A realistic theoretical model of steady Langmuir circulations is constructed. Vorticity in the wind direction is generated by the Stokes drift of the gravity-wave field acting upon spanwise vorticity deriving from the wind-driven current. We believe that the steady Langmuir circulations represent a balance between this generating mechanism and turbulent dissipation.

Nonlinear equations governing the motion are derived under fairly general conditions. Analytical and numerical solutions are sought for the case of a directional wave spectrum consisting of a single pair of gravity waves propagating at equal and opposite angles to the wind direction. Also, a statistical analysis, based on linearized equations, is developed for more general directional wave spectra. This yields an estimate of the average spacing of windrows associated with Langmuir circulations. The latter analysis is applied to a particular example with simple properties, and produces an expected windrow spacing of rather more than twice the length of the dominant gravity waves.

The relevance of our model is assessed with reference to known observational features, and the evidence supporting its applicability is promising.

Long waves are generated in a laboratory-size rectangular basin, which is heated uniformly from below. Their subsequent decay is measured, and the decay component due to the action of convective turbulence isolated, using a combination of existing theories and interpretation techniques. An expression is proposed for the turbulent decay decrement as a function of the bulk Rayleigh number. The results agree as well as can be expected with a simple model based on a Reynolds-stress decay estimate obtained by superposing convective thermals on the oscillating flow associated with the long wave.

A theory is developed for the dependence of the Nusselt number on the Rayleigh number in turbulent thermal convection in horizontal fluid layers. The theory is based on a number of assumptions regarding the behaviour in the molecular boundary layers and on the assumption of a buoyancy-defect law in the interior analogous to the velocity-defect law in flow in pipes and channels. The theory involves an unknown constant exponent s and two unknown functions of the Prandtl number. For either s = ½ or s = 1/3, corresponding to two different theories of thermal convection, and for a given Prandtl number, constants can be chosen to give excellent agreement with existing data over nearly the whole explored range of Rayleigh numbers in the turbulent case. Unfortunately, comparisons with experiment do not permit a definite choice of s, but consistency with the chosen form of the buoyancy-defect law seems to suggest s = 1/3, corresponding to similarity theory.

Experiments have been performed in a low-speed wind tunnel to determine the detention time of airborne smoke particles that become trapped in the wake vortex (or bubble) region behind flat disks placed perpendicular to the flow. Using a laser transmissometer to detect the smoke, its detention time was obtained from the time-dependent decay of the smoke in the disk bubble during the time immediately following the removal of the source of smoke. The dimensionless group H, the product of the detention time and the mainstream air velocity divided by the disk diameter, is seen to be a constant equal to 7.44 ± 0.52 for Reynolds numbers in the range 2000–40000. This result is compatible with a simple fluid-mechanical model which describes the transport of fluid-borne scalar entities across the bubble boundary by turbulent diffusion. The investigation suggests that H should be unique for the flow about a disk over a wide range of conditions, and further suggests the possibility that similar unique values for H can exist for flow about other obstacles. The number H has potential applications in a number of physical and engineering research areas.

Results of hot-wire measurements in a plane incompressible jet are reported. The flow was found to be self-preserving beyond x/d > 40 and measurements were made up to x/d = 120. The quantities measured include mean velocities, turbulence intensities and third- and fourth-order terms, as well as two-point correlations and the intermittency factor. Conditional sampling techniques were used to obtain exclusively data within the turbulent zone of the jet. The results are compared with previous investigations.

This is the third paper in a sequence providing data on turbulent free shear flows.

A numerical study is made of the temporal eigenvalue spectrum of the Orr-Sommerfeld equation for the Blasius boundary layer. Unlike channel flows, there is no mathematical proof that this flow has an infinite spectrum of discrete eigenvalues. The Orr-Sommerfeld equation is integrated numerically, and the eigenvalues located by tracing out the contour lines in the complex wave velocity (c = cr + ici) plane on which the real and imaginary parts of the secular determinant are zero. This method gives only a finite and small number of discrete eigenvalues for a wide range of Reynolds numbers and wavenumbers. The spectrum of plane Poiseuille flow is used as a guide to study the spectrum of an artificial two wall flow which consists of two Blasius boundary layers. As the upper boundary of this flow moves to infinity, it is found that the portion of the spectrum with an infinite number of eigenvalues moves towards cr = 1 and the spacing between eigenvalues goes to zero. It is concluded, on the basis of this result and the contour method, that the original few eigenvalues found are the only discrete eigenvalues that exist for Blasius flow over a wide portion of the c plane for cr < 1 and cr > 1. It is suggested that the discrete spectrum is supplemented by a continuous spectrum which lies along the cr = 1 axis for ci < −α/R.

Flow control by a wide, deep weir in a rotating fluid is investigated theoretically and experimentally. A strong (vertical) vorticity constraint due to frame rotation is combined with conservation of the Bernoulli function along streamlines and a standard hydraulic control assumption to show that the volume flux over the barrier is \[ Q = g^{-1}\left[\frac{2}{3}g(H - b_0)-\frac{1}{3}f^2l^2 \right]^{\frac{3}{2}}, \] where H is the depth of the fluid column upstream, bo is the crest height, f is the Coriolis parameter, and l is a length-scale measure of the breadth of the weir. The component of the velocity parallel to the weir crest is computed from conservation of potential vorticity to be v = −fl; perpendicular to the crest, we recover the standard hydraulic relation u = (gh0)½.

Experimental investigations of upstream height and streamline deflexion as functions of rotation are described. It is found that agreement with theory is good up to a certain rate of rotation, above which the finite width of the experimental weir becomes important.

Slow, steady, mechanically driven, axisymmetric motion of a stably stratified, electrically conducting, rotating fluid is studied. Attention is focused upon the parameter values for which hydromagnetic effects first become important in a rotating stratified fluid and upon the nature of their influence on the interior flow of that fluid. It is found that hydromagnetic effects are able to alter the flow of a stratified rotating fluid at much weaker magnetic field strengths than the flow of an unstratified fluid. Specifically, the interior azimuthal flow is altered if E/α2 [Lt ] σS [Lt ] 1 or if E [Lt ] α2 and 1 [Lt ] σS, where E = ν/ΩL2, $E = \nu/\Omega L^2,\quad\alpha^2 = \overline{\sigma}B^2/\rho\Omega $ and $S = \overline{\alpha}\Delta Tg\nu/\Omega^2\kappa L$. The hydromagnetic effects act to decrease the vertical shear in the azimuthal flow from the levels which would occur in the absence of magnetic fields.

The method of Vickery for calculating the drag of plane lattice structures normal to a turbulent stream is extended to cases of increased solidity. The analysis incorporates an extended version of Taylor's theory for the flow through a porous plate, and a simplified version of Hunt's analysis of the distortion of a turbulent flow by the mean flow field of a body. Some comparisons are made with experimental data.