Revisiting tidal rectification by bottom topography

Tidal rectification plays a key role in controlling mean transport in coastal areas and coast-basin material exchange. To calculate mean flows, conventional approaches require high-resolution basin-scale numerical simulations which demands substantial computational resources. This study revisits tidal rectification governed by topographic variation and bottom friction, and proposes a new analytical solution.

The first step is to derive solutions in the simplest possible configuration. We thus revisit solutions in one-dimensional (1D) configurations, using a Lagrangian approach from which Eulerian results are derived. Exact solutions are provided for the frictionless case and new approximate solutions are developed for a more realistic quadratic bottom friction.

We then analyze the influence of viscosity on solutions from numerical models. We find that the latter has moderate influence when quadratic bottom friction is considered. However, when the steady rectified current extends over regions deeper than a critical depth, viscosity can lead to spurious effects and alter the accuracy of the numerical results. We show the critical depth can be expressed as a function of friction coefficient, tidal flux and topography variation length-scale.

We finally extend the analytical solutions derived for the 1D case to the two-dimensional (2D) case. The 2D solutions are compared to results from an ocean general circulation model solving the full barotropic equations in an academic configuration with a complex topography and a quadratic bottom friction. Comparison between analytical solutions and numerical simulations shows good agreement for both the magnitude and direction of the steady rectified tidal current. Sensitivity tests to bottom friction and tide amplitude show that the steady rectified current is parallel to the isobaths and independent of the magnitude of the bottom friction coefficient at first order.