This paper examines the linear stability of the Blasius boundary layer over compliant walls to three-dimensional (oblique) disturbance wave modes. The formulation of the eigenvalue problem is applicable to compliant walls possessing general material anisotropy. Isotropic-material walls and selected classes of anisotropic-material walls are studied. When the properties of the wall are identical with respect to all oblique wave directions, the stability eigenvalue problem for unstable three-dimensional wave modes may be reduced to an equivalent problem for two-dimensional modes. The results for isotropic-material walls show that three-dimensional Tollmien–Schlichting instability modes are more dominant than their two-dimensional counterparts when the walls are sufficiently compliant. The critical Reynolds number for Tollmien-Schlichting instability may be given by three-dimensional modes. Furthermore, for highly compliant walls, calculations based solely on two-dimensional modes are likely to underestimate the maximum disturbance growth factor needed for transition prediction and correlation. However, because the disturbance growth rates on highly compliant walls are much lower than those on a rigid wall, significant delay of transition may still be possible provided compliance-induced instabilities are properly suppressed. Walls featuring material anisotropy which have reduced stiffness to shear deformation in the transverse and oblique planes are also investigated. Such anisotropy is found to be effective in reducing the growth rates of the three-dimensional modes relative to those of the two-dimensional modes.

A new singular boundary-integral equation of the second kind is presented for the stresses on a rigid particle in motion in Stokes flow. The integral equation is particularly suitable for the mobility problem – when the forces and moments on the particle are given. A generalized Faxén law is also presented. The power of the method is demonstrated by easily reproducing known results as well as new ones, both analytically and numerically, in infinite medium as well as in confined regions.

Results are presented from analyses of high-precision time series of measurements of temperature and total heat transport obtained in a high-Prandtl-number (Pr = 26) fluid contained in a rotating, cylindrical annulus subject to a horizontal temperature gradient. Emphasis is placed on regions of parameter space close to the onset of irregular and/or chaotic behaviour. Two distinct transitions from oscillatory to apparently chaotic flow have been identified. The first occurs in an isolated region of parameter space at moderate to high Taylor number in association with a transition to a lower azimuthal wavenumber, in which a quasi-periodic (m = 3) amplitude vacillation (on a 2-torus) gives way to a low-dimensional (D ∼ 3) chaotically modulated vacillation at very low frequency (apparently organized about a 3-torus). The spatial structure of the chaotic flow exhibits the irregular growth and decay of azimuthal sidebands suggestive of a nonlinear competition between adjacent azimuthal wavenumbers. The other main transition to aperiodic flow occurs at high Taylor number as the stability parameter Θ is decreased, and is associated with the onset of ‘structural vacillation’. This transition appears to be associated with the development of small-scale instabilities within the main m = 3 baroclinic wave pattern, and exhibits a route to chaos via intermittency. The nature of the apparent chaos in these two aperiodic regimes is discussed in relation to possible mechanisms for deterministic chaos, apparatus limitations, and to previous attempts to model nonlinear baroclinic waves using low-order spectral models.

An asymptotic theory of two-dimensional planetary solitary eddies is presented. Previous studies in one-and-a-half layer models have discovered special classes of radially symmetric structure which are associated with eddies of permanent form. We generalize these studies by including an active lower layer and by considering the effects of azimuthal structure. Accordingly, we stress two main results; namely, (i) permanent-form two-layer eddies with essentially arbitrary radial structure exist, provided that the eddy includes a weak imbedded dipolar asymmetry and an appropriate counter-rotating deep flow, and (ii) fluid trapped under an eddy in Taylor columns can significantly affect eddy properties if the trapped fluid possesses non-trivial potential vorticity.

The structural permanency in our solutions arises from a balance between nonlinear steepening, driven by the continuity equation, and planetary dispersion. The structural asymmetries affect eddy propagation, either by dipole interaction within the layer (as occurs in modons) or by pressure forces acting between layers. The primary role of the deep counter-rotating flow is to balance the net upper-layer transport. The interesting layer-layer interaction, however, involves higher-order dynamics and is sensitive to the continuity of the potential-vorticity field. In general, these eddies trap fluid both in the upper thermocline and in the lower layer.

The dominance of oceanic anticyclones over cyclones is relatively well known. A main conclusion of this study is that the class of long-lived anticyclones is considerably broader than previously realized. This may help explain the observed bias toward anticyclonic eddies. A second conclusion is that estimates of material transport by eddies may need to account for the movement of fluid outside the main bowl of the eddies.

Bénard convection of a two-component liquid is considered. The liquid displays Soret effects and the boundary temperatures are fixed to span the solidification temperature of the mixture. Near the lower, heated plate the material is liquid and near the upper cooled plate there is a layer of pure solid solvent; all the solute is rejected during freezing. Linear stability theory is used to determine the effects on the critical conditions for Soret convection in the presence of the solidified layer and the interface between solid and liquid.

Experiments on mixtures of ethyl alcohol and water are performed using interferometry, photography and thermocouple measurements. The measured onset of instability to travelling waves at negative Soret coefficient compares well with those predicted by our linear theory. In the absence of ice the waves develop at finite amplitude to a fixed-amplitude state. However, when ice is present, these waves fail to persist but evolve to a state of steady finite-amplitude (overturning) convection. These differences are attributed to the presence of the ice and the nonlinear density profile of the basic state, both of which act as sources of non-Boussinesq effects.

In the present paper we obtain a theoretical expression for the temperature fluctuation spectrum for a Prandtl number of approximately one and for the region where both viscosity and molecular heat conductivity are important. An asymptotic theory for very large wavenumbers of the temperature spectrum in the turbulent flow is developed. The assumption of smallness of the correlation coefficient between the product of small-scale components of velocities at two points and the corresponding product of small-scale components of temperatures is used. The results of simultaneous measurements of streamwise velocity fluctuations and temperature fluctuations carried out in the plane of symmetry of a two-dimensional wake behind a slightly heated cylinder (Rλ = 270) in a wind tunnel is consistent with this assumption.

The main result of the theory developed is the appearance of a bump in the temperature spectrum for a Prandtl number of approximately one.

An asymptotic analysis is developed for turbulent boundary layers in strong adverse pressure gradients. It is found that the boundary layer divides into three distinguishable regions: these are the wall layer, the wake layer and a transition layer. This structure has two key differences from the zero-pressure-gradient boundary layer: the wall layer is not exponentially thinner than the wake; and the wake has a large velocity deficit, and cannot be linearized. The mean velocity profile has a y½ behaviour in the overlap layer between the wall and transition regions.

The analysis is done in the context of eddy viscosity closure modelling. It is found that k-ε-type models are suitable to the wall region, and have a power-law solution in the y½ layer. The outer-region scaling precludes the usual ε-equation. The Clauser, constant-viscosity model is used in that region. An asymptotic expansion of the mean flow and matching between the three regions is carried out in order to determine the relation between skin friction and pressure gradient. Numerical calculations are done for self-similar flow. It is found that the surface shear stress is a double-valued function of the pressure gradient in a small range of pressure gradients.