Resonant motions of a combined wind and wave concept (STC) in waves may induce significant loads in the structural components (such as wind turbine blades, nacelle or the interface between the spar and the torus). One type of resonant motions is related to the so-called Mathieu instability. For the STC under the survival mode where the torus is locked to the spar at the mean water level (MWL mode), the large heave motion in severe waves induces a significant change in the buoyancy center and therefore leads to a periodic change in the restoring term for the pitch motion. When the wave period reaches the half of the natural period, the Mathieu instability (a dynamic instability in pitch for this case) occurs and leads to significant pitch motions.

The purpose of this study is to numerically predict such unstable motions for regular and irregular wave conditions and to compare the results with the experimental observations. First, a literature study on Mathieu instability is carried out to understand the mechanism behind this phenomenon. Then the results of the STC concept from the experiments carried out by Dr. Ling Wan are investigated in order to study the developments of the Mathieu unstable pitch motions and the corresponding wave conditions in which they occur. Finally, a numerical model of Mathieu instability for analysis of the STC pitch motions is established to get insight into the phenomenon.

The numerical model is compared with the experimental results of Dr. Ling Wan. A sensitivity study using the numerical model is then carried out to investigate the conditions where the Mathieu instability may occur.