The mean and fluctuating velocities in a turbulent boundary layer on a cylinder have been experimentally characterized for the case where the boundary layer is thick compared to the radius of transverse curvature. The mean velocity measurements suggest a mixed scaling for the ‘‘log law of the wall’’ using the wall coordinate yUτ/ν and the ratio of the local boundary layer thickness to the radius of the cylinder δ/a. A relation for the slope and intercept of the log law of the wall as functions of δ/a based on empirical results and simple analysis is presented. Measurements of the Reynolds stress for δ/a of order 10 show that the Reynolds stress drops off much more quickly with distance from the wall than for a turbulent boundary layer on a flat plate. Both the Reynolds stress data and the turbulent intensity in the mean flow direction data are functions of the inverse radial distance from the center of the cylinder.
Thirty years of theoretical and experimental research have yet to resolve a number of questions regarding the vibratory response of, and acoustic radiation from, a structure excited by a turbulent boundary layer (TBL). The most important questions are: (a) Can the TBL be characterized as a Thevenin source—particularly when vibratory power flow into the structure is maximized at hydrodynamic coincidence? Alternatively, at what level does structural vibration fundamentally change the character of the TBL? (b) Is the low wave number portion of the wall pressure spectrum of dominant importance in structural excitation away from hydrodynamic coincidence? Or do structural discontinuities cause the convective ridge of wall pressure to be of greater practical interest? (c) Can one quantify the radiation from a turbulent boundary layer about a rigid finite body? Is it dipole or quadrupole? What is the role of fluctuating wall shear stress? Current research on dense fluid loading and on modeling the behavior of the TBL is yielding new, and sometimes surprising, answers to some of these questions. Free resonant structural vibration in the dense fluid limit and the use of a bounded, non-causal, Green function representing the TBL are two of the surprises discussed.
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