A one-dimensional representation ofresidual currents in the Severn Estuary and associated observations

Abstract

A one-dimensional hydrodynamical model is used to describe the cross-sectionally averaged Stokes drift and Eulerian residual (tidally averaged) currents in a section of the Severn Estuary between Porthcawl and Sharpness. Residual variables are computed for periodic M2 tides, and as functions of time during simulated spring-neap cycles. The results for periodic M2 tides show that the landward directed Stokes drift has a spatially averaged value of 3·5 cm s−1 in the Severn Estuary, which, in the absence of freshwater inputs and meteorological perturbations, is balanced by seaward flowing Eulerian residual currents. The residual setup of water (i.e.: the mean surface elevation relative to the value at the seaward boundary) is mainly determined by the magnitudes of the axial density gradients and friction, with the friction dominating for typical salinity distributions; the landward flow of water due to the Stokes drift contributes to the set-up, which drives the seaward residual currents against the opposing frictional forces. It is shown that the magnitude of the Stokes drift is mainly determined by the estuary's geometry, the strength of the tidal streams and the friction (regardless of whether a quadratic or linearized friction law is assumed), the effects of density gradients and axial momentum advection and dispersion being negligible. The frictional dissipation in the Severn Estuary, which amounts to 3×109 watts for M2 tides in the region between Porthcawl and sharpness, is balanced by a landward residual flow of energy across the mouth, which is very nearly proportional to the Stokes drift at the mouth. The axial residual currents and Stokes drift have maximum and minimumspeeds at spring and neap tides respectively, the speeds at average spring tides being roughly seven times those for average neap tides, and twice those for M2 tides. The neap to spring part of the tidal regime is a period of increasing estuarine residual volume and landward flowing Lagrangian residual currents (∼1 mm s−1 near the mouth); the reverse is true for spring to neap tides. The computed values of the Stokes drift are compared with observations at nine anchor stations and covering 28 tidal cycles; the agreement between observations and theory is generally good.