Correlation equation for the marine drag coefficient and wave steepness

This work questions, starting from dimensional considerations, the generality of the belief that the marine drag coefficient levels off with increasing wind speed. Dimensional analysis shows that the drag coefficient scales with the wave steepness as opposed to a wave-age scaling. A correlation equation is employed here that uses wave steepness scaling at low aspect ratios (inverse wave steepnesses) and a constant drag coefficient at high aspect ratios. Invoked in support of the correlation are measurements sourced from the literature and at the FINO1 platform in the North Sea. The correlation equation is then applied to measurements recorded from buoys during the passage of hurricanes Rita, Katrina (2005) and Ike (2008). Results show that the correlation equation anticipates the expected levelling off in deeper water, but a drag coefficient more consistent with a Charnock type relation is also possible in more shallower water. Some suggestions are made for proceeding with a higher-order analysis than that conducted here.