In addition to the enormous aerodynamical literature concerned with the disturbances to a uniform stream produced by the presence of obstacles, there is a very extensive litrature on disturbances to irrotational non-uniform streams. The smaller body of work on disturbances to rotational streams is concerned principally with two-dimensional disturbances to a parallel shear flow; these are fairly easy to treat because the vortex lines are straight; they remain parallel and do not get stretched at all during the motion.

A flat strip, of infinitesimal thickness and infinite lenght, is located in a viscous incompressible fluid, and both the strip and fluid are at rest initially. The strip is abruptly set into steady motion parallel to its length. An unsteady uni-directional flow of the fluid results, and there is a variable skin friction on the strip which must be overcome to maintain its velocity. In the early stages of motion, the skin friction is large, with a local behaviour which resembles that for a flat strip of infinite width. The skin friction near each edge of the strip can be more accurately represented by referring to the semi-infinite configuration that is realized on displacement of the other edge to infinity. At this stage, the results depend on separate consideration of the two limiting configurations, and the way to further improvements is not clearly delineated. The object of this paper is to provide a formulation which contains the preceding information and allows a systematic evaluation of all additional refinements. Thus, it is shown that the total skin friction on a strip of width 2a, moving with velocity V in a fluid whose coefficients of viscosity and kinematic viscosity are μ, ν, takes the form $D = 2\pi V \left[\frac {2a}{\surd (\pi vt)} + 1 - \frac {2}{\pi}\int ^\infty _1 \frac{1}{u^2} \surd \left(\frac {u-1}{u+1}\right) \rm {erfc} \left(\frac {au}{\surd (vt)} \right)du \right].$ Here the first two terms stem from the infinite and semi-infinite strip distributions, and the integral, containing a complementary error function, furnishes all corrections of the lowest exponential order, in the initial stages of motion, when $a| \surd (vt) \gg 1$ 1. The calculation is based on a new integral equation which makes explicit the effects of an isolated edge, and by iteration provides the interaction effects between edges at a finite separation.

The motion of a viscous fluid contained between two rotating, circular cylinders whose axes are set slightly apart is considered. The equations of viscous motion are linearized by expanding the stream function in the form $\sum\limits^\infty_{n=0}\psi _n \gamma^n$, where γ is a parameter which depends on the distance between the cylinder axes. The ensuing analysis appears to hold for all values of the fluid viscosity v, and in particular for small values of v.

The asymptotic behaviour of the solutions for small v is examined, attention being mainly confined to the first order stream function ψ1 and the corresponding component of vorticity ζ1. Outside the boundary layers, where, for small v, ψ1 may be expanded asymptotically as $\sum \limits ^\infty _{n=0} \psi^{(n)}_1 v^{n|2$, the terms ζ(n)1 of the corresponding expansions for the vorticity are shown to be uniform throughout the fluid. It is noted that the asymptotic expansions of ψ1 for the region of the boundary layers and for the region outside the boundary layers may be combined in a single expansion which holds in both regions. The leading terms of this expansion are calculated by boundary layer methods.

A solution is given for the sound waves generated when an infinite wedge passes at supersonic velocity through the plane interface between different media. The results are then applied to the particular case when the two media consist of the same perfect gas at different temperatures. It is observed that the flow can be deduced for any symmetrical aerofoil of infinite span by superposition, and the case of a double wedge is considered in detail.

A mechanism for the generation of surface waves by a parallel shear flow U(y) is developed on the basis of the inviscid Orr-Sommerfeld equation. It is found that the rate at which energy is transferred to a wave of speed c is proportional to the profile curvature -U"(y) at that elevation where U = c. The result is applied to the generation of deep-water gravity waves by wind. An approximate solution to the boundary value problem is developed for a logarithmic profile and the corresponding spectral distribution of the energy transfer coefficient calculated as a function of wave speed. The minimum wind speed for the initiation of gravity waves against laminar dissipation in water having negligible mean motion is found to be roughly 100cm/sec. A spectral mean value of the sheltering coefficient, as defined by Munk, is found to be in order-of-magnitude agreement with total wave drag measurements of Van Dorn. It is concluded that the model yields results in qualitative agreement with observation, but truly quantitative comparisons would require a more accurate solution of the boundary value problem and more precise data on wind profiles than are presently available. The results also may have application to the flutter of membranes and panels.

The turbulence produced by a multiplicity of small air jets has been investigated and comparisons are made with other turbulent flows. The eddy Reynolds number is large (Rλ = 250).

The energy spectrum was measured, as well as the skewness and kurtosis of ∂u/∂x. The effect of the finite length of the hot wire is considered and the corrected results indicate that the spectrum follows the law of Kolmogoroff in an intermediate range and appers to fall off with the (−6)-power of the frequency in the viscous range. This range is limited at the upper end of the frequency range by electrical noise. Special precautions reduced this noise to the level of thermal agitation in the hot wire.

The ultimate limit to spectral analysis is imposed by the molecular agitation of the gas. This limit is evaluated and compared with the spectrum of turbulence. It appears that the spectrum of ∂3u/∂x3 merges with the spectrum of molecular agitation without a distinctive separation.

In this work a method is given for finding the position of ring singularities in a three-dimensional potential field having axial symmetry, by consideration of the very much easier case of a similar two-dimensional potential function. It is seen that the traces of these ring singularities on a plane through the axis of symmetry occur at points corresponding to those of the singularities existing in the two-dimensional plane when the axial velocity potential functions are the same. It is thought that this might be of value in the plotting of stream surfaces.