  We present a spherically-symmetric, steady-state model of galaxy clusters in
which radiative cooling from the hot gas is balanced by heat transport through
turbulent mixing. We assume that the gas is in hydrostatic equilibrium, and
describe the turbulent heat diffusion by means of a mixing length prescription
with a dimensionless parameter alpha_mix. Models with alpha_mix ~ 0.01-0.03
yield reasonably good fits to the observed density and temperature profiles of
cooling core clusters. Making the strong simplification that alpha_mix is
time-independent and that it is roughly the same in all clusters, the model
reproduces remarkably well the observed scalings of X-ray luminosity, gas mass
fraction and entropy with temperature. The break in the scaling relations at kT
\~ 1-2 keV is explained by the break in the cooling function at around this
temperature, and the entropy floor observed in galaxy groups is reproduced
naturally.
