A search for the dominant free surface-fluctuation frequency downstream of the oscillating hydraulic jump with the Bayesian spectral density approach

Abstract

In this study the dynamics of the free surface fluctuation behind the oscillating hydraulic jump was modeled with a single-degree-of-freedom (SDOF) oscillator. Through the Bayesian spectral density approach, the uncertain parameters, namely the dominant frequency of the power spectrum, the damping ratio and the spectral intensity, were successfully identified based on laboratory measurements of six oscillating jumps with the Froude number ranging from 2.63 to 3.62. The identified dominant frequencies were found to be in good agreement with those estimated by a simple surface-roller generation–advection model, thus confirming the periodic large-scale turbulence formation process at the jump front. Meanwhile, the observed increase of the identified damping ratio with the Froude number is consistent with the increase of energy dissipation at higher Froude number. At the same time, the constant trend of spectral intensity implies that there is no significant change in the variance of the free surface fluctuation within the tested Froude number range.