On a layer model for spilling breakers: a preliminary experimental analysis

Abstract

Accurate and reliable experimental data of a sloshing-induced, rapidly-evolving spilling breaker, are used to understand the specific physics of this phenomenon and to partially evaluate a simplified analytical model by Brocchini and co-workers (Brocchini , 1996; Misra et al., 2004, 2006). Such model is based on a three-layer structure: an underlying potential flow, a thin, turbulent single-phase layer in the middle and a turbulent two-phase layer (air–water) on the upper part. The experiments were carried out by using a 3 m long, 0.6 m deep and 0.10 m wide tank, built in Plexiglas and forced through an hexapode system, this allowing for an high accuracy of the motion. Mean and turbulent kinematic quantities were measured using the Particle Image Velocimetry (PIV) technique. To ensure repeatability of the phenomenon, a suitable breaker event was generated to occur during the first two oscillation cycles of the tank. The tank motion was suitably designed using a potential (HPC) and a Navier–Stokes solver. The latter, was useful to understand the dimension of the area of interest for the measurements. The evolution of the breaker is described in terms of both global and local properties. Wave height and steepness show that after an initial growth, the height immediately decays after peaking, while the wave steepness remains constant around 0.25. The evolution of the local properties, like vorticity and turbulence, vortical and turbulent flows displays the most interesting dynamics. Two main stages characterize such evolution. In stage (1), regarded as a ‘‘build-up’’ stage, vorticity and TKE rapidly reach their maximum intensity and longitudinal extension. During such stage the thickness of the single-phase turbulent region remains almost constant. Stage (2), is regarded as a ‘‘relaxation’’ stage, characterized by some significant flow pulsation till the wave attains a quasi-steady shape. In support to the analytical, three-layer model of Brocchini and co-workers it is demonstrated that the cross-flow profile of the mean streamwise velocity U inside the single-phase turbulent layer is well represented by a cubic polynomial. However, differently from available steady- state models the coefficient of the leading-order term is function of time: A = A(s,t). During stage (1) a fairly streamwise-uniform distribution of U is characterized by A(s, t ) ≈ 1, while during stage (2) U is less uniform and A varies over a much larger range.