  A model for homogeneous anisotropic incompressible turbulence is proposed.
The model generalizes the GISS model of homogeneous isotropic turbulence; the
generalization involves the solution of the GISS equations along a set of
integration paths in wavenumber (k-) space. In order to make the problem
tractable, these integration paths ("cascade lines") must be chosen in such a
way that the behaviour of the energy spectral function along different cascade
lines should be reasonably similar. In practice this is realized by defining
the cascade lines as the streamlines of a cascade flow; in the simplest case
the source of this flow may be identified with the source function of the
turbulence. Owing to the different approximations involved, the resulting
energy spectral function is not exact but is expected to give good
approximative values for the bulk quantities characterising the turbulent
medium, and for the measure of the anisotropy itself in particular.
  The model is then applied to the case of low Prandtl number thermal
convection. The energy spectral function and the bulk quantities characterizing
the flow are derived for different values of the parameter $S=Ra \sigma$. The
most important new finding is that unlike the anisotropy of the most unstable
mode in linear stability analysis the anisotropy of the turbulence does not
grow indefinitely with increasing S but it rather saturates to a relatively
moderate finite asymptotic value.
