We study the convection of an electrically conducting liquid in a horizontal cylinder (horizontal Bridgman configuration). A uniform steady vertical magnetic field is externally imposed. The thermal and magnetic Prandtl numbers are assumed equal to zero. The thermal field is obtained assuming pure conduction and certain conditions at the boundaries, so that the heat flux is axial and uniform. The influence of the cylinder's cross-sectional shape is examined. In the high Hartmann number limit (Ha [Gt ] 1), an analytical solution is found for the fully established flow. With electrically insulating walls, the magnetically damped convective velocity varies as Ha-2 when the cross-section has a horizontal plane of symmetry, while it varies as Ha-1 for non-symmetrical shapes. When the walls are perfectly conducting, the damped velocity always varies as Ha-2.

Nonlinear interactive effects in a bubbly cloud have been studied by investigating the frequency response of a bubble layer bounded by a wall oscillating normal to itself. Averaged equations of motion are used and the Rayleigh–Plesset equation is used to include the bubble dynamics. Energy dissipation due to viscous and thermal effects are included while relative motion between the two phases, liquid compressibility and viscous dissipation in the liquid have been ignored. First, a fourier analysis of the Rayleigh–Plesset equation is used to obtain an approximate solution for the nonlinear response of a single bubble in an infinite fluid. This is used in an approximate calculation of the nonlinear frequency response of a bubble layer. Finite thickness of the bubble layer results in characteristic natural frequencies of the layer all of which are less than the natural frequency of a single bubble. The presence of bubbles of different sizes in the layer causes a phenomenon called harmonic cascading. This phenomenon consists of a large response at twice the excitation frequency when the mixture contains bubbles with a natural frequency equal to twice the excitation frequency. The details of these results along with most important limitations of theory are presented.

The present work deals with the buckling phenomenon characteristic of highly viscous liquid jets slowly impinging upon a plate. The quasi-one-dimensional equations of the dynamics of thin liquid jets are used as the basis for the theoretical analysis of buckling. With the problem linearized, the characteristic equation is obtained. Its solutions show that instability (buckling) sets in only in the presence of axial compression in the jet, and when the distance between the nozzle exit and the plate exceeds some critical value. The latter is calculated. It is shown that buckling instability corresponds to the rectilinear jet/folding jet bifurcation point. The value of the folding frequency is calculated at the onset of buckling. The theoretical results are compared with Cruickshank & Munson's (1981) and Cruickshank's (1988) experimental data and the agreement is fairly good.

Three components of mean velocity and the corresponding Reynolds shear stresses have been measured in fully developed concentric and eccentric annulus flows of a Newtonian fluid at bulk-flow Reynolds numbers of 8900 and 26600 and a weakly elastic shear-thinning polymer at effective bulk-flow Reynolds numbers of 1150, 6200 and 9600. The diameter ratio was 0.5 with eccentricities of 0, 0.5 and 1.0, and the use of a Newtonian fluid of refractive index identical to that of the Perspex working section facilitated the measurements by laser velocimetry.

With the Newtonian fluid, the distribution of static pressure measurements on the outer wall is shown to be linear, with friction factors for concentric-annulus flows some 8% higher than in a smooth round pipe and for the eccentric flows of eccentricities of 0.5 and 1.0 it was lower by, respectively 8 and 22.5% than that of the concentric-annulus flow. In the former case, the law of the wall was confirmed on both inner and outer walls of the annulus at both Reynolds numbers. This was also the case for the outer wall in the eccentric-annulus flows, except in the smallest gap, but the near-inner-wall flow was not represented by a logarithmic region particularly in the smallest gap. The locations of zero shear stress and zero velocity gradient were displaced by amounts which were, like the secondary flows measured in the eccentric annulus of 0.5, almost within the measurement precision. In the eccentric-annulus flow with eccentricity of 1.0, there was a secondary flow with two circulation cells on each side of the plane of symmetry and with a maximum velocity of 2.2% of the bulk velocity.

The measurements with the non-Newtonian fluid were less detailed since refraction limited the flow accessible to the light beams. The average wall shear stress coefficient was similar to that for the Newtonian fluid in the laminar region of the concentric-annulus flow and higher for the two eccentric-annulus flows. Transition was extended to an effective Reynolds number well above that for the Newtonian fluid with a drag reduction of up to 63%. The near-outer-wall flows had logarithmic forms between the Newtonian curve and that of the maximum drag-reduction asymptote, and all fluctuation levels were less than those for the Newtonian fluid, particularly the radial and tangential components.

Turbulent vortices in the wake of a circular cylinder have been examined in some detail following their detection by a method based on vorticity concentration and circulation. The experimental data were obtained at a Reynolds number Re = 5600 (based on the free-stream velocity and cylinder diameter) with an array of eight X-wires aligned in the plane of mean shear. Distributions of conditionally averaged vorticity and circumferential velocity within vortices are in reasonable agreement with those inferred from an Oseen vortex. The conditionally averaged streamwise velocity distribution through the vortex centre has a maximum at the centre, implying a vortex convection velocity greater than the local mean velocity. An Oseen vortex model reproduces the measured mean velocity and Reynolds stresses reasonably well. Results are also given for the streamwise variations of vorticity concentration, circulation and size of the vortices.

A Galerkin method is used to study the two-dimensional modes of oscillatory convection in a gravitationally modulated fluid layer with rigid, isothermal boundaries heated either from below or from above. Nonlinear solutions are obtained for dimensionless frequencies ω (frequency is made non-dimensional with the timescale d2/κ where d is the depth of the fluid layer and κ is the thermal diffusivity) in the range 100–3000, dimensionless accelerations ε (εg is the amplitude of the externally imposed oscillatory vertical acceleration and g is the constant vertical acceleration of gravity) in the range of 1–104, and Prandtl numbers P in the range 0.71 (air) to 7 (water). The problem of convective onset is explored for a broader range of parameters than heretofore considered, including Prandtl numbers between 0.71 and 50. Both synchronous and subharmonic modes of convection are identified and it is found that finite-amplitude synchronous convection can be unstable to subharmonic modes.

The nonlinear evolution of a pair of initially linear oblique waves in a high-Reynolds-number shear layer is studied. Attention is focused on times when disturbances of amplitude ε have O($\epsilon^{\frac{1}{3}} R $) growth rates, where R is the Reynolds number. The development of a pair of oblique waves is then controlled by nonlinear critical-layer effects (Goldstein & Choi 1989). Viscous effects are included by studying the distinguished scaling ε = O(R-1). When viscosity is not too large, solutions to the amplitude equation develop a finite-time singularity, indicating that an explosive growth can be induced by nonlinear effects; we suggest that such explosive growth is the precursor to certain of the bursts observed in experiments on Stokes layers and other shear layers. Increasing the importance of viscosity generally delays the occurrence of the finite-time singularity, and sufficiently large viscosity may lead to the disturbance decaying exponentially. For the special case when the streamwise and spanwise wavenumbers are equal, the solution can evolve into a periodic oscillation. A link between the unsteady critical-layer approach to high-Reynolds-number flow instability, and the wave/vortex approach of Hall & Smith (1991), is identified.