Effects of shallowness on the development of free-surface mixing layers

Abstract

The development of two shallow mixing layers with different water depths is analyzed experimentally by means of laser Doppler anemometry. The experiments show that bottom friction plays an important role in the growth of the mixing layer width and in the strength and dimensions of the large quasi two-dimensional turbulence structures therein. It is found in this study that the initial growth rate of both mixing layers is similar to what has been found for deep water plane mixing layers. Further downstream the reduction of the growth rate can be ascribed to the decrease of the velocity difference between the two ambient streams in combination with the suppression of the growth of the large turbulence structures. In the most shallow mixing layer considered, the influence of the bottom friction is dominant, impeding the further growth of the mixing layer width. It is demonstrated that the reduced mixing layer growth is related to a loss of coherence in the large turbulence structures. This loss of coherence also reduces the characteristic length-scale that establishes the lateral mixing of matter and momentum in the mixing layer. Eventually the water depth becomes the dominant length scale that determines the characteristic motion of the turbulence in that case. From the energy density spectra of the turbulence fluctuations and from the phase relation between the two velocity components in the horizontal plane it is concluded that large structures contribute most to the exchange of momentum in the mixing layer and thus to the Reynolds-stresses.