A maximum entropy distribution for wave heights of non-linear sea waves

摘要

Based on the maximum entropy principle, a probability density function (PDF) for the zero-crossing wave height (H)of random waves is derived as the simple form fn (H) = αHγe-βHn ( n is a selectable positive integer) through solving a variational problem subject to some quite general constraints. This PDF maximizes the information entropy of H, and its parameters α, γ and β are expressed ear sea waves with large uncertainty, and its parameters can be simply determined from available data. Comparisons between the PDF with n = 3 and n = 4 and the observed distributions of H from wave records measured in the East China Sea and in a wind-wave tunnel show fairly satisfying agreements.