ALBERT

Beschreibung: The theoretical study presented in this paper was inspired by the recent report (Krämer 1960) of experiments showing that considerable reductions in the drag of an underwater solid body were achieved by covering it with a skin of flexible material; apparently this effect was due to the boundary layer being stabilized in the presence of the skin, so that transition to a turbulent condition of flow was prevented or at least delayed. The stability problem for flow past a flexible boundary is here formulated in a general way which allows a full exploration of the possibility of a stabilizing effect without the need to assign specific properties to the flexible medium; the collective properties of possible boundaries are represented by a ‘response coefficient’ α (a sort of ‘effective compliance’) measuring the deflexion of the surface under a travelling sinusoidal distribution of pressure.A remarkably simple analytical connexion is established between the present general problem and the corresponding stability problem for the boundary layer on a rigid plane wall, and hence many details of the existing theory of hydrodynamic stability are immediately useful. However, the presence of the flexible boundary admits possible modes of instability additional to those which already exist when the boundary is rigid, and clearly every mode must be considered with regard to practical measures for stabilization—that is to say, it might be useless to inhibit one mode by a device which lets in another. What is believed to be an essentially complete interpretation of the over-all possibilities is deduced on recognizing three more or less distinct forms of instability. The first comprises waves resembling the unstable waves which can arise in the presence of a rigid boundary, but now being modified by the effects of flexibility. These waves tend to be stabilized when the boundary has a compliant response to them, which means the respective wave velocity has to be less than the velocity of free surface waves on the boundary; but it is found that the effect of internal friction in the flexible medium is actually destabilizing. The second form of instability is essentially a resonance effect and comprises waves travelling at very nearly the velocity of free surface waves. These waves can only be excited when the latter velocity falls below the free-stream velocity; they are scarcely affected by the viscosity of the fluid since the ‘wall friction layer’ is largely cancelled, so that damping due to the medium itself becomes the only stabilizing factor. The third form is akin to Kelvin–Helmholtz instability.This interpretation of the theoretical results seems to point to the essential factors in the operation of a flexible skin as a stabilizing device, and accordingly in the concluding secttion of the paper two alternative sets of criteria are proposed each of which would provide a logical basis for designing such a device. The principle of the first alternative explains the success of Gamer's invention, but the second appears equally promising and the relative advantages of the two can really be proved only by further experiment.

Beschreibung: It is shown that for the steady isoenergetic rotational flow of an ideal gas, both the specific enthalpy and the speed of sound can be expressed as functions of the velocity. As a result, it is possible to formulate the equations of motion so that the velocity is the only dependent variable. For a gas whose enthalpy and sound speed are functionally related, the results are a generalization of those for a perfect gas. If the enthalpy and sound speed are independent variables, the new formulation leads to a single vector equation whose solution completely determines the flow.

Beschreibung: The purpose of this note is to describe a particular class of steady fluid flows, for which the techniques of classical hydrodynamics and boundary-layer theory determine uniquely the asymptotic flow for large Reynolds number for each of a continuously varied set of boundary conditions. The flows involve viscous layers in the interior of the flow domain, as well as boundary layers, and the investigation is unusual in that the position and structure of all the viscous layers are determined uniquely. The note is intended to be an illustration of the principles that lead to this determination, not a source of information of practical value.The flows take place in a two-dimensional channel with porous walls through which fluid is uniformly injected or extracted. When fluid is extracted through both walls there are boundary layers on both walls and the flow outside these layers is irrotational. When fluid is extracted through one wall and injected through the other, there is a boundary layer only on the former wall and the inviscid rotational flow outside this layer satisfies the no-slip condition on the other wall. When fluid is injected through both walls there are no boundary layers, but there is a viscous layer in the interior of the channel, across which the second derivative of the tangential velocity is discontinous, and the position of this layer is determined by the requirement that the inviscid rotational flows on either side of it must satisfy the no-slip conditions on the walls.

Beschreibung: An experiment has been performed to determine the cavity pressure and cavity length for the flow under a curved two-dimensional turbulent jet discharging parallel to a flat plate at some distance from the surface. The measurements agree quite closely with the predictions of a simple analysis of the flow when a value is assigned to the spread parameter for the curved jet which is somewhat different from that for the plane jet.Detailed pressure and velocity measurements show that the rate of growth of the curved jet is in fact closely similar to that of the plane jet. This suggests that the adjustment of the spread parameter should be regarded simply as a convenient device for taking into account the quantitative errors of the assumptions made in the analysis.

Beschreibung: Some results of an experimental investigation of forces associated with the subsonic flow of air around a circular cylinder in a wind tunnel are presented. The oscillating forces due to the downstream vortex street are studied for Reynolds numbers in the ‘critical’ range 4 × 104 to 6 × 105. Of particular interest is the observation, at the onset of transition to turbulence, of a spanwise wave or cell pattern near the cylinder surface, which is stabilized in a striking manner by the use of the fine threads as a visualization technique.

Beschreibung: The Rayleigh instability of an incompressible, infinitely conducting, inviscid fluid of variable density is investigated under the influence of an horizontal magnetic field and coriolis forces. After establishing the equations of the problem when both the density and the magnetic field vary with distance in the upward direction, two special cases of density distribution are studied in detail. Both the magnetic field and coriolis forces are found to have a stabilizing influence on the configuration and further it is concluded that they may bring about stability in the configuration when it is thoroughly unstable without them.

Beschreibung: Earlier work on the dynamics of a perfectly conductive gas in situations where all variables depend on one space co-ordinate only is extended to the case where the magnetic field has a component in the direction of variation. The theory is developed for an arbitrary gas in equilibrium, subject only to certain reasonable restrictions.The first main section studies the variation of the transverse field component in slow and fast simple waves and the tendency of compressive waves in which the transverse field does not change sign to steepen into shocks.The next section develops a symmetrical treatment of the Rayleigh, Fanno and other processes of ordinary steady one-dimensional gasdynamics, generalized to allow for electromagnetic effects. The slow, fast and Alfvén wave speeds are critical. A particular case of this analysis is a generalization of ordinary gasdynamics which allows for the effect of transverse forces such as occur in turbo-machinery.The final section is an exhaustive study of shocks in the presence of a field component normal to the shock front. From the generalized Rayleigh line it is established that there are up to six different types of shocks, all compressive and distinguishable by the relative magnitudes of the upstream and downstream normal velocities in comparison with the local slow, fast and Alfvén wave speeds.Some aspects of shock structure are discussed briefly.