Group seminar on 15. November, 14:15 CET

Random Moving Surfaces: A Summary of Longuet-Higgins (1957)

Dr. Richard Blender

In this summary talk, the study of Longuet-Higgins (1957) on random moving surfaces and their statistical properties is presented. The aim of this publication was to help to interpret observations of ocean surface waves in terms of involved surface height waves. The applied geometric model is a superposition of continuous horizontal waves with multivariate Gaussian amplitudes and uniform random phases. In the talk, the mathematical basics and some specific statistical properties are presented. The energy spectrum and its moments are defined, which are often the single accessible observables. Geometric characteristics of the wave field are described, for example wave groups, short and long crested waves, zero-crossings and specular points, which are defined as points of reflection and determined by the height gradient. The talk outlines the calculations which are necessary to determine statistical properties with an emphasis on the specific energy moments. The talk ends with a brief outlook on extremes.

Reference:

Longuet-Higgins, M. S. (1957). The statistical analysis of a random, moving surface. Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 249(966), 321-387.