finding would tend to confirm Sarpkaya's measurements of amplified hydrodynamic forces due to sur- 

 face roughness in addition to the force amplification due to lock-on. A comprehensive study of the 

 effects of surface roughness on the steady drag forces on stationary cylinders was made by Miller (36) 

 for the case of a stationary cylinder, and another recent report by Hove, et al. also considers this prob- 

 lem in some detail (37). 



2. 7 Shear (Nonuniform Flow) Effects. The effects of velocity gradients (shear) are difficult to quan- 

 tify on the basis of available evidence, especially for structures and cables which are vibrating. How- 

 ever, the sparse information that is available suggests that a full-scale cylindrical structure or cable will 

 vibrate at large displacement amplitudes even in the presence of nonuniform flow effects if the reduced 

 damping is sufficiently small and the critical reduced velocity is exceeded. Detailed experiments 

 reported by Howell and Novak (20) and by Kwok and Melbourne (38) give strong evidence that a flexi- 

 ble bluff structure with a circular cross-section will vibrate resonantly at large displacement amplitudes 

 when a turbulent boundary layer type of shear flow is incident upon the cylinder. Kwok and Melbourne 

 measured maximum tip displacements comparable to those in Fig. 2.2 for reduced dampings in the 

 range Ar^ = 2 to 12 {iJ^l ~ 0.5 to 3). 



Stansby (39) investigated the phenomenon of lock-on for the cross flow vibrations of circular 

 cylinders in a linear shear flow and has compared the results to similar experiments in uniform flow. 

 From these experiments Stansby developed empirical equations to predict the bounds for lock-on in a 

 shear flow, based upon the assumption of universal similarity in the wakes of bluff bodies (25,26). 

 However, these results are limited to cylinders with small length/diameter ratios (L/D = 8 to 16), rela- 

 tively low Reynolds number (Re = 3000 to 10,000) and small displacement amplitudes ( YiD < 0.2). 



A recent paper and a report by Fischer, Jones and King (16,40) describes some problems that 

 were anticipated during the installation of foundation piles for the Shell Oil production platform in the 

 Cognac field of the Gulf of Mexico. The problems stemmed largely from the anticipated vortex-excited 

 oscillations of the piles during two operations: while they were being lowered from a derrick barge into 



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