Rare Events Prediction: Rogue Waves and Drags

Abstract

Rogue waves are rare events with unusually large wave amplitudes. In this thesis the multicanonical procedure is applied to the one-dimensional nonlinear Schrödinger equation in conjunction with a high order finite difference solution procedure to determine the probability distribution function of rogue wave power and heights. The analysis demonstrates a logarithmic dependence of the slope of the probability distribution function on the nonlinearity coefficient at large heights. The results of the multicanonical procedure helps explain the mechanism of rogue waves and confirms that the nonlinearity generates rogue waves. Small deformation of an obstacle in fluid flows can in extreme cases result in anomalous drag coefficients. A multicanonical procedure is applied to the two-dimensional Navier-Stokes equation in conjunction with the lattice Boltzmann method to determine the probability distribution functions of the drags generated by a two-dimensional square/rectangular obstacle in quasi-random input flow patterns and for random surface roughness. The results demonstrate that the multicanonical method can estimate the probability distribution function in low-probability regions with far less computational effort than standard techniques.