THE ANISOTROPY OF LOW PRANDTL NUMBER TURBULENT CONVECTION

A model for homogeneous anisotropic incompressible turbulence is propo sed. The model generalizes the GISS model of homogeneous isotropic tur bulence; the generalization involves the solution of the GISS equation s along a set of integration paths in wavenumber (k-) space. In order to make the problem tractable, these integration paths (''cascade line s'') must be chosen in such a way that the behaviour of the energy spe ctral function along different cascade lines should be reasonably simi lar. In practice this is realized by defining the cascade lines as the streamlines of a cascade flow; in the simplest case the source of thi s flow may be identified with the source function of the turbulence. O wing to the different approximations involved, the resulting energy sp ectral function is not exact but is expected to give good approximativ e 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 th e flow are derived for different values of the parameter S = Rasigma. The most important new finding is that unlike the anisotropy of the mo st unstable mode in linear stability analysis the anisotropy of the tu rbulence does not grow indefinitely with increasing S but it rather sa turates to a relatively moderate finite asymptotic value.