Seminar 2025-03-12: Krzysztof Podgórski

Topic Velocities of moving random surfaces

Abstract For a stationary two-dimensional random field evolving in time, one can derive statistical distributions of appropriately defined velocities utilizing a generalization of the Rice formula. The theory can be applied to practical problems where evolving random fields are considered to be adequate models. Examples include changes of atmospheric pressure, variation of air pollution, or dynamical models of the sea surface elevation. In particular, statistical properties of velocities can be obtained both for the sea surface and for the envelope field based on this surface. Additional extension can be obtained by studying three-dimensional geometry of spatial waves. Their statistical distributions can be presented in explicit integral forms for the deep water seas modeled as Gaussian fields. The proposed approach allows for investigation of the effect that shape and directionality of the sea spectrum have on the joint distributions of the size characteristics.