Lateral Circulation in an Elongated Curved Tidal Channel

Abstract

Abstract The dynamic theory of curvature-induced lateral circulation has been developed for open channel flows but not for oscillatory tides. A linear three-dimensional analytical model was developed to investigate the lateral circulation in an elongated tidal channel with mildly curved bends of which the radius of curvature is larger than the width. The curvature-induced lateral circulation has two components with the same amplitude, namely, a periodic component having an overtide frequency and a steady component. The combination of the two components allows the strength of the lateral circulation to vary periodically and the rotation direction to be unchanged during a tidal period. Friction modifies the strength and structure of the lateral circulation. The phase between the lateral flow and streamwise tidal flow decreases with increasing friction, indicating that the two flows are not necessarily in phase unless friction is strong. The lateral circulations driven by the Coriolis and curvature centrifugal forces augment each other during one phase and compete in the opposite phase, and the relative importance of the two circulations is determined by the Rossby number and friction. The adaptation time is the same for spinup and spindown of the curvature-induced lateral circulation and is determined by water depth and vertical eddy viscosity. The estimation of the adaptation time depends on the leading modes because the transition solution of the curvature-induced lateral circulation comprises a series of cosine modes. These results provide a theoretical basis for interpreting curvature-induced lateral circulation in tidal channels and coastal headlands. Significance Statement The dynamic theory of curvature-induced lateral circulation in a tidal flow remains unexplored. The purpose of this study is to understand the essentials of curvature-induced lateral circulation in an elongated tidal channel using a three-dimensional analytical model. The results showed that the curvature-induced lateral circulation has two components with the same amplitude: a periodic component having an overtide frequency and a steady component. This is significantly different from the curvature-induced lateral circulation associated with open channel flows, which is steady and in phase with the streamwise flow. Future work may show the role of curvature-induced lateral circulation in streamwise dynamics and mass transport.