Study of waves on thin liquid films sheared by turbulent gas flows

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Abstract
Waves that occur at the interface of a thin, horizontal liquid film sheared by a concurrent turbulent gas flow are investigated. Observations using liquids in the range of 13–15 cP indicate that broad-crested, steady, periodic waves appear as the gas velocity is increased above the point of neutral stability. For a sufficiently large gas Reynolds number, steady solitary waves appear. These travel at speeds significantly faster than the periodic waves. However, if the liquid flow rate is increased, solitary waves do not form. To quantitatively describe the waves, a weakly nonlinear wave equation is derived using boundary-layer approximations. The equation is valid for liquid Reynolds numbers of O (1–100) and reveals the presence of both kinematic and dynamic processes, which may (i) act together or (ii) singularly dominate the wave field. For the latter case, reduced forms of the evolution equation are derived. Linear stability analysis of the complete equation and its reduced forms is used to determine the parameter ranges where either dynamic or kinematic processes dominate. The evolution equation in its nonlinear forms should be capable of describing and predicting the amplitudes, shapes, and interactions of finite amplitude waves.

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