This paper considers three separate test programs in which modelling of the Morison force coefficients, CM and Co, has been conducted on vertical surface-piercing cylinders from laboratory measurements. Conditions under test included the so-called "troublesome" range of Keulegan-Carpenter number, viz 5 to 15, and the use of a variety of wave inputs: a range of uni-directional Pierson Moskowitz wave spectra; two levels of directional spread for multidirectional wave testing again using Pierson Moskowitz wave spectra and the use of Swept Sine Waves ("regular" waves with a slowly varying frequency that ranges over a predetermined band). An additional feature for two of these test programs was the use of force measurements obtained from instrumented discrete segments of cylinder from which "local" values of force coefficients could be obtained (as opposed to values for the cylinder "as-a-whole"). Frequency-dependent formulations for CM and CD (viz CM(f) and CD(f) as well as the traditional "constant-valued" models were fitted to the measurements using a spectral description, the former being based upon either a linearised or fully non-linear systems analysis approach. Results obtained were found to lend support to the assumption that is often made that these force coefficients can be taken as constant-valued when applying the Morison equation and that a linearisation of the drag force term is often acceptable for rigid vertical cylinders.
In the case of a unit length of vertical cylinder of diameter D this equation can be expressed as: (equation shown in paper) represent the so-called constant-valued forms of the inertia and drag force coefficients respectively and u(z, t) represents the alongwave water particle velocity at position z here assumed to be the central location of the unit length segment of cylinder under consideration.