The Wavenumber-Frequency Spectrum of Free-Surface Waves in a Turbulent, Shallow Water Flow

The characterisation of the dynamic free-surface of a shallow open-channel flow is of considerable interest for many engineering applications since it is related to the transport and mixing processes, particularly near the interface [1]. The rough water surface of open-channels also displays distinctive patterns which are believed to reflect the characteristics of turbulent structures within the flow [2]. In this manner the free surface patterns can be related to the underlying flow conditions [3]. In spite of its importance, the mechanism which leads to the generation of waves at the surface of turbulent flows and the roughness pattern behaviour are still a poorly explored topic. The wavenumber-frequency spectrum of surface waves defines the spatial and temporal behaviour of the free-surface roughness completely. We suggest an analysis procedure that enables us to determine such spectrum from time series of the surface elevation measured at a set of points distributed non-equidistantly in the flow. The procedure is applied to measured data obtained with an array of conductance wave probes in a rectangular laboratory flume. The results show evidence of the existence of a complex three-dimensional distribution of dispersive gravity waves travelling on the surface. In addition to the dispersive gravity waves, an additional pattern of nondispersive waves appears to travel at the mean flow surface velocity. This latter type of waves is likely to be generated by the direct interaction with turbulent structures which originate within and are transported by the flow. It is suggested that the application of the proposed method to a wider range of flows will help to clarify the surface-turbulence interaction mechanism, and to define a set of key surface roughness parameters which would simplify the modelling and remote measurement of open channel flows.