Nearshore mixing due to the effects of waves and currents

Analytical, experimental and computational studies were carried out to investigate the mixing and dispersion of neutrally buoyant tracer in the nearshore region due to the effects of waves and currents. The main objective of this study was to quantify the mixing processes in the nearshore region. Theoretical approaches were developed to quantify the contribution of diffusive and dispersive mixing in the nearshore due to wave activity. An analytical model was developed to quantify the diffusive and dispersive mixing mechanisms based on mathematical solutions for the advection-diffusion equation. Mixing under the combined effects of waves and currents were studied through measurement of hydrodynamic and fluorometric tracing experiments from a largescale facility at the Danish Hydraulic Institute, Denmark. The experiments were conducted in a shallow water basin for a range of hydrodynamic conditions covering wave steepness between 2 – 5%. Data from detailed measurements were used to examine the spreading of a solute inside the surf zone and seawards of the breaker region. The overall depth-averaged on-offshore mixing coefficient obtained from the hydrodynamic experimental studies were compared to the mixing coefficients determined from the tracer measurements. It was shown that inside the surfzone, the shear dispersion is the dominant mixing factor, which is almost an order of magnitude greater than the diffusive mixing. The location of the breaker point and the wave height across the nearshore is shown to be important for determining the mixing coefficient. Further detailed spatial and temporal variations of flow hydrodynamics across the nearshore were investigated through a series of laboratory experiments with the use of Particle Image Velocimetry. The experiments were undertaken in a dedicate wave flume at the University of Warwick. Through analysis of the PIV data, new information on the spatial variation of diffusion and dispersion in the shallow water column of the nearshore region was obtained. Flow visualisation of the PIV results identified three distinct hydrodynamic processes during the bore, undertow and the bore/undertow interaction, which were the primary mixing mechanisms in the nearshore region. The temporal variation of dispersion coefficient shows that intense shearing mechanisms exist during wave bore/undertow interactions. The numerical capabilities of Smoothed Particle Hydrodynamics, a Lagrangian, meshless, particle-based method in modelling the nearshore hydrodynamics were explored in this study. The numerical data was used to quantify the mixing processes. By using suitable estimates of turbulent diffusion and cross-shore wave-induced velocity, a theoretical approximation of the overall mixing within the surfzone and seaward of the breaker region can be obtained. A comparison between the theoretical model and previous laboratory and field studies on the nearshore mixing suggests that the mixing is proportional to wave height (H1.5). It is demonstrated that inside the surfzone, the mixing is dominated by the vertical structure of the cross-shore velocity. The pioneering Royal society works of Svendsen & Putrevu (1994) identified the temporally-averaged dispersion, as a function of distance from the shore. Using a combination of experimental, mathematical and numerical formulations, this study has identified and quantified for the first time, the temporal and spatial dispersive mixing processes in the nearshore (over the full wave cycle), within the challenging and complex environment of the surf zone. It has been shown that the cross-shore circulation provides lateral mixing that exceeds that of the turbulence by an order of magnitude inside the surfzone. The turbulence still remains an essential part of the flow since it is the primary driver which through the vertical mixing is responsible for defining the vertical velocity profiles, which then determine strength of the dispersion