The flows of a Maxwellian fluid between two rotating coaxial disks and about a rotating disk are discussed. Asymptotic solutions are derived and numerical solutions are reported for a Weissenberg number up to 10 and a Reynolds number of up to 50. The solutions show transverse wave propagation. Also, at low Weissenberg number the moment coefficient for a rotating disk wetted on both sides is inversely proportional to the square root of the angular velocity of the disk. At high Weissenberg number it is inversely proportional to the angular velocity of the disk. The transition occurs at a Weissenberg number of unity.

We study the flow of a heavy, viscous, possibly non-Newtonian axisymmetric jet of liquid of density ρ falling under gravity g into a lighter liquid of density $\tilde{\rho}$. If the change in the momentum of the entrained lighter liquid is neglected the jet will ultimately reach a modified Torricelli limit with a speed given by \[ U(x) = \left[2\frac{\delta\rho}{\rho}gx \right]^{\frac{1}{2}} \] and an asymptotic radius \begin{equation} a(x) = \left[\frac{2Q^2}{(\delta\rho /\rho)gx} \right]^{\frac{1}{4}}, \end{equation} where x is the downstream distance, $\delta\rho = \rho - \tilde{\rho} > 0$ and 2Q is the volume flow. An exact asymptotic solution perturbing the Torricelli limit with effects of surface tension, viscosity and elasticity is given in powers of x−¼. An extended unsteady problem including effects of entrainment is formulated in terms of nonlinear ordinary differential equations which also account for weak radial variations of the velocity across the cross-section of the jet. These equations are solved in a boundary-layer approximation which gives \begin{equation} a(x)\approx 1.171\left(\frac{\tilde{\rho}}{x}\right)^{\frac{1}{20}}\frac{Q^{\frac{3}{10}}\tilde{\mu}^{\frac{1}{5}}}{(\delta\rho g)^{\frac{1}{4}}}, \end{equation} where $\tilde{\mu}$ is the viscosity of the ambient fluid. Equation (1) is in agreement with experimental observations of jets of liquid into air. Equation (2) is in agreement with experimental observations of jets of liquids into liquids.

The validity of recent shallow-flow equations with bed curvature is examined. Subcritical, critical and supercritical steady-flow solutions are identified, and the point of critical flow on the bed located, in terms of a generalized Froude number. Experiments on steady flow over both a symmetric and unsymmetric bed profile show that the theory satisfactorily predicts the free-surface and bed-pressure profiles over −2 [lsim ] kh 0·54 (where k is the bed curvature and h is the flow depth normal to the bed).

Time series of amplitude, frequency, wavenumber and phase speed are measured in an unstable deep-water wavetrain using a Hilbert-transform technique. The modulation variables evolve from sinusoidal perturbations that are well described as slowly varying Stokes waves, through increasingly asymmetric modulations that finally result in very rapid jumps or ‘phase reversals’. These anomalies appear to correspond to the ‘crest pairing’ described by Ramamonjiarisoa & Mollo-Christensen (1979). The measurements offer a novel local description of the instability of deep-water waves which contrasts markedly with the description afforded by conventional Fourier decomposition. The measurements display very large local modulations in the phase speed, modulations that may not be anticipated from measurements of the phase speeds of individual Fourier components travelling (to leading order) at the linear phase speed (Lake & Yuen 1978).

We consider the linear stability of the cocurrent flow of two fluids of different viscosity in an infinite region (the viscous analogue of the classical Kelvin-Helmholtz problem). Attention is confined to the simplest case, Couette flow, and we solve the problem using both numerical and asymptotic techniques. We find that the flow is always unstable (in the absence of surface tension). The instability arises at the interface between the two fluids and occurs for short wavelengths, when viscosity rather than inertia is the dominant physical effect.