How fast are the two-dimensional Gaussian waves?

Anastassia Baxevani, Krzysztof Podgórski and Igor Rychlik

Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,

ISSN 1403-9338
For a stationary two-dimensional random field evolving in time, we derive the intensity distributions of appropriately defined velocities of crossing contours. The results are based on a generalization of the Rice formula. The theory can be applied to practical problems where evolving random fields are considered to be adequate models. We study dynamical aspects of deep sea waves by applying the derived results to Gaussian fields modeling irregular sea surfaces. In doing so, we obtain distributions of velocities for the sea surface as well as for the envelope field based on this surface. Examples of wave and wave group velocities are computed numerically and illustrated graphically.
Key words:
directional spectrum, Gaussian sea, Rice formula, velocities, level crossing contours, wave groups