  This paper provides a detailed study of scale-by-scale budgets in turbulent
Rayleigh-B\'enard convection and aims at testing the applicability of
Kolmogorov (1941) and Bolgiano (1959) theories for this flow. Particular
emphasis is laid on anisotropic and inhomogeneous effects: the SO(3)
decomposition of structure functions (Arad et al 1999) and a method of
description of inhomogeneities proposed by Danaila et al (2001) are used to
derive inhomogeneous and anisotropic generalizations of Kolmogorov and Yaglom
equations applying to RB convection. The various terms in these equations are
computed using data from a DNS of turbulent Boussinesq convection at
$\rayleigh=10^6$ and $\prandtl=1$ with aspect ratio A=5. The analysis of the
isotropic component demonstrates that the shape of the third-order velocity
structure function is significantly influenced by buoyancy forcing and
large-scale inhomogeneities, while the mixed third-order structure function
appearing in Yaglom equation exhibits a clear scaling exponent 1 in a small
range of scales. The magnitudes of the various low $\ell$ degree anisotropic
components of the equations are also estimated and are shown to be comparable
to their isotropic counterparts at moderate to large scales. Finally, a
qualitative analysis shows that the influence of buoyancy forcing at scales
smaller than the Bolgiano scale is likely to remain important up to
$\rayleigh=10^9$, thus preventing Kolmogorov scalings from showing up in
convective flows at lower Rayleigh numbers.
