Controls of topographic Rossby wave properties and downslope transport in dense overflows

Antarctic Bottom Water is primarily formed via overflows of dense shelf water (DSW) around the Antarctic continental margins. The dynamics of these overflows therefore influence the global abyssal stratification and circulation. Previous studies indicate that dense overflows can be unstable, energizing Topographic Rossby Waves (TRW) over the continental slope. However, it remains unclear how the wavelength and frequency of the TRWs are related to the properties of the overflowing DSW and other environmental conditions, and how the TRW properties influence the downslope transport of DSW. This study uses idealized high-resolution numerical simulations to investigate the dynamics of overflow-forced TRWs and the associated downslope transport of DSW. It is shown that the propagation of TRWs is constrained by the geostrophic along-slope flow speed of the DSW and by the dynamics of linear plane waves, allowing the wavelength and frequency of the waves to be predicted a priori. The rate of downslope DSW transport depends nonmonotonically on the slope steepness: steep slopes approximately suppress TRW formation, resulting in steady, frictionally-dominated DSW descent. For slopes of intermediate steepness, the overflow becomes unstable and generates TRWs, accompanied by interfacial form stresses that drive DSW downslope relatively rapidly. For gentle slopes, the TRWs lead to the formation of coherent eddies that inhibit downslope DSW transport. These findings may explain the variable properties of TRWs observed in oceanic overflows, and imply that the rate at which DSW descends to the abyssal ocean depends sensitively on the manifestation of TRWs and/or nonlinear eddies over the continental slope.