We report on the eclipse mapping analysis of an ensemble of light curves of the dwarf nova V2051 Oph with the aim to study the spatial distribution of its steady-light and flickering sources. The data are combined to derive the orbital dependency of the steady-light and the flickering components at two different brightness levels, named the faint and bright states. The differences in brightness are caused by long-term variations in the mass transfer rate from the secondary star. Eclipse maps of the steady-light show enhanced emission along the ballistic stream trajectory, in a clear evidence of gas stream overflow. We identify two different and independent sources of flickering in V2051 Oph. Low-frequency flickering arises in the overflowing gas stream and is associated to the mass transfer process. It maximum emission occurs at the position of closest approach of the gas stream to the white dwarf, and its spatial distribution changes in response to variations in mass transfer rate. High-frequency flickering originates in the accretion disk, showing a radial distribution similar to that of the steady-light maps and no evidence of emission from the hot spot, gas stream or white dwarf. This disk flickering component has a relative amplitude of about 3 per cent of the steady disk light, independent of disk radius and brightness state. If the disk flickering is caused by fluctuations in the energy dissipation rate induced by MHD turbulence, its relative amplitude lead to a viscosity parameter alpha= 0.1-0.2 at all radii for the quiescent disk. This value seems uncomfortably high to be accommodated by the disk instability model [abridged].
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