Abstract
Abstract. In order to easily enforce solid-wall boundary conditions in the presence of complex coastlines, we propose a new mass and energy conserving Brinkman penalization for the rotating shallow water equations. This penalization does not lead to higher wave speeds in the solid region. The error estimates for the penalization are derived analytically and verified numerically for linearized one-dimensional equations. The penalization is implemented in a conservative dynamically adaptive wavelet method for the rotating shallow water equations on the sphere with bathymetry and coastline data from NOAA's ETOPO1 database. This code could form the dynamical core for a future global ocean model. The potential of the dynamically adaptive ocean model is illustrated by using it to simulate the 2004 Indonesian tsunami and wind-driven gyres.
Highlights
Handling coastlines is crucial for realistic twodimensional or three-dimensional ocean models
A novel Brinkman penalization of the rotating shallow water equations is implemented in our dynamically adaptive wavelet model on the sphere (Dubos and Kevlahan, 2013; Aechtner et al, 2014) to simulate oceanic flows with realistic coastlines and bathymetry over scales ranging from subkilometric to global
Where the parameters α and control the accuracy of the boundary condition approximation. (For stable numerical implementation of the penalization, the discontinuities in φ and σ are smoothed over a few grid points.) Physically, a large jump in porosity leads to a large jump in impedance that causes inertia–gravity waves to be almost perfectly reflected at the solid boundary, while a strong linear friction term rapidly damps velocity fluctuations approximating a noslip velocity boundary condition
Summary
Handling coastlines is crucial for realistic twodimensional or three-dimensional ocean models. Three-dimensional global ocean models usually treat coastlines as fixed, rigid boundaries This is a simpler setting for which numerous methods have been designed in the broader context of computational fluid dynamics A novel Brinkman penalization of the rotating shallow water equations is implemented in our dynamically adaptive wavelet model on the sphere (Dubos and Kevlahan, 2013; Aechtner et al, 2014) to simulate oceanic flows with realistic coastlines and bathymetry over scales ranging from subkilometric to global. We illustrate the potential of the new method by applying it to two global ocean flows: tsunami propagation and winddriven gyres These simulations have realistic bathymetry and coastlines from the 1 arcmin NOAA ETOPO1 global relief database (Amante and Eakins, 2009). We intend to extend the methods presented here to build a full dynamically adaptive global ocean circulation model
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
