Three-dimensional tidal flow in a fjord-like basin with converging width: An analytical model

Abstract

A three-dimensional analytical model was used to understand tidal dynamics in deep and narrow (fjord-like) basins. This model allows the width of the basin to decay exponentially with along-channel distance from the mouth. Both the length scale of exponential convergence math formula and the friction parameter math formula (vertical eddy viscosity) were the free parameters. Model results show amplification of the tidal amplitude toward the head of the basin. Amplification depends on the narrowing rate of the funnel-like width of the channel and on friction. Cross-channel variations in along-channel tidal flow are also sensitive to the friction parameter. A typical along-channel tidal flow distribution was found across the channel when the vertical eddy viscosity was characteristic of a basin with strong friction, or the Stokes number was larger than 0.1 (St > 0.1). Maximum along-channel tidal velocities (ranging from 0.25 to 0.5 m s−1 depending on width convergence strength) were located in the center of the basin and at the surface. Decreasing values of the Stokes number, St < 0.1, resulted in along-channel velocity maxima located near the lateral boundaries and subsurface in the middle of the channel. These tidal flow distributions were explained by a critical value of St and were verified with observations from Reloncavi Fjord, Chilean Patagonia yielding good agreement.