Topographic Effect on the Energetics of Geostrophic Adjustment

In this work, the impact of topography on the geostrophic adjustment process is discussed with a simple two-layer shallow water model, in which the lower-layer fluid is initially stationary while the upper-layer is perturbed by the impulsive injection of momentum. During the geostrophic adjustment process of this ideal model, the initial kinetic energy is released and a fraction of it is converted into potential energy of the final geostrophically adjusted state. Thus, after the geostrophic adjustment, the kinetic energy of the system is reduced while the potential energy is enhanced. As the topographic effect is considered, it is found that the decrease of the kinetic energy (△KE) and the increase of the potential energy (△PE) of the system are weakened as compared to the case that the lower boundary is flat. Furthermore, the topographic effect on △PE is less pronounced than that on △KE, which implicates that the topography tends to inhibit the energy dispersion of the inertio-gravity wave. The numerical simulation of the geostrophic adjustment process shows that, due to the impact of topography, the convergence and divergence in the low layer are reduced and the undulation of the interface between the lower-layer and upper-layer is weakened. This means that the amplitude of the inertio-gravity wave is decreased, and thus, the energy radiated by the inertio-gravity wave is lessened.