Oscillatory Gravity Waves in Flowing Water

The main objectives of this paper are (a) to determine the conditions of stability of progressive, oscillatory gravity waves in water flowing over smooth and artificially roughened surfaces and (b) to evaluate the combined effect on the wave propagation by various interrelated characteristics of flowing water, such as viscous shear, turbulent mixing shear, and nonuniform velocity distribution. Because neither experimental nor conclusive theoretical results are available for solving the problems discussed herein, it is necessary to evaluate the effect of various characteristics of flowing water on the velocity of stablewave propagation by comparing results with those obtained from available theories, particularly those of G. G. Stokes2 and D. J. Struik.³ For stable, ascendant, oscillatory gravity waves in smooth and artificially roughened rectangular channels, the period and various geometrical characteristics were measured for range of depth, velocity of flow, and settings of the wave generator. The following results were obtained: 1. For a given flow there is only one neutrally stable wave. All other waves show either an exponential damping or an amplification during their propagation along the channel. It is easy to separate the two regions by means of the surface of neutral stability, which was determined experimentally and is presented graphically. 2. The celerity of a stable ascendant wave is smaller than that obtained from the theories of Messrs. Stokes and Struik. The deviation in wave velocity from that obtained from potential theory increases with increasing Froude numbers and decreases with increasing Reynolds numbers. 3. For a channel with an artificially roughened bottom, the deviation is greater than that for a channel with a smooth bottom. 4. As described by Mr. Struik, the experimentally determined profiles of E1t11ble oscillatory gravity waves vary about the theoretical profiles.