An Improved Integral Model for a Non-Buoyant Turbulent Jet in Wave Environment

The integral model developed by Chin (1988) for modelling a non-buoyant turbulent jet in wave environment is improved by introducing two new parameters, i.e., the jet spreading rate c(1) and the shortening rate p(e). The parameter c(1) is used to simplify the model by explicitly describing the radial velocity and scalar profiles under the assumption of instantaneous Gaussian distribution. By doing so, the governing equations can be easily solved by simultaneously integrating the conservation laws of momentum and scalars across the jet cross-section. The parameter p(e) is used to shorten the initial length of zone of flow establishment (ZFE), so as to more accurately account for the wave effect on the jet initial dilution near the jet nozzle. The parameters are calibrated by the particle image velocimetry (PIV)-measured data from three groups of jet experiments, i.e., the group of vertical jet towards the wave direction (vertical jet), the group of horizontal jet along the wave direction (co-wave jet) and the group of horizontal jet opposing to the wave direction (op-wave jet). The results show that both parameters are well related to the ratio of jet and wave characteristic velocities in the same group, but it is not able to be generalized among different groups. Under the same wave condition, the value of c(1) in the vertical jet is larger than that of the horizontal jets; while the value of p(e) in the vertical jet is smaller than that of the horizontal jets, which indicates that the jet has a faster decay rate of centerline velocity and a wider width of jet cross-section profile in the near field when it is vertically discharged into the wave environment. With the well-calibrated parameters, the improved model can achieve a higher accuracy than the original model developed by Chin (1988).