  A generalization to the Kraichnan gaussian, white noise in time model of
turbulent velocity field is proposed. The generalization is designed to take
into account the effects of stratification in the atmospheric boundary layer by
introducing different scaling exponents for horizontal and vertical velocity
components, leading to strong vertical anisotropy. The inevitable
compressibility of the model leads one to take into account also the density
statistics of the fluid, which will immediately lead to a boundary layer like
structure in the flow statistics and non zero time correlations. Possible
applications for passive scalar, tracer and inertial particle statistics and
their anomalous scaling behavior will be discussed.
