The relative-velocity version of the Morison equation for obstacle arrays in combined steady, low and high frequency motion

This paper revisits the problem of forces on obstacle arrays in combined waves, an in-line steady current and structural dynamic motions. The intended application is the design and re-assessment of dynamically responding offshore platforms. Planar grids of perforated plates are moved in forced motion on three scales through otherwise stationary water. A new analytical wave-current-structure blockage model is developed by building on the existing wave-current blockage model presented by Santo et al. (J. Fluid Mech., vol. 739, 2014b, pp. 143-178) using a similar set of experiments but with forced motion on two scales. The new model, which is an improved Morison relative-velocity formulation, is tested against the experimental data for a range of structural to wave oscillation frequency ratios, f_s=f_w =2, 2.5 and 3. For relatively small current speed (u_c) and oscillatory structural velocity (u_s) compared with the oscillatory wave velocity (u_w), the drag force time history on grids is well approximated by a summation of the wave drag and the current drag components independently, without a u_w × u_c cross-term, consistent with the previous model. The wave drag component contains an additional u_s contribution, while the current drag component may or may not contain an additional us contribution depending on f_s/f_w. The measured drag force is observed to be asymmetric in time due to biasing from the mean flow. This is supported by numerical simulation using a porous block as a numerical model of the grids, although the simulated force asymmetry is weaker. All these effects can be sufficiently accounted for in the analytical model. The new model is shown to fit the variation of the experimental forces and force harmonics in time well for a wide range of cases, requiring only calibration of the Morison type drag and inertia coefficients. In contrast, the industry-standard version of the Morison relative-velocity formulation cannot reproduce the variation of the measured force in time, so present practice should be regarded as inadequate for combined steady, low frequency and high frequency motion acting on obstacle arrays.