Wind-generated waves in thin liquid films

Abstract

In the presence of an air stream, a uniform liquid film on a horizontal flat plate may be unstable to small disturbances, and waves may arise. In this paper the hydrodynamic stability of thin liquid films is examined both experimentally and theoretically.The experiments concern water films thinner than those which have been examined in the past. It is found that, when the film thickness is sufficiently small, a previously unknown type of instability occurs. The theoretical analysis explains this surprising phenomenon.Due to interaction of the mean airflow and small disturbances of the liquid-air interface, normal and tangential stress perturbations are produced at the liquid surface. It is shown that small wave-like disturbances become unstable when the joint influence of the component of normal stress in phase with the wave elevation and the component of tangential stress in phase with the wave slope is sufficient to overcome the ‘stiffness’ of the liquid surface due to gravity and surface tension. It is found that the destabilizing role of the tangential stress component is dominant for very thin films, and that instability may occur whatever the velocity of the air stream, provided the film is made sufficiently thin.