A Physically Consistent Formulation of Lateral Friction in Shallow-Water Equation Ocean Models

Abstract

Abstract Dissipation in numerical ocean models has two purposes: to simulate processes in which the friction is physically relevant and to prevent numerical instability by suppressing accumulation of energy in the smallest resolved scales. This study shows that even for the latter case the form of the friction term should be chosen in a physically consistent way. Violation of fundamental physical principles reduces the fidelity of the numerical solution, even if the friction is small. Several forms of the lateral friction, commonly used in numerical ocean models, are discussed in the context of shallow-water equations with nonuniform layer thickness. It is shown that in a numerical model tuned for the minimal dissipation, the improper form of the friction term creates finite artificial vorticity sources that do not vanish with increased resolution, even if the viscous coefficient is reduced consistently with resolution. An alternative numerical implementation of the no-slip boundary conditions for an arbi...