Extreme Directional and Planar Profiles for Kuroshio Current Using Inverse FORM and Proper Orthogonal Decomposition

Kuroshio is a major global current that flows near the east coasts of Taiwan and Japan. Kuroshio is a relatively strong current with typical speeds of 3 to 5 knots at the water surface. It is important to properly understand extreme current profiles of these currents for any drilling activity since the response of deepwater risers is known to be sensitive to the shape of the current profile. This paper presents the derivation of extreme two-dimensional (i.e., directional) and planar profiles for Kuroshio currents at a site in Nankai Trough, Japan; water depth is almost 2000 m. About 6000 currents profiles measured over six months in 2010 by JAMSTEC are used. The inverse first-order reliability method (inverse FORM) and proper orthogonal decomposition (POD) technique are employed. While such methodology is well established, its use for this site posed several challenges. Firstly, the first two modes contribute only about 90% of the energy. Therefore, as many as seven modes were included for accuracy. Since an exact solution requiring joint probability distribution for seven variables becomes quite cumbersome, reasonable simplifications were made for efficient calculations. Second, to preserve the directionality in extreme currents, the inverse FORM problem for the two orthogonal components of the current velocity was simultaneously solved, so that extreme profiles for the two planar directions are obtained. Doing so implies solving a four-dimensional inverse FORM problem, even if the full joint distribution of first two modal weights for each direction is used. This four-dimensional problem was reduced to two related two-dimensional problems, wherein the modal vectors in the orthogonal directions are assumed independent; this assumption was found to be valid for this data set. A set containing a limited number of extreme N-year current profiles is derived using the above methodology. It is found that most of the shapes observed in the measured Kuroshio current data are represented in this set of extreme current profiles. The largest riser response obtained from all these current profiles would be the N-year response. A single extreme N-year profile is often sought in analysis, which is also derived from the set of N-year profiles by selecting the profile which maximizes an assumed response function. In summary, this paper presents extreme currents for a site on which little literature exists, and introduces a methodology to derive extreme directional current profiles from measured data.