A mass-spring-damper model for unsteady Ekman boundary layers

Abstract:

The Ekman boundary layer is a central problem in geophysical fluid dynamics that emerges when pressure gradient forces, Coriolis forces, and molecular or turbulent friction forces interact in a flow. The transient version of the problem, which occurs when these forces are not in equilibrium such as when the pressure gradients are changing in time, is solvable analytically only for a limited set of forcing variability modes, and the resulting solutions are not succinct nor easy to interpret. In this talk, we demonstrate that the problem can be reduced to a second-order ordinary differential equation that is very similar to the dynamical equation of a mass-spring-damper system. The evaluation of the proposed model is performed by comparing it to results from a suite of large-eddy simulations. The reduced model can be solved for a wider range of variable forcing conditions and serves to elucidate the physical origin of the inertia (mass), energy storage (spring), and energy dissipation (damper) attributes of the Ekman layer.