The transverse vibratory response of a long, slender vertical top-tension riser, subject to an ocean current, is studied. The problem is treated as a coupled fluid-flow/vibration problem which is solved numerically. The fluid flow part is represented by the 2-D Navier-Stokes equations, with LES and strip theory, which are solved numerically to obtain the flow field and determine the vortex-shedding behavior in the flow. The approach flow is a shear flow ranging in Reynolds number from 8000 to 10,000. Given the flow field and vortex-shedding behavior, the transverse fluid forcing function can be determined at a given instant, which becomes the input to the Euler-Bernoulli beam equation to calculate the displacement of the riser, using a technique that involves the WKB method and modal decomposition. The boundary conditions for the fluid-flow equations are updated each time step as the cylinder moves. The natural frequency of the riser is tension-dominated, not bending stiffness-dominated. With the decrease in tension with increasing depth, the natural frequency is affected. Therefore, the solution will be influenced by the depth-dependent tension. This study has indicated some interesting features regarding the VIV of a variable-tension riser. The vibrational response is greater for a variable-tension riser than for a constant-tension riser, when the variable-tension riser is assumed to have the same top tension as the constant-tension riser. Therefore, it is important to take into account the variable tension when estimating fatigue failures of marine risers.

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