We follow the changes in the structure of the accretion disk of the dwarf nova V2051 Oph along two separate outbursts in order to investigate the causes of its recurrent outbursts. We apply eclipse mapping techniques to a set of light curves covering a normal (July 2000) and a low-amplitude (August 2002) outburst to derive maps of the disk surface brightness distribution at different phases along the outburst cycles. The sequence of eclipse maps of the 2000 July outburst reveal that the disk shrinks at outburst onset while an uneclipsed component of 13 per cent of the total light develops. The derived radial intensity distributions suggest the presence of an outward-moving heating wave during rise and of an inward-moving cooling wave during decline. The inferred speed of the outward-moving heating wave is ~ 1.6 km/s, while the speed of the cooling wave is a fraction of that. A comparison of the measured cooling wave velocity on consecutive nights indicates that the cooling wave accelerates as it travels towards disk center, in contradiction with the prediction of the disk instability model. From the inferred speed of the heating wave we derive a viscosity parameter alpha_{hot} ~ 0.13, comparable to the measured viscosity parameter in quiescence. The 2002 August outburst had lower amplitude (Delta B ~ 0.8 mag) and the disk at outburst maximum was smaller than on 2000 July. For an assumed distance of 92 pc, we find that along both outbursts the disk brightness temperatures remain below the minimum expected according to the disk instability model. The results suggest that the outbursts of V2051 Oph are caused by bursts of increased mass transfer from the mass-donor star.
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