Stochastic analysis of the pressure field in the hydraulic jump region via Taylor hypothesis

Some cases of damage experienced on chute and spillway stilling basins operating under flood conditions have shown the importance to understanding the hydrodynamic force involved in the design of the lining. The computations of the slab uplift force, starting from the pressure field acting on the bottom, require the knowledge of the spatial covariance function of the fluctuating pressures in hydraulic jump region. This needs the simultaneous acquisition of pressure data in a large number of mesh points in the slab area. From an experimental point of view, this simultaneous acquisition at a large number of probes can be prohibitive because it is too expensive in terms of time consumption and laboratory setup. To overcome these problems one can invoke the Taylor hypothesis that allows defining the spatial correlation via autocorrelation at a single point, by assuming a proper value of the propagation celerity of the fluctuating pressure. The objective of this paper is to explore the validity of the Taylor hypothesis and provide a criterion to define this celerity. This is performed via an experimental analysis, for several Froude numbers of the hydraulic jump incident flow. For all test series, the pressure spatial correlation related to several pivot points was obtained. By comparison with autocorrelation in time-resolved single-point measurements at the pivot, the pressure celerity value on the slab surface was obtained. At constant Froude number, a relationship able to define this celerity in space is pointed out. The spatial covariance of pressure fluctuations, as calculated by the proposed approach, shows a good agreement with measurements and verifies the validity of the Taylor hypothesis. As a consequence the possibility is highlighted to use single point pressure measurements in order to estimate the force acting on a slab in spillway stilling basins.