A model of the free surface dynamics of shallow turbulent flows

Understanding the dynamic free surface of geophysical flows has the potential to enable direct inference of the flow properties based on measurements of the free surface. An important step is to understand the inherent response of free surfaces in depth-limited flows. Here a model is presented to demonstrate that free surface oscillatory spatial correlation patterns result from individual surface features oscillating vertically as they advect over space and time. Comparison with laboratory observations shows that these oscillating surface features can be unambiguously explained by simple harmonic motion, whereby the oscillation frequency is controlled by the root-mean-square water surface fluctuation, and to a lesser extent the surface tension. This demonstrates that the observed “complex” wave pattern can be simply described as an ensemble of spatially and temporally distributed oscillons. Similarities between the oscillon frequency and estimated frequency of near-bed bursting events suggest that oscillon behavior is linked with the creation of coherent flow structures.