The general nature of the flow at large distances from a two-dimensional body moving uniformly through an unbounded, linearly stratified, non-diffusive viscous fluid is considered. The governing equations are linearized using the Oseen and Boussinesq approximations, and the boundary conditions at the body are replaced by a linearized momentum-integral equation. The solution of this linear problem shows a system of jets upstream and a pattern of waves downstream of the body. The effects of viscosity on these lee waves are considered in detail.

A study is made of the stability of a viscous, incompressible fluid with a finite conductivity flowing between parallel planes in a parallel magnetic field. The general form of the magnetohydrodynamic stability equation is a sixth-order differential equation. The complete sixth-order differential equation is solved numerically as an eigenvalue problem. Stability curves are obtained for a range of values of the magnetic Reynolds number Rm and the Alfvé n number A based on two-dimensional disturbances. It is found that the minimum critical Reynolds number is raised as Rm increases for a given A2 and as A2 increases for a given Rm, respectively. The stability curve closes and finally degenerates to a point which gives the critical value for Rm or A2. Results obtained for two-dimensional disturbances are modified to take into account three-dimensional disturbances. Then the minimum critical Reynolds number where three-dimensional disturbances become apparent is obtained, below which two-dimensional disturbances are the most unstable.

When a horizontal layer of fluid is heated from below and cooled from above with the mean temperature and physical parameters of the fluid constant, the two-dimensional roll is known to be the stable solution near the critical Rayleigh number. In this study, with the mean temperature changing steadily at a rate η, the Rayleigh number and the velocity and temperature fields governed by the Boussinesq equations are expanded in two parameters: η, and the amplitude ε. Hexagons are shown to be the stable solution near the critical Rayleigh number. The direction of the motion depends upon the sign of η. A finite amplitude instability is possible with an associated hysteresis in the heat flux as the critical Rayleigh number is approached from below or from above.

It has been found in part 1 (Krishnamurti 1968) that when the mean temperature of a fluid layer is changing at a constant rate η, hexagonal flows are stable in a range of Rayleigh numbers near the critical. The direction of flow depends upon the sign of η. The static state is unstable to finite amplitude disturbances at Rayleigh numbers below the critical point predicted by linear theory.

The validity of this theory is tested in an experiment in which the heat flux is measured as a function of η and Rayleigh number. The horizontal plan form is determined from the side by continuously exposing a photographic film moving in a vertical direction as tracers in different regions of the fluid are illuminated. Finite amplitude instability and hexagonal cells are indeed observed.

On the basis of previous work by the author, equations are derived describing one-dimensional unsteady flow in bubble-fluid mixtures. Attention is subsequently focused on pressure waves of small and moderate amplitude propagating through the mixture. Four characteristic lengths occur, namely, wavelength, amplitude, bubble diameter and inter-bubble distance. The significance of their relative magnitudes for the theory is discussed. It appears that for high gas content the dispersion is weak and then the conservation of mass and momentum lead to equations similar to the Boussinesq equations, describing long dispersive waves of finite amplitude on a fluid of finite depth. For waves propagating in one direction only, the corresponding equation is similar to the Korteweg–de Vries equation.

It is shown that for mixtures of low gas content the frequency dispersion is in most cases not small. Finally, solutions of the Korteweg–de Vries equation representing cnoidal and solitary waves in a bubble–liquid mixture are given explicitly.

The representation of a biharmonic function in terms of analytic functions is used to transform a problem of two-dimensional Stokes flow into a boundary-value problem in analytic function theory. The relevant conditions to be satisfied at a free surface, where there is a given surface tension, are derived.

A method for dealing with the difficulties of such a free surface is demonstrated by obtaining solutions for a two-dimensional, in viscid bubble in (a) a shear flow, and (b) a pure straining motion. In both cases the bubble is found to have an elliptical cross-section.

The solutions obtained can be shown to be unique only if certain restrictive assumptions are made, and if these are relaxed the same methods may give further solutions. Experiments on three-dimensional inviscid bubbles (Rumscheidt & Mason 1961; Taylor 1934) demonstrate that angular points appear in the bubble surface, and an analysis is presented to show that such a discontinuity in a two-dimensional free surface is necessarily a genuine cusp and the nature of the flow about such a point is examined.

Lift can be generated on a circular cylinder with its axis normal to an air flow by blowing a sheet of air tangentially round the upper surface from a narrow slot or slots. This lift force may be estimated by matching the external inviscid flow field with separation points calculated by Spalding's unified boundary-layer theory. The theory reproduces experimental results reasonably well, except in certain special conditions fully discussed.

This investigation is concerned with the convective motions in a shallow layer of silicone oil on a plane, circular copper plate which is heated at the rim and cooled at the centre and at the same time rotated around a vertical axis. The oil is in touch with a glass lid, which is cooled uniformly. With sufficient heating axially symmetric concentric rings develop. The details of the motion can be described as a superposition of a circulation due to the horizontal temperature gradient and a circulation of opposite sense due to the centrifugal force, with the motions due to the vertical instability. There seems to be a conversion into rolls whose axes point radially, if the centrifugal circulation becomes too strong.

A solution is offered for the flow induced by a two-dimensional line sink in a saturated, density-stratified porous medium. It is found that fluid is selectively withdrawn from a thin layer at the elevation of the line sink and not from the entire medium. The velocity distributions predicted by the theory are checked by experiments in a Hele–Shaw cell and good agreement found.

Power spectral density measurements were made of the water surface displacement in a wind-generated wave train in the Stanford wind, water-wave research facility. Growth rates of different components were determined from the measured spectra. The resulting values were compared with those predicted by the viscous Reynolds stress mechanism of energy transfer from wind to wave which was proposed by Miles. Where the growth was exponential the theory could be made to predict growth rates successfully at wave frequencies less than 3·5 c/s. At higher frequencies the theory predicted values an order of magnitude larger than those measured. Limited regions of linear growth were found at the lowest wind speed for components with frequencies less than 2·5 c/s. The scatter in the data did not permit a quantitative comparison with theory to be made for this range.

The stability of the flow of two layers of viscous liquids down an incline is investigated. The problem is governed by two competing long-wavelength modes associated with the surfaces. One mode, calling it the first mode, is faster than the second one. When the two layers have the same coefficient of dynamic viscosity, the second mode was found earlier by the author to be the governing mode for most cases. The situation is greatly altered when viscosity is not the same for the two layers. The second mode is dramatically stabilized for the range of viscosity ratio, m, less than unity, and the first mode is now generally the governing mode in that range. The overall effect is stabilizing compared with m = 1.

A relative stability index is also introduced to compare the result with that of the homogeneous case. It is found that the presence of the upper layer is generally destabilizing compared with that of a homogeneous fluid of the same total depth.

The current I flowing in the steady electrocapillary discharge of saturated aqueous and alcohol solutions of sodium chloride was found to be proportional to e−α/V, where V is the applied potential and α is a constant under fixed experimental conditions.

A theoretical description is given for infinitesimal non-axisymmetric disturbances of a shear flow caused by differential rotation. It is assumed that the deviations from the state of rigid rotation are small corresponding to the case of small Rossby number. The shear flow becomes unstable at a finite critical value of the Rossby number, at which the inertial forces overcome the friction in the Ekman boundary layers and the constraint imposed by the variation in depth of the container. The governing equation is closely related to the Rayleigh stability equation in the theory of hydrodynamic stability of plane parallel flow. Experimental observations by R. Hide show reasonable agreement with the theoretical predictions.

The first-order laminar shear layer between two parallel streams has been calculated exactly for compressible and incompressible two-dimensional flow. Turbulent flow has been included by using Prandtl's hypothesis for the eddy viscosity. Results are presented for a wide range of the appropriate parameters. The problem is solved by writing the momentum and energy equations as a pair of coupled integral equations in Crocco variables; these are solved by the method of successive approximation after using a simple transformation to weaken the singularity at the outer edges of the boundary layer. This approach yields uniquely the shear stress and temperature as functions of the tangential velocity u. The so-called third boundary condition, derived by Ting (1959), is then readily satisfied in evaluating the transverse component of velocity v by quadrature. Experimental results are presented in the turbulent incompressible case. Good agreement with the exact theoretical results is obtained when one stream is much faster than the other, but this falls off as the speeds of the streams tend to equalize.

Estimates of the eigenvalues C belonging to the manifold of solutions of the Orr-Sommerfeld equation are constructed by application of elementary isoperimetric inequalities. The inequalities also lead to a considerable improvement on the estimate of (αR) regions of linear stability given by Synge.