Tidal power from wedge-shaped estuaries ? an analytical model with friction, applied to the Bristol Channel

Abstract

The analytical wedge-shaped model of tidal propagation with friction described in an earlier paper which has complex Bessel function solutions, has been applied to the Bristol Channel with the introduction of a power-generating barrier. An analytical solution is possible for a linear flow condition at the barrier, assuming time variation at a single dominant tidal frequency, which requires symmetrical lunar operation of the barrage. Having obtained an analytical expression for the available power, the flow condition at the barrier is optimized to maximize the available power. If a phase lag is introduced between the water head and the flow at the barrier, significant increases in power are attainable. Variation of the upper end boundary condition indicates that closing off the upper Severn Estuary to tidal propagation would enable more power to be extracted at the barrage. Modification of the mouth boundary condition to take into account the response of the external sea to variations of flow across the mouth indicates a small reduction in available power. The model is intended as a simple indicator of the overall dynamics, rather than a prediction of the detailed response to the introduction of a barrier.