For a stationary two dimensional random field evolving in time, we
derive statistical distributions of appropriately defined velocities.
The results are based on a genaralisation of the Rice formula.We discuss
importance of identifying the correct form of the distribution which
accounts for the sampling bias. The theory can be applied to practical
problems where evolving random fields are considered to be adequate
models. We present an application of the theory where the sea surface is
modelled as a Gaussian field. In particular we study statistical
properties of velocities both for the sea surface and for the envelope
field based on this surface. For wave and wave group velocities,
numerical computations of distributions are presented and illustrated
graphically.
|