Three-dimensional wave distortion and disintegration of thin planar liquid sheets

Abstract

Three-dimensional dilational and sinuous wave propagation on infinite or semi-infinite thin planar sheets flowing into a gas of negligible density is investigated. The assumption of thin sheets allows the reduction of the problem dimensionality by integration across the sheet thickness. For finite-amplitude disturbances, the strongest nonlinear effects occur when the cross-sectional wavenumber (l) is close to the streamwise wavenumber (k). First, dilational wave propagation is considered. When l is close to k for infinite sheets, higher harmonics are generated in the streamwise direction, and the standing wave with finite amplitude in the cross-sectional plane becomes flat. As time passes, the waves return to the initial wave shape. This process is repeated in a cycle