Tidal Straining, Mixing and Lagrangian Flow Residuals Around Headlands
Scott J. Couch and Graham J.M. Copeland
Tidal flow past an idealized triangular headland was investigated using an explicit finite difference solver for the equations of shallow water flow. Flow separation and transient eddies developed downstream from the tip of the headland on each successive half tidal cycle. Details of the flow patterns were studied using Lagrangian particle tracks. Mixing and dispersion diagrams were created that showed the effect of the eddies on sets of colour-coded particles. These revealed both the inter-mixing of water masses originally located on each side of the headland and the straining of discrete volumes of water originating from locations seaward of the headland tip. The pattern of Eulerian tidal residuals was contrasted with the pattern of Lagrangian tidal residuals. The patterns were found to be very different from one another; the Lagrangian residuals revealed complex detail with some systematic features. It is only the Lagrangian residuals that can be used to make valid inferences about the mixing of dissolved or suspended material when the length-scale of the tidal excursion is similar to the size of the headland and of the eddies. In such cases, the use of the Eulerian residuals is invalid. The mixing rates were also quantified by evaluating the effective diffusion coefficient for the eddy system. Four distinct stages of development of dispersion were identified and elucidated by the use of mixing diagrams. The impact of transient eddies was shown to be confined to a distinct mixing zone within which high rates of strain and diffusion were observed.