This book addresses the processes of stochastic structure formation in two-dimensional
geophysical fluid dynamics based on statistical analysis of Gaussian random fields as well as
stochastic structure formation in dynamic systems with parametric excitation of positive random
fields f(r t) described by partial differential equations. Further the book considers two
examples of stochastic structure formation in dynamic systems with parametric excitation in the
presence of Gaussian pumping. In dynamic systems with parametric excitation in space and time
this type of structure formation either happens - or doesn't! However if it occurs in space
then this almost always happens (exponentially quickly) in individual realizations with a unit
probability. In the case considered clustering of the field f(r t) of any nature is a general
feature of dynamic fields and one may claim that structure formation is the Law of Nature for
arbitrary random fields of such type. The study clarifies the conditions under which such
structure formation takes place. To make the content more accessible these conditions are
described at a comparatively elementary mathematical level by employing ideas from statistical
topography.
