  The fluctuating accretion model of Lyubarskii (1997) and its extension by
Kotov et al. (2001), seeks to explain the spectral-timing properties of the
X-ray variability of accreting black holes in terms of inward-propagating mass
accretion fluctuations produced at a broad range of radii. The fluctuations
modulate the X-ray emitting region as they move inwards and can produce
temporal-frequency-dependent lags between energy bands, and energy-dependent
power spectral densities (PSDs) as a result of the different emissivity
profiles, which may be expected at different X-ray energies. Here we use a
simple numerical implementation to investigate in detail the X-ray
spectral-timing properties of the model and their relation to several
physically interesting parameters, namely the emissivity profile in different
energy bands, the geometrical thickness and viscosity parameter of the
accretion flow, the strength of damping on the fluctuations and the temporal
coherence (measured by the `quality-factor', Q) of the fluctuations introduced
at each radius. We find that a geometrically thick flow with large viscosity
parameter is favoured, and confirm that the predicted lags are quite robust to
changes in the emissivity profile, and physical parameters of the accretion
flow, which may help to explain the similarity of the lag spectra in the
low/hard and high/soft states of Cyg X-1. We also demonstrate the model regime
where the light curves in different energy bands are highly spectrally
coherent. We compare model predictions directly to X-ray data from the Narrow
Line Seyfert~1 galaxy NGC 4051 and the BHXRB Cyg X-1 in its high/soft state and
show that this general scheme can reproduce simultaneously the time lags and
energy-dependence of the PSD.
