Flapping Instability of Vertically Impinging Turbulent Plane Jets in Shallow Water

A submerged, vertical, turbulent plane jet impinging onto a free water surface will be self-excited into a flapping oscillation when the jet velocity, exiting the jet orifice, exceeds a critical value. The dependence of the critical velocity W0c and the flapping frequency f0 on the water depth H and the jet orifice width d was investigated in detail in this study. The jet flapping motion was visualized by a laser induced fluorescence technique and measured with a laser Doppler velocimeter; a supplemental measurement of the displacement of water surface by a surface wave gauge was made. The jet flapping characteristics are interpreted in terms of the effective water depth given by He = H-z0, where z0 is the virtual origin of the jet. The critical jet exit velocity was found to increase linearly with the effective water depth and to decrease with the square root of the jet orifice width. The flapping frequency decreased with the root square of the effective water depth and independent of the jet orifice width. These results led to a critical condition for the onset of instability as St = 0.929[(H – z0)/d]–3/2, where St is the critical Strouhal number defined by St = f0d/W0c.