The dynamics of propagation and disintegration of laminar liquid jets moving in air has been investigated theoretically. It is assumed that the jet is thin, i.e. the ratio of the characteristic transverse size to the longitudinal one is small. It is assumed also that the lateral surface of the jet is free of shearing forces and is ‘almost free’ of normal ones in the sense that the normal tractions other than isotropic pressure are small in comparison with the internal stresses acting in the jet cross-section.
Asymptotic quasi-one-dimensional equations of the continuity, momentum and moment of momentum of liquid motion in the jet have been derived. These equations were used as a basis for studying the process of growth of long-wave bending (transverse) disturbances of high-velocity jets of circular cross-section during their motion through air. The instability condition has been obtained and the growth rate of small bending disturbances of the jet has been found; the evolution of the jet shape at the stage of finite disturbances is investigated.