The Reduction of Skin Friction Drag 



most there are difficulties. Many of these difficulties are related to kinds of in- 

 stability other than those considered in the analysis which suggested the experi- 

 ment. For instance, with a gas film one has an interfacial instability of the 

 Kelvin- Helmholtz (Lamb (1945)) type. With a heated wall one has a gravitational 

 instability due to the density differences, which can be shown to be analogous to 

 the instability on a wall concave in the streamwise direction (Goertler (1959), 

 Kirchgaessner (1962)). The boundary layer over a flexible surface is subject to 

 two types of instability not present in the boimdary layer over a rigid surface 

 (Benjamin (1963)). Furthermore, the difficulties mentioned earlier relative to 

 freedom from disturbances, both at the surface and in the free stream, are not 

 easily overcome. It should be remembered that natural transition due to the 

 growth of small disturbances seldom occurs earlier than a length Reynolds 

 number of 10^. Simply by removing all the disturbances this figure can be in- 

 creased by a factor of about twenty-five, but a limit is reached in this direction. 

 It has been suggested by Betchov (1960) that this limit is due to amplified mole- 

 cular agitation. To achieve a substantial reduction in drag, the length Reynolds 

 number must be increased at least an order of magnitude beyond this. Further- 

 more, at these high Reynolds numbers the laminar boundary layer is very thin. 

 The requirements on smoothness and in general the tolerances on construction 

 of the surface are proportional to the inverse of the "Reynolds number per foot," 

 and are extremely stringent. If all other disturbances are removed, the velocity 

 field associated with a sound field can disturb the boundary layer, particularly 

 in a gas-liquid combination. This velocity field in a liquid is ordinarily much 

 smaller for a given sound pressure level than in a gas (by the ratio of the values 

 of the product of density and speed of sound), but if there is a gas-liquid inter- 

 face this does not appear to be true. Considered from all points of view it seems 

 desirable to examine the possibility of altering a turbulent boundary layer so as 

 to reduce the drag. If this can be done then all the difficulties mentioned above 

 are eliminated. 



NONCONVENTIONAL TECHNIQUES 



General Considerations 



Several approaches have been suggested by means of which the turbulent 

 boundary layer may be altered. In order to understand how these may work, it 

 is necessary to recall to mind the physical principles which govern the normal 

 turbulent boundary layer. For simplicity, let us consider the boundary layer 

 with zero pressure gradient. These principles are (cf, Townsend (1956)): 



1. Reynolds number similarity: that the turbulence, once fully established, 

 is predominantly inertial in the energy containing range (that part of the spec- 

 trum responsible for drag and heat transfer); i.e. ,— that the structure of these 

 eddies is essentially independent of viscosity. 



2. The "Law of the Wall"— that there is a layer of turbulent fluid near the 

 wall that has no characteristic length scale other than distance to the wall, and 

 that this layer has a single characteristic velocity, and therefore a universal 

 structure. By the first principle, this layer is independent of viscosity, so that 

 the Reynolds stress is constant. Defining the characteristic velocity /^* as the 



921 



