode B occurs through a supercritical bifurcation with no frequency shift near threshold. Simulations of the three-dimensional wake for fixed Reynolds number and increasing spanwise dimension show that large systems evolve to a state of spatiotemporal chaos, and suggest that three-dimensionality in the wake leads to irregular states and fast transition to turbulence at Reynolds numbers just beyond the onset of the secondary instability. A key feature of these ‘turbulent’ states is the competition between self-excited, three-dimensional instability modes (global modes) in the mode A wavenumber band. These instability modes produce irregular spatiotemporal patterns and large-scale ‘spot-like’ disturbances in the wake during the breakdown of the regular mode A pattern. Simulations at higher Reynolds number show that long-wavelength interactions modulate fluctuating forces and cause variations in phase along the span of the cylinder that reduce the fluctuating amplitude of lift and drag. Results of both two-dimensional and three-dimensional simulations are presented for a range of Reynolds number from about 10 up to 1000.

The presence of a three-phase region, where three immiscible phases are in mutual contact, causes additional difficulties in the investigation of many fluid mechanical problems. To surmount these difficulties some assumptions or specific hydrodynamic models have been used in the contact region (inner region). In the present paper an approach to the numerical solution of dynamic contact-line problems in the outer region is described. The influence of the inner region upon the outer one is taken into account by means of a solution of the integral mass and momentum conservation equations there. Both liquid–fluid–liquid and liquid–fluid–solid dynamic contact lines are considered. To support the consistency of this approach tests and comparisons with a number of experimental results are performed by means of finite-element numerical simulations.

A time-averaged length scale can be defined by a pair of successive turbulent-velocity derivatives, i.e. [dnu(x)/ dxn]′/ [dn+1u(x)/ dxn+1]′. The length scale associated with the zeroth- and the first-order derivatives, u′/u′x, is the Taylor microscale. In isotropic turbulence, this scale is the average length between zero crossings of the velocity signal. The average length between zero crossings of the first velocity derivative, i.e. u′x/u′xx, can be reliably obtained by using the peak-valley-counting (PVC) technique. We have found that the most probable scale, rather than the average, equals the wavelength at the peak of the dissipation spectrum in a plane mixing layer (Zohar & Ho 1996). In this study, we experimentally investigate the generality of applying the PVC technique to estimate the dissipation scale in three basic turbulent shear flows: a flat-plate boundary layer, a wake behind a two-dimensional cylinder and a plane mixing layer. We also analytically explore the quantitative relationships among this length scale and the Kolmogorov and Taylor microscales.

When a tank of fluid with a solute gradient is subjected to lateral heating, a series of horizontal convection cells is generated when the critical condition is exceeded. This phenomenon has been observed experimentally and simulated by two-dimensional numerical schemes by a number of previous investigators. In each of the convection cells, relatively warm and solute-rich fluid flows from the hot to the cold wall along the top of the cell while the return of the relatively cool and solute-poor fluid is along the bottom of the cell. This situation is conducive to the onset of salt fingers. We recently performed a series of such experiments with salt-water and ethanol–water solutions. By using flow visualization techniques, salt fingers in longitudinal rolls typical of those occurring in shear flows were observed. Salt fingers were observed as soon as convection was initiated, and they advanced with the convection front. Experiments with an ethanol–water solution showed that salt fingers can be generated by flows driven by a surface tension gradient and that the effect of solute concentration on surface tension plays an important role in the process.

Pendant liquid bridges are defined as pendant drops supporting a solid axisymmetric endplate at their lower end. The stability and shape properties of such bridges are defined in terms of the capillary properties of the system and of the mass and radius of the lower free-floating endplate. The forces acting in the pendant liquid bridge are defined exactly and expressed in dimensionless form. Numerical analysis has been used to derive the properties of a given bridge and it is shown that as the bridge grows by adding more liquid to the system a maximum volume is reached. At this maximum volume, the pendant bridge becomes unstable with the length of the bridge increasing spontaneously and irreversibly at constant volume. Finally the bridge breaks with the formation of a satellite drop or an extended thread. The bifurcation and breakage processes have been recorded using a high-speed video camera with a digital recording rate of up to 6000 frames per second. The details of the shape of the bridge bifurcation and breakage for many pendant bridge systems have been recorded and it is shown that satellite drop formation after rupture is not always viscosity dependent. Bifurcation and breakage in simulated low gravity demonstrated that breakage was very nearly symmetrical about a plane through the middle of the pendant bridge.

The stability of plane channel flow between compliant walls is investigated for disturbances which have the same symmetry, with respect to the channel centreline, as the Tollmien–Schlichting mode of instability. The interconnected behaviour of flow-induced surface waves and Tollmien–Schlichting waves is examined both by direct numerical solution of the Orr–Sommerfeld equation and by means of an analytic shear layer theory. We show that when the compliant wall properties are selected so as to give a significant stability effect on Tollmien–Schlichting waves, the onset of divergence instability can be severely disrupted. In addition, travelling wave flutter can interact with the Tollmien–Schlichting mode to generate a powerful instability which replaces the flutter instability identified in studies based on a potential mean-flow model. The behaviour found when the mean-flow shear layer is fully accounted for may be traced to singularities in the wave dispersion relation. These singularities can be attributed to solutions which represent Tollmien–Schlichting waves in rigid-walled channels. Such singularities will also be found in the dispersion relation for the case of Blasius flow. Thus, similar behaviour can be anticipated for Blasius flow, including the disruption of the onset of divergence instability. As a consequence, it seems likely that previous investigations for Blasius flow will have yielded very conservative estimates for the optimal stabilization that can be achieved for Tollmien–Schlichting waves for the purposes of laminar-flow control.

The effects of a free boundary on the stability of a baroclinic parallel flow are investigated using a reduced-gravity model. The basic state has uniform density stratification and a parallel flow with uniform vertical shear in thermal-wind balance with the horizontal buoyancy gradient. A finite value of the velocity at the free (lower) boundary requires the interface to have a uniform slope in the direction transversal to that of the flow. Normal-mode perturbations with arbitrary vertical structure are studied in the limit of small Rossby number. This solution is restricted to neither a horizontal lower boundary nor a weak stratification in the basic state.

In the limit of a very weak stratification and bottom slope there is a large separation between the first two deformation radii and hence short or long perturbations may be identified:

(a) The short-perturbation limit corresponds to the well-known Eady problem in which case the layer bottom is effectively rigid and its slope in the basic state is immaterial.

(b) In the long-perturbation limit the bottom is free to deform and the unstable wave solutions, which appear for any value of the Richardson number Ri, are sensible to its slope in the basic state. In fact, a sloped bottom is found to stabilize the basic flow.

At stronger stratifications there is no distinction between short and long perturbations, and the bottom always behaves as a free boundary. Unstable wave solutions are found for Ri→∞ (unlike the case of long perturbations). The increase in stratification is found to stabilize the basic flow. At the maximum stratification compatible with static stability, the perturbation has a vanishing growth rate at all wavenumbers.

Results in the long-perturbation limit corroborate those predicted by an approximate layer model that restricts the buoyancy perturbations to have a linear vertical structure. The approximate model is less successful in the short-perturbation limit since the constraint to a linear density profile does not allow the correct representation of the exponential trapping of the exact eigensolutions. With strong stratification, only the growth rate of long enough perturbations superimposed on basic states with gently sloped lower boundaries behaves similarly to that of the exact model. However, the stabilizing tendency on the basic flow as the stratification reaches its maximum is also found in the approximate model. Its partial success in this case is also attributed to the limited vertical structure allowed by the model.

A non-parallel linear stability analysis which utilizes the assumptions made in the parabolized stability equations is applied to the buoyancy-driven flow in a differentially heated cavity. Numerical integration of the complete Navier–Stokes and energy equations is used to validate the non-parallel theory by introducing an oscillatory heat input at the upstream end of the boundary layer. In this way the stability properties are obtained by analysing the evolution of the resulting disturbances. The solutions show that the spatial growth rate and wavenumber are highly dependent on the transverse location and the disturbance flow quantity under consideration. The local solution to the parabolized stability equations accurately predicts the wave properties observed in the direct simulation whereas conventional parallel stability analysis overpredicts the spatial amplification and the wavenumber.

A novel wake structure, observed as penny-shaped air bubbles rise at moderate Reynolds number through a thin layer of water bound between parallel glass plates inclined at a shallow angle relative to the horizontal, is reported. The structure of the wake is revealed through tracking particles suspended in the water. The wake completely encircles the rising bubble, and is characterized by a reverse surface flow or ‘edge jet’ which transports fluid in a thin boundary layer along the bubble surface from the tail to the nose at speeds which are typically an order of magnitude larger than the bubble rise speed. A consistent physical explanation for the wake structure is proposed. The wake is revealed to be a manifestation of the three-dimensionality of the flow in the suspending fluid. The bubble surface advances through a rolling motion, thus generating regions of surface divergence and convergence at, respectively, the leading and trailing edges of the bubble. A nose-to-tail gradient in surfactant concentration is thus established, and the associated surface tension gradient drives the edge jet. The dependence of the wake structure on the suspending fluid is examined experimentally.

Surfactants play an anomalous role in the reported flow, serving to promote rather than suppress surface motions. The wake structure is an example of a mechanically forced Marangoni flow, and so represents a mechanical analogue of that accompanying thermocapillary drop motion in microgravity. A theoretical model is developed which reproduces the salient features of the flow, and on the basis of which an estimate is made of the mechanically induced surface tension gradient along the bubble surface.

We formulate a simple theoretical model that permits one to investigate surface-tension-driven flows with complex interface geometry. The model consists of a Hele-Shaw cell filled with two different fluids and subjected to a unidirectional temperature gradient. The shape of the interface that separates the fluids can be arbitrarily complex. If the contact line is pinned, i.e. unable to move, the problem of calculating the flow in both fluids is governed by a linear set of equations containing the characteristic aspect ratio and the viscosity ratio as the only input parameters. Analytical solutions, derived for a linear interface and for a circular drop, demonstrate that for large aspect ratio the flow field splits into a potential core flow and a thermocapillary boundary layer which acts as a source for the core. An asymptotic theory is developed for this limit which reduces the mathematical problem to a Laplace equation with Dirichlet boundary conditions. This problem can be efficiently solved utilizing a boundary element method. It is found that the thermocapillary flow in non-circular drops has a highly non-trivial streamline topology. After releasing the assumption of a pinned interface, a linear stability analysis is carried out for the interface under both transverse and longitudinal temperature gradients. For a semi-infinite fluid bounded by a freely movable surface long-wavelength instability due to the temperature gradient across the surface is predicted. The mechanism of this instability is closely related to the long-wave instability in surface-tension-driven Bénard convection. A linear interface heated from the side is found to be linearly stable. The possibility of experimental verification of the predictions is briefly discussed.

Svendsen & Putrevu (1994) revealed that the much larger off-shore than vertical effective viscosity for longshore currents is the consequence of a shear dispersion mechanism. The multi-mode representation for the flow gives a mathematical framework within which a more general derivation can be made. It is shown that to a first approximation the horizontal shear dispersion tensor for velocity is the same as that for solutes.

Both necessary and sufficient conditions are derived in a systematic, rigorous way for a Reynolds stress model to preserve both frame indifference and positive semi-definiteness of the Reynolds stresses and to satisfy the principle of material frame indifference (PMFI). Also developed are two approximate theories, a linear theory and a quadratic theory, to simplify the work of developing models satisfying such conditions. The results are also valid for the higher-order correlations and the SGS Reynolds stresses. This leads to the results either confirming the previous intuitive arguments or offering new insights into turbulence modelling, and is of significance in clarifying some controversies in the literature, examining how well existing models preserve the physics, and developing new models.

An examination of various existing models with respect to the necessary and sufficient conditions obtained in the present work shows that no one model can simultaneously satisfy the invariance, the realizability and the PMFI. This offers answers to some fundamental questions regarding the existing models, such as the reason why k−ε and k−l models fail to give accurate predictions for the normal Reynolds stresses.

The conservative evolution of weakly nonlinear narrow-banded gravity waves in deep water is investigated numerically with a modified nonlinear Schrödinger equation, for application to wide wave tanks. When the evolution is constrained to two dimensions, no permanent shift of the peak of the spectrum is observed. In three dimensions, allowing for oblique sideband perturbations, the peak of the spectrum is permanently downshifted. Dissipation or wave breaking may therefore not be necessary to produce a permanent downshift. The emergence of a standing wave across the tank is also predicted.