In-line force from combined wave and current flow on oscillating cylinders

The flow pattern and force coefficients For oscillating cylinders are different from those for fixed structures, Experiments have been carried out to study wave-current-structure interactions by oscillating a vertical cylinder in the cross-now and inline direction with a steady flow and/or waves regular and irregular. An important goal of the work has been to develop a generalized approach for estimating the hydrodynamic interaction of slender cylinders in a wide variety of flow conditions and to determine the necessary force coefficients for such complicated flow conditions. The present paper deals with results of cylinder oscillations parallel to waves and current and concentrates on the in-line force components. Evidence has been produced suggesting that both the relative velocity extension of the Morison equation and a linear version of this model are suitable models to estimate the in-line hydrodynamic forces in the flow condition considered. It has been found that the linear form of the "generalized" Morison equation based on the relative velocity approach gives the same or even better quality of fit as the quadratic form, if the associated value of the linearized drag coefficient is used. Extensive analysis of the force coefficients of the relative velocity model has been carried out to seek a good correlation between the drag and inertia coefficients (C-Dr and C-Mr) on the one hand and the relevant nondimensional parameters on the other. The results of this investigation have revealed no single parameter with which the drag and inertia coefficients may be correlated without the need for other parameters. However, the force coefficients correlate better with some parameters than with others. The ratio between total oscillatory velocity (u(m) + (x) over dot (m)) and the steady velocity (V) is a significant parameter for the combined flow field of an oscillating cylinder in waves and current.