Generation of waves in the concurrent flow of air and a liquid

If air flows concurrently with a liquid, there are critical air velocities above which two‐dimensional and three‐dimensional waves appear at the interface. The physical process responsible for these transitions is as follows: The disturbance in the velocity field in the air caused by these waves gives rise to pressure and shear stress variations over the wavy surface. Pressure variations in phase with the wave slope and shear stress variations in phase with the wave height transmit energy from the air flow to the liquid film. If the rate at which energy is transmitted to the waves by these mechanisms is not larger than the rate of viscous dissipation in the liquid, the waves will decay. The model of the gas flow proposed by Miles and Benjamin is used to calculate shear stress and pressure variations over the wavy surface. The agreement between predicted and measured critical air velocities, wave lengths, and wave velocities is good.