14, 
256 Lecture 14 
The fundamental work on flow noise was performed by Lighthill as early 
as 1951 in connection with the noise produced by jets. The Ordnance Research 
Laboratory became interested in flow noise in 1954. During an experimental 
test run of a vehicle, the main motor was shut off and the recording continued. 
Analysis of the recording indicated that the dead-interval noise—the flow noise— 
was appreciable. This incident gave rise to a continuous study of flow noise at 
this laboratory. Three aspects of flow noise were studied: 
1. The flow noise generated by a turbulent boundary layer (nearfield and 
radiation field) 
2. The flow noise produced by the surface roughnesses of the vehicle 
3. The flow noise produced by cavity resonance and by wall vibrations 
2. THE NEARFIELD FLOW NOISE GENERATED BY A TURBULENT BOUNDARY LAYER 
Probably the most interesting of the three components of flow noise is that 
produced by the turbulence in the boundary layer. The velocity fluctuations 
caused by the turbulent eddies increase the transportation of momentum and 
generate the surface drag. The surface drag can be computed with the aid of the 
Stokes—Navier equations [1, 2]; it is found to be 
r= p<u'v' >= pv*? (1) 
where u’ and vy’ are the components of the fluctuating velocity in the direction of 
the main flow and transverse to it. The magnitude v*=,/ <u'v’>is defined as the 
root-mean-square average of the velocity components and is the shear velocity. 
This velocity v* determines the shear force near the wall or surface drag. 
The surface drag has been thoroughly studied for channels [2], plates [1], 
and even for rotating cylinders [3]. The experimental results show that the sur- 
face drag is approximately proportional to the square of the free-stream ve- 
locity uo. The surface drag can, therefore, be expressed as the product of the 
coefficient of drag cg and the square of the free-stream velocity: 
r= 7egpus (2) 
where p denotes the density of the fluid. The coefficient of drag proves to be 
practically constant; it is approximately equal to 3-107? whenever the flow is 
turbulent. It changes by only a factor of three when the velocity is changed by 
a factor of as much as 5,000. Since the surface drag is generated in the inner 
part of the boundary layer, we might expect that it would not directly depend 
on the curvature of the surface nor onthe size of the body that generated it. 
This conclusion is verified by measurements with rotating cylinders [3]. No 
dependence on the ratio of diameter to height was found. 
The fluctuating velocity v* can be estimated by equating the theoretical and 
the experimental results: 3 
dca pus = 3.1073. pu = pv*? (3) 
or 
v* = 0.04 uo (4) 
