How fast are the two-dimensional Gaussian waves?
Anastassia Baxevani, Krzysztof Podgórski and Igor Rychlik
Centre for Mathematical Sciences
Lund Institute of Technology,
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
directional spectrum, Gaussian sea, Rice formula, velocities, level crossing
contours, wave groups