Hydraulic Structures: Fourth Edition

14.12.3 Cross-flow oscillations

It is shown in Fig. 14.22 that the peak response of the cylinder in the cross-

flow direction occurs at values of V/fnDgreater than those for in-line oscil-

lations. The onset of cross-flow oscillations is expressed in terms of the

critical value of V/fnDas a function of the Reynolds number of the flow

(Fig. 14.24). No cross-flow oscillations have been observed for Ks10.

The damping associated with marine structures is the sum of the

structural damping and fluid dynamic drag. Both of these are difficult to

evaluate. Structural damping, which is expressed in terms of the logarith-

mic decrement (^) s, is usually estimated from full-scale tests. Typically
values of (^) s, as given in Hallam, Heaf and Wootton (1978) are as follows:
for structural steel, (^) s0.02;
for concrete, (^) s0.05 (uncracked) or (^) s0.16 0.36 (cracked);
for wood, (^) s0.05 0.2;
for marine steel structures, (^) s0.08 0.20;
for marine concrete structures, (^) s0.06.
The other source of damping is the drag force arising from the oscillatory
motion in the fluid. Equation (14.61) gives the drag force FDas
FD CD |u|uD CD |x ̇|x ̇D.

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2

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2

616 WAVES AND OFFSHORE ENGINEERING

Fig. 14.24 Criterion for onset of instability with respect to cross-flow oscil-

lations (Hallam, Heaf and Wootton, 1978)