Received: 29 Apr 2015 – Accepted for review: 06 May 2015 – Discussion started: 01 Jun 2015
Abstract. We present a new equation describing the hydrodynamics in infinitely long tidal channels (i.e., no reflection) under the influence of oceanic forcing. The proposed equation is a simple relationship between partial derivatives of water level and velocity. It is formally derived for a progressive wave in a frictionless, prismatic, tidal channel with a horizontal bed. Assessment of a large number of numerical simulations, where an open boundary condition is posed at a certain distance landward, suggests that it can also be considered accurate in the more natural case of converging estuaries with nonlinear friction and a bed slope. The equation follows from the open boundary condition and is therefore a part of the problem formulation for an infinite tidal channel. This finding provides a practical tool for evaluating tidal wave dynamics, by reconstructing the temporal variation of the velocity based on local observations of the water level, providing a fully local open boundary condition and allowing for local friction calibration.
How to cite. Diederen, D., Savenije, H. H. G., and Toffolon, M.: The open boundary equation, Ocean Sci. Discuss., 12, 925–958, https://doi.org/10.5194/osd-12-925-2015, 2015.