Statistics for velocities of random waves
K. Podgórski, I. Rychlik and E. Sjö
Centre for Mathematical Sciences
Lund Institute of Technology,
The sea surface is best modeled as a random field evolving in time.
Although a great deal of research has been done on statistical distributions
of static characteristics of sea waves, little is known about statistical
properties of wave dynamics. By studying distributions for velocities
of sea surface motions we are making a step forward in this direction. We
extend the approach from the pioneering work of Longuet-Higgins (1957) by
taking into consideration the geometry of the sea as well as its evolution
in time. We discuss the following velocities: 1) the ratio of the wave length
and the wave period, 2) velocity in the direction of the gradient of the
sea surface, 3) velocity of upcrossings and local maxima, 4) velocity of
crossing contours, 5) velocity of wave groups. We derive intensity distributions
for these quantities and discuss their interpretation. The results involve
generalizations of Rice's formula. They are illustrated by computing these
distributions for an example of directional Gaussian sea.
directional spectrum, Gaussian sea, Rice's formula, velocity of local maxima,
velocity of level-crossings, level crossing
contours, wave groups.