Lagrangian measurement of steep directionally spread ocean waves

Abstract

The notion that wave-following buoys provide less accurate measurements of extreme waves than their Eulerian counterparts is a perception commonly held by oceanographers and engineers (Forristall 2000, J. Phys. Oceanogr., 30, 1931-1943). By performing a direct comparison between the two types of measurement under laboratory conditions, we examine one of the hypotheses underlying this perception and establish whether wave measurement buoys in extreme ocean waves correctly follow steep crests and behave in a purely Lagrangian manner. We present a direct comparison between Eulerian gauge and Lagrangian buoy measurements of steep directionally spread and crossing wave groups on deep water. Our experimental measurements are compared to exact (Herbers and Janssen 2016, J. Phys. Oceanogr., 46, 1009-1021) and new approximate expression for Lagrangian second-order theory derived herein. We derive simple closed-form expressions for the second-order contribution to crest height representative of extreme ocean waves, namely for a single narrowly spread wave group, two narrowly spread crossing wave groups, and a strongly spread single wave group. In the limit of large spreading or head-on crossing, Eulerian and Lagrangian measurements become equivalent. For the range of conditions we test, we find that our buoy behaves in a Lagrangian manner, and our experimental observations compare extremely well with predictions made using second-order theory. Generally, Eulerian and Lagrangian measurements of crest height are not significantly different for all degrees of directional spreading and crossing. However, second-order bound-wave energy is redistributed from super-harmonics in Eulerian measurements to sub-harmonics in Lagrangian measurement, which affects the ‘apparent’ steepness inferred from time histories and poses a potential issue for wave buoys that measure acceleration.