Classical theories of turbulence do not describe accurately inertial range
scaling laws in turbulent convection and notably fail to model the shape of the
turbulent spectrum of solar photospheric convection. To understand these
discrepancies, a detailed study of scale-by-scale budgets in turbulent
Rayleigh-B\'enard convection is presented, with particular emphasis placed on
anisotropy and inhomogeneity. A generalized Kolmogorov equation applying to
convection is derived and its various terms are computed using numerical
simulations of turbulent Boussinesq convection. The analysis of the isotropic
part of the equation shows that the third-order velocity structure function is
significantly affected by buoyancy forcing and large-scale inhomogeneities.
Anisotropic contributions to this equation are also shown to be comparable to
their isotropic counterpart at moderate to large scales. Implications of these
results for convection in the solar photosphere, mesogranulation and
supergranulation are discussed.Comment: 6 pages, 3 figures -- To appear in the Proceedings of Symposium no.
239 "Convection in Astrophysics", International Astronomical Union., held
21-25 August, 2006 in Prague, Czech Republi
