  The amplitude and phase modulation observed in a significant fraction of the
RR Lyrae variables - the Blazhko effect - represents a long-standing enigma in
stellar pulsation theory. No satisfactory explanation for the Blazhko effect
has been proposed so far. In this paper we focus on the Stothers (2006) idea,
in which modulation is caused by changes in the structure of the outer
convective zone, caused by a quasi-periodically changing magnetic field.
However, up to this date no quantitative estimates were made to investigate
whether such a mechanism can be operational and whether it is capable of
reproducing the light variation we observe in Blazhko variables. We address the
latter problem. We use a simplified model, in which the variation of turbulent
convection is introduced into the non-linear hydrodynamic models in an ad hoc
way, neglecting interaction with the magnetic field. We study the light curve
variation through the modulation cycle and properties of the resulting
frequency spectra. Our results are compared with Kepler observations of RR Lyr.
We find that reproducing the light curve variation, as is observed in RR Lyr,
requires a huge modulation of the mixing length, of the order of +/-50 per
cent, on a relatively short time-scale of less than 40 days. Even then, we are
not able to reproduce neither all the observed relations between modulation
components present in the frequency spectrum, nor the relations between Fourier
parameters describing the shape of the instantaneous light curves.
