Convective transport of fast ions in the toroidal field ripples of a tokamak was investigated experimentally and theoretically. Comprehensive numerical computations of this effect were performed on the basis of the previously developed theory. Simultaneously, detailed experimental studies were made of the energetic ions in the T-4 and T-10 tokamaks. The experiments demonstrate that the ion distribution function is substantially different from the Maxwellian one, being strongly enriched with fast particles at the plasma column periphery. The local trapped-ion distribution is, in addition, asymmetric throughout the plasma cross-section. A detailed comparison with the numerical results shows that the observed effects can be explained in terms of the kinetic convective transport theory. Kinetic convection is shown to contribute significantly to energy transport. With increasing ion temperature, convective ripple transport may become dominant. Therefore, the variation of rippling may become an effective means of controlling the temperature and ignition regimes of a thermonuclear reactor. The results obtained demonstrate that transport processes in modern tokamaks have to be described in terms of kinetic theory.