Abrupt depth transitions (ADTs) have recently been identified as potential causes of `rogue’ ocean waves. When stationary and (close-to) normally distributed waves travel into shallower water over an ADT, distinct spatially localized peaks in the probability of extreme waves occur. These peaks have been predicted numerically, observed experimentally, but not explained theoretically. Providing this theoretical explanation using a leading-order-physics-based statistical model, we show the peaks arise from the interaction between linear free and second-order bound waves, also present in the absence of the ADT, and new second-order free waves generated due to the ADT.

Short Bio: Ton van den Bremer is a Senior Research Fellow and Royal Academy of Engineering Research Fellow at the University of Oxford. He is also the Edward and Catherine Wray Tutor and Fellow in Engineering  at Worcester College. He holds an MEng in Civil Engineering from Imperial College London (2009) and MPhil in Economics (2011) as well as a DPhil in Engineering Science (2015) from the University of Oxford. From 2015-2017, he was a Chancellor’s Fellow in Geophysical Fluid Mechanics at the University of Edinburgh, and he presently also holds a Visiting Professorship at the University of Edinburgh. Ton’s research interests are in geophysical fluid mechanics, understanding the role of nonlinearity in oceanic and atmospheric gravity waves. For his Royal Academy of Engineering Research Fellowship, he is examining the role of waves in the transport and spreading of plastic pollution in the ocean. Ton is also interested in stochastic processes, applied to the economics of natural resources and climate.