Abstract
The modelling of time-varying shallow flows, such as tides and storm surges, is complicated by the nonlinear dependency of bed shear stress on flow speed. For tidal flows, Lorentz’s linearisation circumvents nonlinearity by specifying a (steady) friction coefficient r based on a tide-averaged criterion of energy equivalence. However, this approach is not suitable for phenomena with episodic and irregular forcings such as storm surges. Here, we studied the implications of applying Lorentz’s energy criterion in an instantaneous sense, so that an unsteady friction coefficient r(t) adjusts to the temporal development of natural wind-driven flows. This new bed-stress parametrisation was implemented in an idealised model of a single channel, forced by time-varying signals of wind stress (acting over the entire domain) and surface elevation (at the channel mouth). The solution method combines analytical solutions of the cross-sectionally averaged linearised shallow-water equations, obtained in the frequency domain, with an iterative procedure to determine r(t). Model results, compared with a reference finite-difference solution retaining the quadratic bed shear stress, show that this new approach accurately captures the qualitative and quantitative aspects of the surge dynamics (height and timing of surge peaks, sloshing, friction-induced tide-surge interaction) for both synthetic and realistic wind forcings.
Funder
Nederlandse Organisatie voor Wetenschappelijk Onderzoek
Subject
Ocean Engineering,Water Science and Technology,Civil and Structural Engineering
Reference17 articles.
1. Sea-Level Science. Understanding Tides, Surges, Tsunamis and Mean Sea-Level Changes;Pugh,2014
2. The interaction of surge and tide in the North Sea and River Thames
3. Tide-surge interaction and its role in the distribution of surge residuals in the North Sea
4. Contrasting the goals, strategies, and predictions associated with simplified numerical models and detailed simulations;Murray,2003
5. Het in rekening brengen van den weerstand bij schommelende vloeistofbewegingen;Lorentz;De Ingenieur,1922