Theoretical and experimental studies have been performed on fully developed twodimensional turbulent channel flows in the low Reynolds number range that are subjected to system rotation. The turbulence is affected by the Coriolis force and the low Reynolds number simultaneously. Using dimensional analysis, the relevant parameters of this flow are found to be Reynolds number Re* = u*D/v (u* is the friction velocity, D the channel half-width) and Ωv/u2* (Ω is the angular velocity of the channel) for the inner region, and Re* and ΩD/u* for the core region. Employing these parameters, changes of skin friction coefficients and velocity profiles compared to nonrotating flow can be reasonably well understood. A Coriolis region where the Coriolis force effect predominates is shown to exist in addition to conventional regions such as viscous and buffer regions. A flow regime diagram that indicates ranges of these regions as a function of Re* and |Ω|v/u2* is given from which the overall flow structure in a rotating channel can be obtained.

Experiments have been made in the range of 56 ≤ Re* ≤ 310 and -0.0057 ≤ Ωv/u2* ≤ 0.0030 (these values correspond to Re = 2UmD/v from 1700 to 10000 and rotation number R0 = 2|Ω|D/Um up to 0.055; Um is bulk mean velocity). The characteristic features of velocity profiles and the variation of skin friction coefficients are discussed in relation to the theoretical considerations.

An experimental study of the effect of riblets on three-dimensional nonlinear structures, the so-called Λ-vortices on laminar-turbulent transition showed that riblets delay the transformation of the Λ-vortices into turbulent spots and shift the point of transition downstream. This result is opposite to the negative influence of such ribbed surfaces on two-dimensional linear Tollmien-Schlichting waves (the linear stage of transition). Thus, the ribbed surface influences laminar-turbulent transition structures differently: a negative influence on the linear-stage transition structures and a positive influence on the nonlinear-stage transition structures. It is demonstrated that transition control by means of riblets requires special attention to be paid to the choice of their location, taking into account the stage of transition.

A deep-water long-crested breaking wave is generated from a time-stepping numerical model, then replicated in a wave flume. The numerical model is based on the boundary integral method and measurements of the internal kinematics are made during the breaking process with Particle Image Velocimetry (PIV). Velocity measurements are obtained throughout the wave crest, including the plunging spout. After a small shift of the numerical data to match the surface profiles, the predicted and measured kinematics are found to be in good agreement, within the limits of experimental error.

The linear stability of a simple two-layer shear flow with an upper-layer potential vorticity front overlying a quiescent lower layer is investigated as a function of Rossby number and layer depths. This flow configuration is a generalization of previously studied flows whose results we reinterpret by considering the possible resonant interaction between waves. We find that instabilities previously referred to as ‘ageostrophic’ are a direct extension of quasi-geostrophic instabilities.

Two types of instability are discussed: the classic long-wave quasi-geostrophic baroclinic instability arising from an interaction of two vortical waves, and an ageostrophic short-wave baroclinic instability arising from the interaction of a gravity wave and a vortical wave (vortical waves are defined as those that exist due to the presence of a gradient in potential vorticity, e.g. Rossby waves). Both instabilities are observed in oceanic fronts. The long-wave instability has length scale and growth rate similar to those found in the quasi-geostrophic limit, even when the Rossby number of the flow is O(1).

We also demonstrate that in layered shallow-water models, as in continuously stratified quasi-geostrophic models, when a layer intersects the top or bottom boundaries, that layer can sustain vortical waves even though there is no apparent potential vorticity gradient. The potential vorticity gradient needed is provided at the top (or bottom) intersection point, which we interpret as a point that connects a finite layer with a layer of infinitesimal thickness, analogous to a temperature gradient on the boundary in a continuously stratified quasi-geostrophic model.

It is known that certain configurations which possess curvature are prone to a class of instabilities which their ‘flat’ counterparts will not support. The main thrust of the study of these centrifugal instabilities has concentrated on curved solid boundaries and their effect on the fluid motion. In this article attention is shifted towards a fluid-fluid interface observed within a curved incompressible mixing layer. Experimental evidence is available to support the conjecture that this situation may be subject to centrifugal instabilities. The evolution of modes with wavelengths comparable with the layer's thickness is considered within moderately curved mixing layers. The high Taylor/Görtler number régime is also discussed which characterizes the ultimate fate of the modes.

The flow of two-dimensional deformable drops through branching (bifurcating) tubes is studied numerically using a boundary integral formulation. The undeformed drop diameter is assumed to be less than the tube diameter. Capillary numbers between 10−2 and 1 are considered. Flow in the branching tube is characterized by the fraction of fluid which enters each of the two downstream branches. The likelihood of drops entering the high-flow-rate branch increases as (i) the viscosity ratio between the drops and suspending fluid decreases, (ii) the capillary number increases, and (iii) the drop size increases. Hydrodynamic interactions between the suspended drops increase the number of drops which enter the low-flow-rate branch. The implications of these results for dispersion processes and local transport are explored. The disturbance flow created by drops passing over ‘dead-end’ pores or cavities results in fluid transfer between the pore and the free stream; suspensions may then be effective in improving the ‘cleaning’ of porous materials.

The receptivity problem is considered for pipe flow with periodic blow–suction through a narrow gap in the pipe wall. Axisymmetric and non-axisymmetric modes (1, 2, and 3) are analysed. The method of solution is based on global eigenvalue analysis for spatially growing disturbances in circular pipe Poiseuille flow. The numerical procedure is formulated in terms of the collocation method with the Chebyshev polynomials application. The receptivity problem is solved with an expansion of the solution in a biorthogonal eigenfunction system, and it was found that there is an excitation of many eigenmodes, which should be taken into account. The result explains the non-similar character of the amplitude distribution in the downstream direction that was observed in experiments.

It is shown that a train of long waves can suppress a short-wave field due to four-wave resonance interactions. These interactions lead to the diffusion (in Fourier space) of the wave action of the short-wave field, so that the wave action is transported to the regions of higher wavenumbers, where it dissipates more effectively. The diffusion equation is derived.

Rotating fluid-filled containers are systems which admit inertial oscillations, which at appropriate frequencies can be represented as inertia wave modes. When forced by a time-dependent perturbation, systems of contained inertia waves have been shown, in a number of experimental studies, to exhibit complex and varied breakdown phenomena. It is particularly hard to determine a forcing amplitude below which breakdowns do not occur but at which linear wave behaviour is still measurable. In this paper, experiments are presented where modes of higher order than the fundamental are forced. These modes exhibit more complex departures from linear inviscid behaviour than the fundamental mode. However, the experiments on higher-order modes show that instabilities begin at nodal planes. It is shown that even a weakly nonlinear contained inertia-wave system is one in which unexpectedly efficient interactions with higher-order modes can occur, leading to ubiquitous breakdowns. An experiment with the fundamental mode illustrates the system's preference for complex transitions to chaos.

Detailed three-dimensional phase-averaged measurements of the spanwise and streamwise vorticity formation and evolution in a forced mixing layer have been obtained. A plane two-stream mixing layer with a velocity ratio (U2/U1) of 0.6, a maximum Reynolds number (Reδ) of about 3150 and laminar initial boundary layers was generated in a mixing layer wind tunnel. Acoustic forcing, consisting of a fundamental roll-up frequency and its subharmonic, was used to phase-lock the initial development and first pairing of the spanwise vortical structures. For the first time, phase-averaged measurements of all three velocity components have been obtained on a three-dimensional grid, yielding the spanwise and streamwise vorticity distributions without invoking Taylor's hypothesis. The phase-averaged results show that the streamwise vorticity first appears in the form of ‘ribs’ just upstream of the first spanwise vortex roll-up. At the same time, the first spanwise roller becomes kinked, thus also contributing to the streamwise vorticity. As a result, in cross-stream cuts through the spanwise rollers, the streamwise vorticity appears in a ‘three-tier’ arrangement with opposite-signed vorticity in the centre. In terms of phase-averaged quantities, the maximum streamwise vorticity in the initial ribs is equivalent to about 10–15% of the peak spanwise vorticity and the streamwise rib circulation is equivalent to about 5–10% of the spanwise circulation. Further downstream, the peak streamwise vorticity decreases with increasing distance, while the average circulation remains approximately constant. Downstream of the pairing, the streamwise vorticity levels in the spanwise rollers are reduced. However, the spanwise spacing of the streamwise vortices does not increase within the measurement domain. Phase-averaged Reynolds stress measurements show that relatively high stress levels (periodic and random) were generated in the cores of the spanwise vortices.

The process of unsteady two-dimensional boundary-layer separation at high Reynolds number is considered. Solutions of the unsteady non-interactive boundary-layer equations are known to develop a generic separation singularity in regions where the pressure gradient is prescribed and adverse. As the boundary layer starts to separate from the surface, however, the external pressure distribution is altered through viscous—inviscid interaction just prior to the formation of the separation singularity; hitherto this has been referred to as the first interactive stage. A numerical solution of this stage is obtained here in Lagrangian coordinates. The solution is shown to exhibit a high-frequency inviscid instability resulting in an immediate finite-time breakdown of this stage. The presence of the instability is confirmed through a linear stability analysis. The implications for the theoretical description of unsteady boundary-layer separation are discussed, and it is suggested that the onset of interaction may occur much sooner than previously thought.

An example of non-uniqueness in the two-dimensional, linear water wave problem is obtained by constructing a potential which does not radiate any waves to infinity and whose streamline pattern represents the flow around two surface-piercing bodies. The potential is constructed from two wave sources which are positioned in the free surface in such a way that the waves radiated from each source cancel at infinity. A numerical calculation of the streamline pattern indicates that there are at least two streamlines which represent surface-piercing bodies, each of which encloses a source point. A proof of the existence of these lines is then given.

The oscillation of a moderately underexpanded choked jet impinging upon a flat plate is investigated both analytically and numerically. The feedback mechanism between oscillations of the standoff-shock and the plate is clarified. Pressure waves produced by the motion of the shock are reflected by the plate. In addition, oscillations in the shock position lead to downstream entropy fluctuations, which generate pressure waves as they are convected through the stagnation flow near the plate. A linear stability analysis is used to investigate the stability threshold and frequencies of oscillation, as a function of jet pressure ratio and nozzle-to-plate distance. The analytical predictions are compared to results from a numerical simulation and to the experimental data of Powell (1988) and Mørch (1963, 1964).

We consider weakly nonlinear wave motions in a thermally stratified boundary layer. Attention is focused on the upper branch of the neutral stability curve, corresponding to small wavelengths and large Reynolds number. In this limit the motion is governed by a first harmonic/mean flow interaction theory in which the wave-induced mean flow is of the same order of magnitude as the wave component of the flow. We show that the flow is governed by a system of three coupled partial differential equations which admit finite-amplitude periodic solutions bifurcating from the linear, neutral points.

When a lightly damped fluid resonator is forced near its fundamental frequency, the most usual response is one in which the fluid oscillates in the corresponding eigenmode with an amplitude response similar to that of a Duffing oscillator. Examples are the sloshing of a horizontally oscillated tank or acoustic oscillations in a resonator of general shape. However, multiple eigenmodes can be excited if the spectrum is either commensurate or degenerate and both acoustic resonance and the sloshing of shallow water in a nearly square container exemplify both these exceptional cases. In this paper we investigate how the response of such systems depends on geometry and dispersion.

A method is described for calculating the motion of N spherical particles suspended in a quiescent second-order fluid. The method requires calculation of only the low-Reynolds-number Newtonian velocity profile. This profile is used in conjunction with what has been called the ‘Reciprocal theorem method’ to evaluate particle velocities accurate to leading order in the Deborah number. If the Newtonian velocity field is found by a multipole moment expansion, then it is shown that the method can be integrated neatly into the Stokesian dynamics method of simulating Newtonian suspensions. Simulation results involving two, three, four and six particles are reported as illustrative examples, and are compared with corresponding results for particles in Newtonian fluids and with experimental results found in the literature. In addition, simulations of sedimenting suspensions are performed by using periodic boundary conditions to model an unbounded system, and the observed formation of clusters in the sedimenting system is shown to be in qualitative agreement with experimental observations.

This paper describes experimental observations of a solid sphere suspended by a vertical or inclined jet. A laminar Newtonian jet is able to suspend a sphere only through viscous entrainment at low Reynolds numbers (Re ~ 10). A turbulent Newtonian jet (Re ~ 104) attracts a sphere that is sufficiently large but rejects smaller ones. The Coanda effect is responsible for steady suspension of solid spheres even in highly slanted jets. Anomalous rotation, opposite to the direction of the local shear, occurs under certain conditions, and its physical mechanism cannot be explained based on available information. A viscoelastic laminar jet is narrower than a comparable Newtonian one and it can suspend spheres at Reynolds numbers in the hundreds, precisely the Re range in which a Newtonian jet fails to suspend a sphere. It is suggested that the contrast between laminar Newtonian and viscoelastic jets may be related to a reversal in the pressure distribution on the surface of the sphere caused by non-Newtonian normal stresses. Flow visualization provides insights into the flow field in the jet and around the solid sphere.

Large-eddy simulation (LES) was used to study mixing of turbulent, coannular jets discharging into a sudden expansion. This geometry resembles that of a coaxial jet-combustor, and the goal of the calculation was to gain some insight into the phenomena leading to lean blow-out (LBO) in such combustion devices. This is a first step in a series of calculations, where the focus is on the fluid dynamical aspects of the mixing process in the combustion chamber. The effects of swirl, chemical reactions and heat release were not taken into account. Mixing of fuel and oxidizer was studied by tracking a passive scalar introduced in the central jet. The dynamic subgrid-scale (DM) model was used to model both the subgrid-scale stresses and the subgrid-scale scalar flux. The Reynolds number was 38000, based on the bulk velocity and diameter of the combustion chamber. Mean velocities and Reynolds stresses are in good agreement with experimental data. Animated results clearly show that intermittent pockets of fuel-rich fluid (from the central jet) are able to cross the annular jet, virtually undiluted, into the recirculation zone. Most of the fuel-rich fluid is, however, entrained into the recirculation zone near the instantaneous reattachment point. Fuel trapped in the recirculation zone is, for the most part, entrained back into the step shear layer close to the base of the burner.